Spectral Mapping and Long-Term
Seasonal Evolution of Pluto
By
Alissa M. Earle
B.S. Physics and Mathematics
Siena College, 2013
Submitted to the Department of Earth, Atmospheric, and
Planetary Sciences in partial fulfillment of the requirements for the degree of
Doctor of Philosophy at the Massachusetts Institute of Technology
June 2018
@ Massachusetts Institute of Technology 2018. All rights reserved.
Author....................................................S ig n atu re red acted ......
Department of Earth, Atmospheric, and Planetary Sciences
May 22, 2018
C ertified b y ......................................................... Signature redacted
Richard P. Binzel
Professor of Planetary Sciences and Margaret MacVicar Faculty Fellow
Sig nature redacted Thesis Supervisor
A ccepted by ...................... .........................
Robert van der Hilst
MASSA TOLY NSITUTE Schlumberger Professor of Earth and Planetary Sciences,
Ii OIHead of Department of Earth, Atmospheric and Planetary Sciences
JUN 062018
LIBRARIES
ARCHIVEt
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Spectral Mapping and Long-Term Seasonal
Evolution of Pluto
By
Alissa M. Earle
Submitted to the
Department of Earth, Atmospheric, and Planetary Sciences
on May 2 2nd, 2018, in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
Abstract
NASA's New Horizons mission has provided a wealth of new data about the Pluto system,
including detailed surface geology and volatile distribution maps revealing striking latitudinal
and longitudinal variations. We begin by studying the methane distribution and surface
colors using data from New Horizons' Ralph/MVIC instrument. From this study we find that
Pluto's equatorial region shows a broader diversity of terrains and more stark longitudinal
contrasts than the more homogeneous north polar region. Pluto's south polar region is
currently in constant shadow and thus was not observed by New Horizons. We consider
how this diversity formed and survived in the context of Pluto's extreme Milancovid cycles
and resultant "super seasons". Over timescales of roughly 3 million years Pluto's obliquity
varies by 23 degrees (between 103 degrees and 126 degrees) while its longitude of perihelion
regresses. This pair of cycles create "super season" epochs where one pole experiences a
short intense summer and long winter in constant darkness, while the other experiences a
short winter and much longer, but less intense summer. Through thermal modeling and
volatile sublimation and deposition modeling we determined that Pluto's high obliquity
creates conditions at its equator that favor albedo contrast and can support them on million
year timescales more effectively than Pluto's polar regions can. Finally, we look ahead to a
possible next step in small body spacecraft exploration, a study of Apophis during its 2029
close approach to Earth. Since the earlier portion of this thesis focussed on the encounter,
data collection, and scientific analysis portion of a spacecraft mission (New Horizons), we go
full circle by exploring the early stage of the mission life cycle and the process of going from
science concept to mission design study.
Thesis Supervisor: Richard P. Binzel
Title: Professor of Planetary Sciences and Margaret MacVicar Faculty Fellow
3
4
Acknowledgements
"No one achieves anything alone"
- Leslie Knope, Parks and Recreation
"The ideal thesis advisor would advise you from your first tentative steps on campus,
help you find a thesis topic, help you choose your thesis committee, read your thesis drafts,
and edit them as needed... Ideally, he or she should be a mentor, that rare being who is part
confidant, part parent, spiritual and temporal guide. You will never find such a paragon, but
the closer you get, the better."' I found it. It's Rick Binzel. Thank you Rick for everything.
I would also like to thank the rest of my committee; Leslie Young, Jack Wisdom, and
Taylor Perron, for providing useful feedback, discussion, and insight along the way. As well
as the rest of the 12.410 teaching staff; Amanda, Jane, Mike, Nick, Hosea, Molly, and Anicia,
for their support, enthusiasm, and always being good for a laugh.
Thank you to Alan Stern and the Pluto Underground, for your patience, persistence, and
for getting us to Pluto (with perfect timing in my opinion). Thank you to everyone who
helped get us to Pluto, to the New Horizons Science Team, and especially the Composition
Theme Team. I consider myself incredibly lucky, not only to have been able to work on such
an exciting mission in graduate school but also to be able to work with and learn from a
truly wonderful and talented group of people. And of course I'd like to acknowledge NASA,
for not only financially supporting the New Horizons mission, but also much of the work
done for this thesis.
A huge thank you to Adam, for being there through every accomplishment and every
set-back, for helping me not lose sight of the light at the end of the tunnel, for helping me
stay motivated and also knowing when its time to take a break and relax. Thank you to the
friends who helped get me here and get me through, including but not limited to: Grace,
'Peters, Robert. "Getting What You Came For: Revise Edition". Farrah, Straus, and Giroux, 1997.
5
Eileen, Lisa, Maureen, Godfrey, Hannah, Neesha, Dom, and Steve. And Max and Andrew
for seeing the exciting possibilities when I am distracted by the daunting challenges. And
to the professors and teachers who not only helped lay the groundwork, but also provided
me with some amazing opportunities (and patiently sat through many discussions about my
career path), particularly Rose, Jon, David, John, and John-Michael.
I'd like to acknowledge all of my family for their love, support, and reminding me that
"normal people don't do what [I] do". Especially my Mom for teaching me to love learning,
instilling self-confidence, showing me that strength takes many forms, and for everything
else she has done for us. Thank you Jennie (and Dan) for all the reasons outlined in my
wedding toast and for helping make living in an awesome apartment and keeping my our
horse in grad school possible. And Kevin, I'm not positive but somehow I feel like Space
Bunny has something to do with all this... so thank you for that, and thank you for being my
first friend. Thank you to my Dad; at a time when someone else might have given up on the
challenging, emotionally-unstable horse they had bought their daughters, instead my Dad
encouraged me to keep trying and work through it. And thank you to Doc, the challenging,
emotionally-unstable horse who taught me to be patient and persistent and to pick myself
up, dust myself off, and try again, and has provided a much needed retreat throughout
college and grad school. Having a horse in another state during grad school was not easy,
but it was worth it.
6
TIP1 IRI jjNQj1P,"
Contents
1 Introduction 17
1.1 A very Brief History of Pluto Observations . . . . . . . . . . . . . . . . . . . 17
1.2 The New Horizons Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.1 Mission Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.2 Mission Design and Science Payload . . . . . . . . . . . . . . . . . . . 22
1.2.3 Preliminary Results from New Horizons . . . . . . . . . . . . . . . . . 24
2 Methane Distribution on Pluto as Mapped by the New Horizons Ralph/MVIC
Instrument 27
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..27
2.2 Methods . ....... ... .............. ........ .. ... . ... 29
2.2.1 Data & Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.2 T he M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3 R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.1 T he M aps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3.2 Areas of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.4 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4.1 A nalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.4.2 Slope-MVIC E.W. Units and Comparison with LEISA results . . . . 46
2.5 C onclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7
3 Pluto's Insolation History and "Super Seasons" 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Insolation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3.1 Diurnal Insolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.3.2 Pluto's "Super Seasons" . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.1 Climate Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.4.2 Past Epochs of Higher Atmospheric Pressure . . . . . . . . . . . . . . 70
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4 Long-term Surface Temperature Modeling of Pluto 77
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2 M ethods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.1 Local Temperature Model . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.2 Pluto Albedo Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2.3 Global Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.3 R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3.1 Annual Temperature Patterns - Uniform Albedo Model . . . . . . . . 86
4.3.2 Historical Temperature Extremes - Variegated Albedo Model ..... 88
4.3.3 Comparison with Global Model . . . . . . . . . . . . . . . . . . . . . 88
4.4 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 Albedo Matters: Understanding Runaway Albedo Variations on Pluto 97
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.2 Methods . ........ ...... ....... ........ ..... .... . 101
5.2.1 Basic M odel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
8
5.2.2 Nitrogen Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2.3 Variable Ice Albedo Model . . . . . . . . . . . . . . . . . . . . . . . . 103
5.3 R esults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3.1 Nitrogen Model Results . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3.2 Methane (variable albedo) Model Results . . . . . . . . . . . . . . . . 107
5.3.3 Low-obliquity Model Results . . . . . . . . . . . . . . . . . . . . . . . 108
5.4 D iscussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.4.1 Low Obliquity Trials . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.4.2 Comparison with Observations . . . . . . . . . . . . . . . . . . . . . . 113
5.4.3 Consideration of Thermal Inertia . . . . . . . . . . . . . . . . . . . . 115
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6 Pluto: Context and Conclusions 117
6.1 Context for Pluto Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.2 Summary of Pluto Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.3 Pluto Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7 Apophis and the "Smart Marbles" Package 125
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2 The SET Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.2.1 Mission Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.2.2 Instrumentation and Spacecraft Overview . . . . . . . . . . . . . . . 132
7.2.3 Concept of Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 136
7.3 Trade Space for Measuring Surface Activity . . . . . . . . . . . . . . . . . . 136
7.4 "Smart Marbles" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.4.1 Science Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.4.2 Science Objectives and Rationale . . . . . . . . . . . . . . . . . . . . 141
7.4.3 "Smart Marbles" Design Overview . . . . . . . . . . . . . . . . . . . 143
9
7.4.4 M ission Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
7.5 Conclusions and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 148
Appendices
Appendix A Calculating Pluto's Obliquity Variations using Dobrovolskis et al.
(1997) 153
Appendix B Detailed Exploration of the Trade Space for Measuring Surface
Activity 159
B.1 RRT/RTT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
B.2 Imaging Options ........ ................................. 162
B.3 Lander/Rover ........ ................................... 165
B.4 Laser Doppler Vibrometer ............................ 165
B.5 "Dumb M arbles" ................................... 166
10
List of Figures
1.1 Progress of Pluto Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.1 Schematic showing the process for calculating CH4/NIR and Red/NIR ratios
over the MVIC E.W. and spectral slope parameter space . . . . . . . . . . . 31
2.2 Maps of the MVIC E.W. of the 890 nm methane absorption band produced
from the 8 highest resolution Ralph/MVIC approach images . . . . . . . . . 33
2.3 Maps of the spectral slope produced from the 8 highest resolution Ralph/MVIC
approach im ages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.4 Cylindrical projections of Pluto's surface showing global maps of MVIC E.W.,
Spectral Slope, and Elevation . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.5 Cylindrical projections of Pluto's surface showing the Al-Idrisi Montes and
part of the shoreline of Sputnik Planitia . . . . . . . . . . . . . . . . . . . . 37
2.6 Cylindrical projections of Pluto's surface showing the cellular terrain in Sput-
nik P lanitia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.11 Scatter plots of spectral slope vs MVIC E.W. for each of the images shown in
Figures 2.2 and 2.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.12 Scatter plots of spectral slope vs MVIC E.W. based on the global maps shown
in F igure 2.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
11
2.13 Left: MVIC E.W. as a function of latitude based on the global maps presented
in Figure 2.4. Right: Spectral slope as a function of latitude based on the
global maps presented in Figure 2.4. . . . . . . . . . . . . . . . . . . . . . . 44
2.14 Left: MVIC E.W. as a function of elevation based on the global maps pre-
sented in Figure 2.4. Right: Spectral slope as a function of elevation based
on the global maps presented in Figure 2.4 . . . . . . . . . . . . . . . . . . . 45
2.15 Left: Map of Pluto's surface with mapped elements divided into six categories
based on MVIC E.W. and spectral slope Right: spectral slope vs MVIC E.W.
with points color coded based on MVIC E.W. and spectral slope cutoffs to
group similar terrain types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.16 Histograms of the relative frequency of the six different terrain types intro-
duced in Figure 2.15 as a function of latitude. Correction factors have been
applied to account for pixel widths changing as a function of latitude and the
frequencies have been normalized to the total mapped area . . . . . . . . . . 49
2.7 Cylindrical projections of Pluto's surface showing part of Cthulhu containing
Elliot crater (the large, complex crate in the upper right corner), Virgil Fossa
(the fossa that runs from Elliot crater to the lower left corner of the image),
and Beatrice Fossa (shorter and south of Virgil) . . . . . . . . . . . . . . . . 52
2.8 Cylindrical projections of Pluto's surface showing part of Cthulhu containing
a chain of methane frost covered mountains . . . . . . . . . . . . . . . . . . 53
2.9 Cylindrical projections of Pluto's surface showing part of Viking Terra, the
region west of Sputnik Planitia and north of Cthulhu . . . . . . . . . . . . . 54
2.10 Cylindrical projections of Pluto's surface showing part of Pioneer Terra, the
region north of Tombaugh Regio . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 Variations in Pluto's orbital parameters over the last three million years . . . 59
3.2 Average insolation at each latitude over varying timescales . . . . . . . . . . 63
3.3 Comparison of average and maximum diurnal insolation vs. latitude . . . . . 65
12
L im - -- , , -- .. I- II il I , 1. 11 . I . . 411.11 1 I .I , I I I , 1- 1. . I , I , I - I .- I I , , i , I - I !. I , . . .I I 111 11 1 . - , . I I I I I- 1 7 11 1 -I I I I I I I I . I , I .I I I I
3.4 Diurnally averaged insolation over 1 Pluto orbit for select latitudes . . . . . 66
3.5 Model variation in atmospheric nitrogen pressure over a single Pluto orbit at
three different epochs (Adapted from Stern et al., 2017) . . . . . . . . . . . . 71
3.6 Model of atmospheric molecular nitrogen pressure over a single Pluto orbit at
three different epochs, most extreme case considered (Adapted from Stern et
al., 20 17) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.7 Examples of geomorphological evidence for past epochs of higher atmospheric
pressure on Pluto (Adapted from Stern et al., 2017) . . . . . . . . . . . . . . 74
4.1 Comparison of insolation and temperature averages and maximums . . . . . 81
4.2 Average daily surface temperature over three Pluto epochs . . . . . . . . . . 83
4.3 Simplified albedo model of Pluto . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4 Minimum and maximum temperatures on Pluto over various epochs . . . . . 89
4.5 Historical minimum and maximum temperatures on Pluto . . . . . . . . . . 90
4.6 Comparison of instantaneous global temperatures to instantaneous local equi-
librium temperatures for select latitudes and albedos . . . . . . . . . . . . . 91
4.7 Variations between minimum and maximum temperature for various Pluto
epochs ......... ....................................... 94
5.1 Diurnally averaged insolation over a Pluto year for various epochs . . . . . . 99
5.2 Annually averaged insolation for various obliquity values . . . . . . . . . . . 100
5.3 Nitrogen mass load as a function of latitude modeled over various Pluto epochs 105
5.4 Nitrogen mass load for the three different albedo regions at four different times
over the last Pluto year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.5 Methane mass load as a function of latitude modeled over various Pluto epochs107
5.6 Nitrogen mass load as a function of latitude modeled over various obliquities 109
13
5.7 Albedo sensitivity based on the relative difference between the maximum ni-
trogen mass load reached over the last Pluto year in the bright (0.6) and dark
(0.1) albedo regions for various obliquities . . . . . . . . . . . . . . . . . . . 113
7.1 CAD Model of SET spacecraft layout (Image credit: Amy Vanderhout and
MIT 12.43/16.83 Space Systems Engineering (2017)) . . . . . . . . . . . . . 134
7.2 Proposed timeline of operations for the SET mission (Image credit: Max
Vanatta and MIT 12.43/16.83 Space Systems Engineering (2017)) . . . . . . 137
7.3 Architecture concepts being considered for 'Smart Marbles' (Image credit:
M ax Vanatta) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
B. 1 NASA's Technology Readiness Level (TRL) definitions. A TRL number is
obtained once the description in the diagram has been achieved. (Image credit:
NASA)......... ....................................... 160
14
List of Tables
2.1 Ralph/MVIC Observations . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Pluto's climate zones defined by astronomical cycles . . . . . . . . . . . .
4.1 Minimum and maximum global temperature (K) reached for each epoch .
7.1 Summary of Apophis Properties . . . . . . . . . . . . . . . . . . . . . . .
7.2 Original Science Traceability Matrix for the SET Mission to Apophis. .
7.3 Trade Space for Measuring Surface Activity . . . . . . . . . . . . . . . .
7.4 Updated Science Traceability Matrix (original shown in Table 7.2) for the
SET Mission to Apophis enhanced by the addition of "Smart Marbles" . . .
A.1 Comparison of Pluto system parameters . . . . . . . . . . . . . . . . . . . .
15
29
68
90
127
133
138
147
156
16
1Introduction
1.1 A very Brief History of Pluto Observations
The history of Pluto is linked to the early history of Uranus and Neptune. Neptune was
first observed by Galileo in December of 1612 and January of 1613, but it was not identified
as a planet until September 1846 (Kowal and Drake, 1980). Its existence and position were
predicated by Urbane LeVerrier and John Couch Adams, based on perturbations of the orbit
of Uranus (Leverrier, 1872; Adams, 1846). This success inspired further study of the planets'
orbits and numerous predictions of a ninth planet beyond Neptune, most notably those by
William Pickering and Percival Lowell (Pickering and Pickering, 1909; Lowell, 1915).
Lowell Observatory began its first serious search for the ninth planet in September 1906.
Searches for the ninth planet were conducted throughout the early 1900's. In 1929, Clyde
Tombaugh was hired by Lowell Observatory to continue the search. The following year he
discovered Pluto and on March 13th, 1930 Lowell Observatory announced the discovery of
"Planet X", releasing an initial orbit determination the following month (Slipher, 1930). The
name "Pluto", after the god of the underworld, was chosen for the object, after first being
suggested by Venetia Burney, an 11-year-old girl from Oxford, England (Slipher, 1930). The
astronomical symbol, P, was chosen to represent the first two letters of "Pluto" and as a
17
head-nod to the observatories founder, Percival Lowell. Over the next several months its
orbit was refined and the object was confirmed to be a trans-Neptunian planet. Lowell's
predictions for Pluto's orbit were even closer to its actual orbit then predictions for Neptune
had been, but Pluto was two orders of magnitude fainter than Lowell predicted (Reaves,
1997).
Based on infrared photometry Cruikshank et al. (1976), suggested Pluto's surface was
covered in methane ice, which would imply both a higher albedo and lower density than a
solid rock composition. The presence of methane was confirmed by direct observation a few
years later by Cruikshank and Silvaggio (1980). It was later suggested that Pluto's surface
also contained nitrogen in either an ice or liquid state (Clark et al., 1986). Owen et al. (1993)
was able to confirm the presence of nitrogen through spectral observations.
In 1978 James W. Christy discovered Pluto's largest satellite, Charon, at the U.S. Naval
Observatory. A regular series of astrometric observations of Pluto showed an elongation
that rotated in position angle at regular intervals, matching Pluto's known 6.4 day rotation
period. The elongation was determined to be caused by a satellite, believed to have a
diameter about 0.4 times that of Pluto, orbiting with a synchronous period of ~ 6.4 days at
a distance estimated to be between 15, 000 - 20, 000 km (Christy and Harrington, 1978).
The discovery of Charon made it possible to more accurately constrain the size, mass,
density, and albedo (Lupo and Lewis, 1980). These parameters confirmed Pluto was not
massive enough to account for the residuals in Uranus' orbit that Lowell and Pickering's
predictions had been based on and its discovery was a fortuitous coincidence (Reaves, 1997).
It has since been suggested that the perturbations of Uranus were in fact a calculation error
from using the incorrect masses of the Jovian planets (Standish, 1993).
Another "fortunate coincidence" in the history of Pluto observations is the timing of
Charon's discovery. Shortly after Charon's discovery it was determined that the orientation
of the Pluto-Charon system put Charon's orbital plane in an edge-on alignment (as seen
from Earth) once every 124 years, creating a series of transit, occultation, and eclipse events
18
referred to as "Mutual Events". Andersson (1978) predicted that Pluto and Charon were
heading into their next mutual events season with the first even observable as early as
1979 (later shifted to the early 1980s). This set of events would allow planetary scientists
to measure individual diameters and surface compositions for Pluto and Charon, the bulk
density of the Pluto-Charon system, and albedo maps for both bodies.
The first definitive transit detection was made at McDonald Observatory on February 17,
1985 by Richard Binzel and then confirmed 3.2 days later with detection of the corresponding
occultation from Mauna Kea by David Tholen (Binzel et al., 1985). This initial detection
served to prove the existence of Charon and constrain its orbit enough to determine the
geometry for the entire sequence of mutual events which would last until 1990.
The deepest of the occultation events provided the opportunity to independently deter-
mine the spectra of each object. It was found that Charon's reflectance spectra was indicative
of a water ice composition with no evidence of methane or ammonia frost, while Pluto's was
redder, higher albedo, and showed several methane absorption bands (Sawyer et al., 1987;
Buie et al., 1987). Using the mutual events light curves and least square models Young and
Binzel (1993) were able to generate the first detailed albedo maps of Pluto, mapping the
entire sub-Charon hemisphere.
The Hubble Space Telescopes Advanced Camera for Surveys made it possible to produce
two-color albedo maps for both Pluto and Charon (Buie et al., 2010). These maps were
able to achieve more complete longitudinal coverage than those produced from the mutual
events data, however due to Pluto's changing viewing geometry they do not include the
Southern most latitudes of Pluto (which will not be fully visible again until after the end of
this century).
19
The Hubble Space Telescope also allowed for deeper searches for additional satellites.
Weaver et al. (2006) announced the discovery of Nix and Hydra, making Pluto the first
Kuiper Belt object known to have more than one satellite. Kerberos, with a diameter less
than a 1/3 that of the other small satellites, was discovered in 2011, and Styx, Pluto's
smallest moon, was discovered the following year (Showalter et al., 2012).
It had long been speculated that Pluto had an atmosphere, supported by its surface
volatiles (e.g. Kuiper, 1944), but it was not directly detected until an occultation of a bright
star by Pluto was observed from the Kuiper Airborne Observatory on June 9, 1988 (Elliot
et al., 1989). This event revealed unexpected structure in Pluto's atmosphere and conclu-
sively showed Pluto had an atmosphere of more than a few microbars (Elliot et al., 1989).
Unfortunately, it was not until August 2002 that another occultation of a bright star by
Pluto was observable from Earth, at which point it was determined the Pluto's atmospheric
pressure had increased during 14 years between observable events (Elliot et al., 2003).
By the late 1980s it had become apparent that Pluto and Charon were interesting sci-
entific targets, deserving of further detailed study. It was also becoming apparent that we
were reaching the limit of what could be done to study them with ground based techniques.
The 1989 flyby of Neptune and Triton by Voyager II revealed Triton to be a surprisingly
geologically active world. Since Triton is believed to be a captured KBO and at the time was
thought to be a Pluto analog, the revelation about its surface complexity further supported
the case for Pluto being a mission target of great scientific significance. The first study
of a dedicated Pluto mission resulted in a concept for a 350 kg, RTG-powered (radioiso-
tope thermo-electric generator) spacecraft with a four instrument scientific payload called
"Pluto-350" (Farquhar and Stern, 1990). The 1990s saw several concepts for dedicated Pluto
missions covering a broad range of budgets and complexities however, none them made it
beyond "Phase A" design studies (Stern, 2008). After the failure of two Mars missions, the
"faster, better, cheaper" era at NASA ended in 2000 and ushered in the era of PI-lead pro-
posal competitions (Neufeld, 2016). In January of 2001 NASA released an Announcement
20
of Opportunity competition for a Pluto Kuiper Belt mission, to complete the flyby of Pluto
before the end of 2020. In November of that year the New Horizons missions was selected for
Phase B development (Stern, 2008). The mission continued to face challenges on its journey
from proposal to launch pad, including tight time constraints and repeated threats to its
budget, ultimately it was saved by the start of the New Frontiers program and pressure
from the National Academies' decadal survey, which in mid-2002 ranked a Pluto-Kuiper belt
mission as the number one medium-sized mission (Neufeld, 2016). What started as an effort
to finish the initial recognizance of the solar system by studying the ninth planet had become
a mission to understand the solar systems newly discovered third zone beyond Neptune.
1.2 The New Horizons Mission
1.2.1 Mission Objectives
The New Horizons mission was designed to meet a broad range of Science Objectives
outlined by the Pluto Kuiper Belt Announcement of Opportunity. The three primary ob-
jectives, written as "required Group 1 goals" were for the mission to (1) characterize the
global geology and morphology of Pluto and Charon, (2) map surface composition of Pluto
and Charon, and (3) characterize the neutral atmosphere of Pluto and its escape rate. In
addition, the Announcement of Opportunity also included nine Group 2 (strongly desired)
objectives and four Group 3 (desired) objectives, including tasks such as characterizing the
time variability of Pluto's surface and atmosphere, mapping the surface composition of se-
lected areas of Pluto and Charon in high resolution, searching for neutral species in Pluto's
upper atmosphere and characterizing the energetic particle environment of Pluto and Charon
(the complete, detailed list can be found in Young et al., 2008). The mission, as proposed,
was expected to meet all of the science objectives, with the exception of a Group 3 goal of
searching for magnetic fields of Pluto and Charon, which New Horizons is only able to do
indirectly (Young et al., 2008).
21
1.2.2 Mission Design and Science Payload
The New Horizons mission launched on January 19, 2006 and received a gravity assist
from Jupiter in February 2007 (during which it observed Jupiter and several of its satellites).
In January of 2015 New Horizons began its scientific observations of the Pluto system,
making its closest approach to Pluto (at a distance of 12, 500 km) on July 14, 2015. The
New Horizons spacecraft is now continuing on into the Kuiper belt, where it will flyby the
classical Kuiper Belt object designated (486958) 2014 MU69 , making its closest approach on
January 1, 2019.
New Horizons is the first of NASA's New Frontiers mid-sized planetary exploration mis-
sions. In order to reach Pluto in nine-and-a-half years, the spacecraft's mass had to be kept
below 480 kg, leaving less than 50 kg allotted for the science payload, and only 12 W of
power were to be available to the scientific instruments at any time during the encounter
(Weaver et al., 2008). Thus the seven scientific instruments on New Horizons were selected
to fulfill the science objectives of the mission while being lightweight, low power, and capable
of surviving the nine-and-a-half year, 3 billion mile, journey to the Pluto system. The New
Horizons payload instruments are described in turn.
Ralph is a visible and near infrared imager which consists of a single telescope that
feeds into two focal planes: the Multi-spectral Visible Imaging Camera (MVIC) and the
Linear Etalon Imaging Spectral Array (LEISA) (Reuter et al., 2008). Its primary purpose
is mapping surface geology and composition but it was also used for the study of Pluto's
atmosphere (some of the results from the Ralph/MVIC instrument are presented in Chapter
2).
The LOng-Range Reconnaissance Imager (LORRI) is a narrow-angle Richey-Chretien
telescope used for high-resolution, panchromatic imaging. LORRI was designed to study
the geology and surface morphology of Pluto and its satellites, the collisional history of the
system, the atmosphere-surface interactions on Pluto, and to be able to image the Pluto
22
system at higher resolution than any Earth-based telescope for 90 days prior to encounter.
This incoming detailed reconnaissance was necessary to provide an extended time base for
observations as well as to search for rings and other potential hazards (Cheng et al., 2008).
The ultraviolet imaging spectrograph on New Horizons, Alice, was designed for both
airglow and solar occultation measurements and is used for studying the composition of
Pluto's atmosphere (Stern et al., 2008).
The New Horizons Radio Science Experiment (REX) was designed to perform thermal
scans of Pluto and Charon's surfaces as well as radio occultations to study the atmosphere
of Pluto and look for an atmosphere on Charon (Tyler et al., 2008). The instrument consists
of a small amount of signal processing hardware that was added to the radio system New
Horizons uses for communications and tracking.
The New Horizons payload also includes two in situ particle detection instruments, SWAP
and PEPPSI. The Solar Wind at Pluto (SWAP) instrument measures the angles and en-
ergies of solar wind ions in the Pluto environment (and throughout New Horizons journey
into the Kuiper Belt) (McComas et al., 2008). The Pluto Energetic Particle Spectrometer
Science Investigation (PEPPSI) measures pick-up ions from Pluto's outgassing atmosphere
to characterize Pluto's neutral atmosphere, any extended ionosphere and solar wind interac-
tions, the energetic particle environment around the Pluto system, and provide a check on
the atmospheric escape rate of Pluto (McNutt et al., 2008).
The Student Dust Counter (later renamed the Venitia Burnie Student Dust Counter-
VBSDC) is the first science instrument on a planetary mission to be designed, built, tested
and operated by students. It operates continually and measures the spatial and size distri-
bution of dust along New Horizons' path as it crosses the solar system and heads out into
the Kuiper Belt (Horanyi et al., 2008).
23
1.2.3 Preliminary Results from New Horizons
With almost 60 papers published in just the first 2 years after encounter NASA's New
Horizons mission has clearly generated a wealth of new knowledge about Pluto, its satellites,
and the Kuiper Belt. Here we highlight just a few of the early results from New Horizons
which are most relevant to this thesis.
The initial data returned from New Horizons revealed a diverse and geologically active
world displaying a remarkably broad range of landforms, albedos, colors, and compositions
(Stern et al., 2015). Pluto's surface shows evidence of surface ice convection, volatile trans-
port, glacial flow, and wind streaks (Stern et al., 2015). It also shows a wide range of surface
ages, as evidenced by the varying crater abundances, with some regions showing many large,
deteriorating craters and others being apparently crater free (Robbins et al., 2017).
Spectral imaging of Pluto revealed the complex spatial distribution of N2, CO, CH4 , and
H20 ices and tholin-like material across Pluto's surface (Grundy et al., 2016). Spectral data
combined with geologic evidence point to Pluto having widespread, water-ice "bed-rock"
with a volatile veneer (Grundy et al., 2016; Stern et al., 2015; Moore et al., 2016). Pluto
has the second widest range of albedos of any solar system object (with the widest being
Iapetus), with its brightest and darkest terrains occurring side-by-side around its equatorial
region (Stern et al., 2015). Pluto's equatorial region, particularly between 25'S and 10'N
shows large areas of dark terrain interspersed with bright regions (Stern et al., 2015). The
most notable of these regions, formally named Tombaugh Regio, measures 1, 800 km East to
West and 1, 500 km North to South and straddles the equator on the anti-Charon hemisphere
(Stern et al., 2015).
The western side of Tombaugh Regio, named Sputnik Planitia, stands out for several
reasons. It shows no discernible craters, indicating it's still geologically active (Robbins
et al., 2017). It is also the one region on Pluto that shows an abundance of N2 , CO, and
CH4 ice (Grundy et al., 2016). The polygonal pattern across Sputnik Planitia's surface
24
is believed to be the result of convection, indicating the ice in Sputnik Planitia is several
kilometers deep (McKinnon et al., 2016). Schenk et al. (2015) suggest Sputnik Planitia is
the remnant of a large impact basin that has been infilled with volatile ices.
Image Credit: NASA/JHU-APL/SwRI
Figure 1.1: Progress of Pluto imaging. Left: Hubble image of Pluto from 2003 (one of the
best available images of Pluto at the time I started graduate school in 2013). Center: Image
of Pluto taken by New Horizons' LORRI instrument on June 11th, 2015 (the date of my
general exam). Right: Best, full-disk, enhanced color image of Pluto from New Horizons.
Figure 1.1 illustrates how over the course of my time in graduate school, New Horizons has
changed our view of Pluto from a distant astronomical object to a complex, geologically active
world. New Horizons has provided us with a detailed snapshot of the current state of the
Pluto system. Pluto's surface shows stunning albedo variegations with normal reflectances
from 0.08 - 1.0, a range broader than any other body in the solar system except Saturn's
moon Iapetus (Buratti et al., 2017). Of even further interest, is the complex distribution of
Pluto's volatiles and albedo units, which place Pluto's brightest and most volatile-rich region
(Tombaugh Regio) next to one of its darkest and most volatile depleted (Cthulhu Regio).
This thesis seeks to understand the current state of Pluto's surface by exploring the complex
seasonal cycles it undergoes on million year timescales.
Chapter 2 presents the results of the study of Pluto's methane distribution using data
from New Horizons' Ralph/MVIC instrument and provides an overview of Pluto's complex
volatile distribution. Pluto's complex seasonal cycles (the result of obliquity and longitude
of perihelion variations on million year timescales) and some of their consequences are in-
25
troduced in Chapter 3. Surface temperature modeling is conducted in Chapter 4 to explore
how albedo differences on Pluto could affect surface temperatures and in turn sublimation
and deposition rates. Chapter 5 employs a simple volatile transport model to further this
study and explore the latitudinal limits of runaway albedo variations.
This thesis concludes by looking ahead to a possible next step in small body spacecraft
exploration. We look at a mission concept to study the asteroid Apophis during its 2029 close
approach to the Earth and perform a "pre-Phase A" study of a hardware design intended to
aid the mission in its study of surface seismic activity during the encounter.
26
2Methane Distribution on Pluto as
Mapped by the New Horizons
Ralph/MVIC Instrument
2.1 Introduction
Most of the work for this chapter was originally published in Earle et al. (submitted).
This chapter uses data from the New Horizons spacecraft to explore Pluto's current volatile
distribution and provide context for the modeling performed in the later chapters.
The New Horizons spacecraft is equipped with seven scientific instruments to study the
origin of the Pluto system, the surface processes, volatile transport cycles, and the energetics
and chemistry of the atmosphere (Young et al., 2008; Weaver et al., 2008). This work
addresses results obtained with the Ralph instrument consisting of two components; the
Multispectral Visible Imaging Camera (MVIC) and the Linear Etalon Imaging Spectral
Array (LEISA). MVIC is composed of seven independent CCD arrays most of which operate
in time-delay integration mode (TDI) to produce panchromatic and colored images (by
pairing CCDs with appropriate filters). The calibration and reduction processes for MVIC
images are described in detail in Howett et al. (2017) and Olkin et al. (2017). We use
27
data from the red channel (540-700 nm), near-infrared (NIR) channel (780-975 nm), and
narrow band methane (CH4) channel (860-910 nm) to produce high-resolution methane
"equivalent width" (MVIC E.W.) and spectral slope maps of Pluto's surface. From these
maps we quantitatively study the relationships between methane distribution, redness, and
other parameters like latitude and elevation. Quantifying these relationships provides useful
constraints for volatile transport modeling and for understanding the geomorphology of
Pluto.
Methane was first detected on Pluto's surface from ground-based observations by Cruik-
shank et al. (1976). Ground-based spectral measurements could not spatially resolve Pluto's
surface. However by taking advantage of Pluto's changing viewing geometry, particularly its
6.4 day rotation period, it was determined that the distribution of methane (and other ices)
on Pluto's surface was heterogeneous (e.g. Grundy and Buie, 2001).
New Horizons has allowed us our first detailed look at the heterogeneous distribution of
Pluto's surface ices (Stern et al., 2015). Several papers have already presented studies of
Pluto's surface using data from the LEISA instrument, which has moderate spectral resolu-
tion near-infrared mapping capabilities (Reuter et al., 2008; Grundy et al., 2016; Protopapa
et al., 2017; Schmitt et al., 2017). However, while MVIC lacks the spectral resolution of
LEISA (relying simply on filters), it achieves more than three times the spatial resolution
of the LEISA instrument, providing more detailed and complete coverage of the methane
distribution on Pluto's surface. MVIC also uses the shorter, 890 nm, absorption band to
measure methane abundance, while LEISA uses the infrared bands between 1.25 and 2.5
pam.
28
2.2 Methods
2.2.1 Data & Reduction
Seventeen image sets from the MVIC instrument were used to produce the global maps
presented here. These images were taken over the last 5.5 days of New Horizons' approach
to Pluto. Since Pluto is currently experiencing northern summer (with a sub-solar latitude
of 52'N at the time of encounter), this series of images provides full longitudinal coverage
from the North pole down to 10'S latitude, with limited longitudinal coverage from 10'S
extending slightly beyond 30'S. Table 2.1 outlines the observation details of the 17 image sets
used here, including the mid-time of each observation, image scale, sub-spacecraft longitude
and sub-spacecraft latitude. The RED, NIR, and CH4 MVIC filter images were registered
to the geometry of the corresponding BLUE filter image, using the Integrated Software for
Imagers and Spectrometers (ISIS3) from the United States Geological Survey.
Table 2.1: Ralph/MVIC Observations
Observation Mid-Time Image Scale Sub-s/c Long. Sub-s/c Lat.
(UTC) (km/pix) (Deg E) (Deg N)
2015-07-09 03:41:05.936 127.16 87.4 43.1
2015-07-09 16:56:05.937 114.03 56.3 43.1
2015-07-10 08:55:30.937 98.17 18.8 43.0
2015-07-10 16:52:15.938 90.28 0.2 43.0
2015-07-10 16:55:05.938 90.24 0.0 43.0
2015-07-11 03:34:35.938 79.66 335.1 43.0
2015-07-11 16:46:56.439 66.54 304.1 43.0
2015-07-11 16:49:46.439 66.49 304.0 43.0
2015-07-12 08:23:08.440 51.03 267.6 43.0
2015-07-12 16:53:04.940 42.59 247.4 42.9
2015-07-13 03:38:06.440 31.91 222.6 42.9
2015-07-13 07:38:36.941 27.93 213.2 42.8
2015-07-13 14:50:51.941 20.78 196.5 42.7
2015-07-13 21:08:40.941 14.53 182.1 42.5
2015-07-14 02:47:54.441 8.92 169.5 42.1
2015-07-14 06:50:11.942 4.91 161.4 41.1
2015-07-14 11:10:52.442 0.66 168.0 26.0
29
These images are publicly available through the NASA Planetary Data System (PDS):
Small Bodies Node. Mutually-registered versions of the images, as well as the MVIC E.W.
and spectral slope maps are currently undergoing the PDS review process, after which they
will also be made public through NASA PDS.
2.2.2 The Model
To create the methane absorption "equivalent width" and spectral slope maps, we start
by producing grids of CH4/NIR and Red/NIR ratios over the parameter space of slope and
"equivalent width" values. For spectral slope we use 151 steps ranging from values of -40 to
61.6 % reflectance/nm. For MVIC E.W. we use 201 steps from values of -40 nm to 81 nm.
These limits were chosen to cover the range of extreme cases, including no counts in the
RED filter and no counts in the CH4 filter. To create these grids we make a model spectrum
for each pair of MVIC E.W. and spectral slope values. We start with a line running from
540 nm to 975 nm (to cover the range of the Red and NIR filters) with the given spectral
slope and normalized to one at 890 nm. Since we are working with three values (one for
each filter) rather than a complete spectrum, we cannot measure equivalent width using
traditional techniques and rather use a simplified parameter we call "MVIC E.W.". For
positive MVIC E.W. values we set the area around 890 nm with the given width equal to
zero. For negative MVIC E.W. values we set the value equal to two for an area of the
designated width around the 890 nm band (indicating those wavelengths are reflecting more
light than the surrounding wavelengths).
The model is then multiplied by a solar spectrum and the filter passbands for the MVIC
instrument to determine the predicted values for each filter for the given parameter pair
(see Figure 2.1). Multiplying by the solar spectrum accounts for the fact we are looking at
reflectance spectra (which are inherently dependent on the Sun's spectra), and multiplying
by the filter passbands allows us to account for the quantum efficiency of the chip and the
throughput of the optics and filters in the MVIC instrument. We work in units of photons,
since counts are the native units of the MVIC instrument.
30
14 . w 10 S!r l
L2 Red7O
Example
-eModei w/ 40 Solar 0 Filter
" e.w. = 10 
" Spectrum Passes
s.s. = -10 _ _ _
0*0 w Io W "0 o w 1100 'eo 100 no0 g oo MW 11 00o M M neo I 1100
1.4 1e17 ew = 10 slope = -10
- CH4
1.2- -- Red Total Area=
NIR RED value
1.0
41
0 0.8-Ae
-0. Total Area
0.6- NIR value
0.I
0.4-
PTOtal Area=
CH4 value
500 600 700 800 900 1000 1100
Wavelength (nm)
Figure 2.1: Schematic showing the process for calculating CH4/NIR and Red/NIR ratios
over the MVIC E.W. and spectral slope parameter space. This example is for the case of an
MVIC E.W. of 10 nm and a spectral slope of -10. The ratios are calculated based on the
shaded areas in the final (bottom) diagram, where red is the Red filter, grey the NIR filter,
and blue the CH4 filter.
Calibrated, co-registered MVIC Red, NIR, and CH4 images are input into the code,
which then finds the best match for each pixel on the CH4/NIR and Red/NIR grids. From
here it uses an interpolation routine to find the best common MVIC E.W. and spectral slope
value for that pixel. This process is used for all pixels of the target object and builds up
spectral slope and MVIC E.W. maps for the input images.
Finally we estimate the error for the maps using the errors on the adjustment factors
for each filter presented in Howett et al. (2017). To do this, we first created a grid of 2,500
points, equally spread across the Red/NIR and CH4/NIR parameter space. Then, using the
31
- 1- .1
errors from Howett et al. (2017) we calculate the minimum and maximum possible deviation
of each ratio. These values are all run through the interpolation code to determine the best
common MVIC E.W. and spectral slope values for each pair of ratios. We then take the
mean of the absolute value of the difference between the MVIC E.W. for the original ratio
pair and the deviated ratios (and then repeat this calculation for spectral slope). From
these calculations we determine that the MVIC E.W. values reported below have an error of
1.18 nm and the spectral slope measurements an error of 0.46. These error calculations
are limited by the fact they are not dependent on the flux of a given pixel. They provide a
reasonable estimate for most of Pluto's surface except regions with high incidence or emission
angles, where the extreme viewing geometry and very low flux introduce additional sources
of error. These regions were not included in the production of the global maps (Figure 2.4)
used for most of the analysis presented in this paper (the mosaicking process is described in
detail in the next section).
2.3 Results
2.3.1 The Maps
Figures 2.2 and 2.3 show the MVIC E.W. and spectral slope maps generated from the
eight highest resolution images from the Ralph/MVIC instrument taken on New Horizons'
approach to Plito. The images range in resolution from 42.59 km/pixel to 0.66 km/pixel
and were taken between July 12th and July 14th, 2015 (details about these observations can
be found in Table 2.1).
In Figure 2.2 dark blue areas indicate little to no methane absorption while redder areas
have greater absorption around the 890 nm methane band. However, it is worth noting the
equivalent width is not simply an indicator of methane abundance, as it can also be affected
by dilution state, ice texture, or grain size (Schmitt et al., 2017; Protopapa et al., 2017).
The 890 nm band is a weak band, probing large depths, making it more comparable to the
1950nm doublet (see Figure 13.3 in Schmitt et al. 2017, which maps the 1900 - 2000 nm
32
247.,., 2226 3.215.0
- 13.5
12.0
7.59.0
6.0
1.5
0.0
Figure 2.2: Maps of the MVIC E.W. of the 890 nm methane absorption band produced
from the 8 highest resolution Ralph/MVIC approach images. These values have an error of
1.18 nm. The number in the top, left corner of each panel indicates the sub-spacecraft lon-
gitude of each observation. Note that the images are arranged by observation time/increasing
resolution, thus the sub-spacecraft longitudes are not in order.
integrated band depth) than to medium and strong (1.7 pm and 2.3 pm) methane bands,
so these maps are more sensitive to coarser grained and also purer CH4 than maps based on
those wavelengths. When areas with large equivalent widths are near the limb they appear
particularly red on these maps (indicating greater CH4 absorption), as can be seen along
the lower right edge of several of the maps. This is due to the low signal-to-noise in these
areas.
Figure 2.3 shows the spectral slope maps simultaneously produced while modeling the
equivalent width of the 890 nm methane absorption band. In these maps a larger spectral
slope indicates redder material, while negative slopes indicate bluer material.
The maps shown in Figures 2.2 and 2.3 along with those produced from the nine lower
resolution observations listed in Table 2.1 have been mosaicked together to produce global
MVIC E.W. and spectral slope maps, which are shown in Figure 2.4, along with a topographic
map of Pluto's surface.
33
20.0
17.5
15.0
LA
'010.0 0
7.5
35.0
-5.0
Figure 2.3: Maps of the spectral slope produced from the 8 highest resolution Ralph/MVIC
approach images. These values have an error of 10.46. The number in the top, left corner of
each panel indicates the sub-spacecraft longitude of each observation. Note that the images
are arranged by observation time/increasing resolution, thus the sub-spacecraft longitudes
are not in order.
The mosaic was produced by using USGS's ISIS3 (Integrated Software for Imagers and
Spectrometers) routines. The dataset cubes were prepared for mosaicking by eliminating the
pixels in the terminator region. First, we eliminated pixels having an incidence angle greater
than 80', and an emission angle greater than 75'. The values were empirically chosen by
several trials, aimed to produced a coherent integrated map of planetary surfaces of airless
objects, like Pluto. An upper limit of 800 was selected as the incidence angle cut-off. This
was found to be the best compromise to crop off those ares where shadows are more extensive
than illuminated terrains (and the illuminated pixels have steep slopes). For the emission
angle, we chose a value of 750 as the best one to mask off those areas where severely oblique
geometry smears out the pixels and blurs their values. The ISIS3 routine used for this task
was MASK. Then, Pluto's edge pixels were further cropped using a circular mask (ISIS3's
routine CIRCLE). The mosaic was produced overlapping the 17 selected cubes, in order of
increasing spatial resolution, by using ISIS3's NOSEAM function. In this way, the
34
Q0
60
-30
-60:
-90
0 30 60 90 120 150 180 210 240 270 300 330 360
90 Longitude (deg)
60
30
0
-30
-60
-90
9C
60
0 30 60 90 120 150 180 210 240 270 300 330 360
Longitude (deg)
30
0
-30
270 300 330 360
I-
-o
0)
-J
Figure 2.4: Cylindrical projections of Pluto's surface. Top: global mosaic of maps of the
MVIC E.W. of the 890 nm methane absorption band Middle: global mosaic of spectral
slope maps Bottom: digital elevation model from (Schenk et al., 2016), projected to match
the resolution of the equivalent width and slope maps. The boxes labeled A-F indicate areas
shown in detail in Figures 2.5-2.10 and discussed in subsection 2.3.2. A: al-Idrisi Montes,
B: Sputnik Planitia cellular terrain, C: Northeast Cthulhu (Virgil and Beatrice Fossae and
Elliot Crater), D: Enrigue Montes, E: Viking Terra (Inanna and Dumuzi Fossae), F: Pioneer
Terra.
35
9 )
3
r;i
-o
cv
V
.4-.
4-,(0
-J
-601 Digital Elevation Model
0 30 60 90 120 150 180 210 240
Longitude (deg)
10
8
6
4
2
0
-2
-4
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
-2.5
-5.0
5
4
3
2
1
0
-1
-2
-3
-4
-5
highest spatial resolution cubes are on top of the lowest resolution ones. These maps have
a resolution of 0.65km/pixel to match the resolution of the best available images (however
the resolution on the non-encounter hemisphere is 100's of kilometers per pixel).
2.3.2 Areas of Interest
Using the global mosaics we focus on six areas on Pluto's surface that show particularly
interesting results when comparing the MVIC E.W., spectral slope, and topographic maps.
These areas were selected to highlight interesting features on Pluto (where volatile processes
involving methane are occurring) and demonstrate the level of detail in the high resolution
images and how they could be used for further detailed study of Pluto's surface and the
relationships between geology, color, and composition (note that some of the feature names
on Pluto are formal and others are informal).
Figure 2.5 shows the Al-Idrisi Montes and part of the shore line of Sputnik Planitia.
The Al-Idrisi Montes are located along the northwest shoreline of Sputnik Planitia, which is
believed to be a volatile-filled basin (Stern et al., 2015). The mountains consist of randomly
oriented, closely packed, water ice blocks rising several kilometers above Sputnik Planitia
(Moore et al., 2016; Grundy et al., 2016). The mountain blocks are neutral in color while the
material between them and to the west of them is redder. The upper surfaces and southern
slopes of the blocks show MVIC E.W.s of 4 nm or more, indicating the presence of methane
ice. Sputnik Planitia also shows signs of methane, but with slightly weaker absorptions
between 2 - 4 nm. Comparing the MVIC E.W. and spectral slope maps we see an anti-
correlation between red terrain and broad MVIC E.W.s, a trend we will discuss more in
section 2.4.
Sputnik Planitia is believed to be a nitrogen-dominated, volatile filled basin that under-
goes solid-state convection, creating cells or polygons about 10 -40 km across on the surface
(McKinnon et al., 2016; Protopapa et al., 2017). Part of this cellular/polygonal terrain is
shown in Figure 2.6. From the DEM we see that this is a low lying region of generally
uniform elevation, with some of the cell walls showing up as being slightly lower than the
36
5 150 155 160
Longitude(deg)
5 150 155 160
Lonaitude(dea)
36
32
28
31
3
V
a)
V
3.0
2.4
-
0.0 LO
-0.6
-1.2 3
-1.8
1:, 15! lbU
Longitude(deg)
Lonaitude(dea)
152 153 154 155
Longitude(deg)
156
Figure 2.5: Left: Box "A" in Figure 2.4. Cylindrical projections of Pluto's surface showing
the Al-Idrisi Montes and part of the shoreline of Sputnik Planitia. Top: MVIC E.W. of
the 890 nm methane absorption band. Middle: spectral slope. Bottom: digital elevation
model from (Schenk et al., 2016), projected to match the resolution of the equivalent width
and slope maps. Right: The same set of Figures zoomed closer to show even greater detail.
cells themselves. Comparing the MVIC E.W. map and spectral slope maps we again see an
anti-correlation between the two, with the strongest methane signal showing up along the
37
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
-2.5
-5.0
LA
U,
(D
M
(U
V
24
14
36
32
28
2414
36
32
S28
30
Ch
W 29
a 28 t
3
27
26
151 152 153 154 155 156
Longitude(deg)
31
30
S29
V ..
.28 
27 52:15
21
151 152 153 154 155 156
2 4 L145
5.0
4.5
4.0
3.5
3.0
2.0
1.5 :
1.0
0.5
0.0
20.0
17.5
15.0
12.5
10.0 =
7.5 .
5.0 ?
2.5 3
0.0 g
-2.5 3
-5.0~
3.0
2.4
1.8
1.2
0.6
0.0 0*
-0.6 2
-1.2 3
-1.8
-2.4
-3.0
northern part of Sputnik Planitia and the west edge. Looking at a more detailed level we
notice the centers of the cells appear more methane rich and bluer in color, while the borders
of the cells show less methane absorption and redder spectral slopes.
45 45 -M 45 45 sa. OR
40 40 40 -- -
35 35 35 35~
3o 30 '30 30
25 25 25 . 25
20 20 20 20
15 15 1515
10 10
166 168 170 172 174 176 178 180 166 168 170 172 174 176 178 180 166 168 170 172 174 176 178 180 166 168 170 172 174 176 178 180
Longitude(deg) Longitude(deg) Longitude(deg) Longitude(deg)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -5 -4 -3 -2 -1 0 1 2 3 4 5 -3.0-2.4-1.8-1.M.60.0 0.6 1.2 1.8 2.4 3.0
MVIC EW. (nm) 5.5. (%reflectance/100nm) Elevation (km) LORRI Image
Figure 2.6: Box "B" in Figure 2.4. Cylindrical projections of Pluto's surface showing the
cellular terrain in Sputnik Planitia. Far-Left: MVIC E.W. of the 890 nm methane absorp-
tion band. Mid-Left: spectral slope. Mid-Right: digital elevation model from (Schenk
et al., 2016), projected to match the resolution of the equivalent width and slope maps.
Far-Right: The same region shown from LORRI imaging (cylindrical projection) to show
the cellular patterns.
Part of Cthulhu is shown in Figure 2.7, including Elliot Crater, the large, complex crater
(officially named for the late MIT professor, James Elliot), and Virgil and Beatrice Fossae.
Cthulhu is a large region characterized by dark mantling (possibly the result of atmospheric
tholin deposition) thin enough to not obscure the underlying topography (Moore et al., 2016;
Grundy et al., 2016). Again, we see an anti-correlation between red material and areas with
broad methane equivalent widths, with Cthulhu itself being very red and showing little to
no methane absorption while the area just north of Cthulhu (seen at the top of the image)
is less red and shows MVIC E.W.s of 2 nrm and greater. This trend continues onto the small
38
scale features in these images. The fossae show up bluer and with broader MVIC E.W.s
than the surrounding area. Elliot and the other craters also show this anti-correlation with
their north-facing slopes showing up with broader MVIC E.W.s and bluer spectral slopes,
while their bottoms are red and methane-depleted.
Figure 2.8 shows another interesting part of Cthulhu, a chain of methane topped moun-
tains informally known as Enrique Montes. Again we see a very obvious anti-correlation
between MVIC E.W. and spectral slope. Comparing with the DEM we see the methane rich
(bluer spectral slope) regions are exclusively at higher elevations while the redder, methane
depleted material is mostly at lower altitudes.
Viking Terra, part of which is shown in Figure 2.9, is west of Sputnik Planitia and north
of Cthulhu. Unlike the red, volatile-depleted Cthulhu, Viking is bluer and shows broad
MVIC E.W. methane absorption, particularly between 150 and 30' north latitude where it
borders the northern edge of Cthulhu. This region is heavily cratered and features several
fossae, including Inanna and Dumuzi, which both run the width of the image in the top half
of each image in Figure 2.9. Again we see an anti-correlation between 890 nm MVIC E.W.
and spectral slope. In the fossae and many of the craters we see red bottoms and bluer rims
and walls with broader methane absorption.
Pioneer Terra lies directly north of Tombaugh Regio, and is the most northern latitude
region we consider here, with the images in Figure 2.10 showing a patch of Pioneer Terra
between 550 and 75' north latitude. Unlike the region shown in Figures 2.5, 2.7, and 2.9, the
methane absorption and redness somewhat correlate (although in general this region is also
more neutral to blue than the other regions). The redness and methane absorption also show
noticeable correlation with the higher terrains on the digital elevation model. The craters in
this region do not show up as distinctly in the spectral slope and equivalent maps and are
generally bluer with less methane absorption than the surrounding area.
39
2.4 Discussion
2.4.1 Analysis
Figure 2.11 shows the spectral slope vs. MVIC E.W. for the images shown in Figures 2.2
and 2.3. The first image (with a sub-s/c longitude of 247.70) is dominated by neutral colored
terrain with 890 nm equivalent widths between 0 and 10 nm. All of the images contain some
amount of neutral material, but as Cthulhu rotates into the spacecraft's view more red
material is also present on the plots. The red material shows a strong anti-correlation with
MVIC E.W., with most of the reddest material (with a spectral slope of 10 or more) showing
little to no methane absorption (with MVIC E.W. values of 5 nm or less). The areas with the
broadest equivalent widths are also generally neutral in color (with spectral slopes between
0 and -5). This color range also shows the broadest range of MVIC E.W.s with materials
ranging between some of the broadest MVIC E.W.s (of 15nm or more) to areas that show
little to no methane absorption.
Influence of Latitude
The trends between MVIC E.W. and spectral slope change from one latitudinal region
to another (Figure 2.12). Near the north pole the global maps show little to no absorption
around the 890 nm methane band (with MVIC E.W.s of 5 nm or less) and relatively neutral
colors (with spectral slopes between 5 and -5). At latitudes from 60'N to 90'N there is
a correlation between spectral slope and MVIC E.W. (which match linear fits with slopes
between 0.74 and 0.63), but moving down towards the equator this trend flips with the
reddest spectral slopes showing little to no methane absorption and the areas with the most
methane absorption appearing neutral in color (similar to the trend we saw in Figure 2.11).
This can be seen on a more localized scale by comparing Figure 2.10, which shows the high
latitude Pioneer Terra, with Figures 2.5, 2.7, and 2.9, which show lower latitude regions.
While the MVIC E.W. and spectral slope maps of the lower latitude regions are almost
inverses of each other, the maps of Pioneer Terra correlate.
40
Moving from the pole towards the equator we also see progressively more red material.
The equatorial region shows the broadest range of spectral slopes and MVIC E.W.s; from
Figure 2.4 we see that the reddest material is concentrated around the equator.
20 20 20 20
:247.7 222.6 32
15 0 .I .-
15 - 1-5 -1- 15 -5
10 -10 10 - - - -10
20 20 202
15 - 5 -- -
U 0. 0 0- 0
1 5 1 5 15
-10 -10 .- -10 - - -- .-- 10
-15 -' -15 - -15 - -- 5 '
-10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20
20 20 20 20
1695 161f 168.011515 15
10 10
10 10
0i 5- 5- 
U 0 0 '0~i~
ii1-10
155 15 L110 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20
Equivalent Width Equivalent Width Equivalent Width Equivalent Width
Figure 2.11: Scatter plots of spectral slope vs MVIC B W. for each of the images shown in
Figures 2.2 and 2.3. The number in the upper, right corner of each plot is the sub-spacecraft
longitude at the time of the observation. For the three largest images (with sub-spacecraft
latitudes of 169.5, 161.4, and 168.0) the images have been subsampled for computational
reasons.
To study these latitudinal trends further we take the mean and standard deviation of the
MVIC E.W. (and spectral slope) as a function of latitude (Figure 2.13). This highlights a
couple of trends between MVIC E.W., spectral slope, and latitude. The equatorial latitudes
show much larger standard deviations for both parameters, implying these regions have
more diverse color and volatile distributions than the northern terrain. The albedo maps
presented in Buratti et al. (2017) and the composition maps in Schmitt et al. (2017) also
show more diversity near the equator than at the pole. This is consistent with the results
41
of Earle et al. (2017b, 2018) (see Chapters 4 and 5) which suggest the equatorial latitudes
are more susceptible than the poles to runaway albedo variations, and thus more likely to
form and support stark contrasts in albedo and volatile abundance. Figure 2.13 also shows
that the reddest material is concentrated just below the equator (where Cthulhu is located).
Just north of the equator there is a broad mix of colors that shift towards the blue north
of Cthulhu and into Tombaugh Regio. The northernmost latitudes show a narrow range of
neutral colors. This is in agreement with the report by Olkin et al. (2017) of relatively blue
terrain in Tombaugh Regio, red terrain in Cthulhu and yellow terrain at the north pole.
20 20 , 1 20 - 20
15- 90N-80N 15- 80N-70N 15- 70N-60N 15- 60N-50N
C 10 - - 10 -- 10 -10 -
5 - - 5 5- 5- ICI
Sy=0.7374x-0.7512 y=0.6263-1.3887 --y=. 6 7 2x- 2 .157.
-10 - r2=0.3686 -10 - r2=0.3539 - -10 r=0.0704 - ~10-
10 -50 10 1520 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20
20 , , , 20 20 20
15 50N-40 15 40N-30N 15 -. 30N-20 15-. 20N-10N
10 -.- - 10- 10- 10 --
5 - 5 -- 5 5- -
0 0 [0i-
-5--5 -5 . , -5-
-10-. . J 1 * -10 1
-15 -15 -15
-10 -5 0 5 10 15 20 -10 -5 0 510 15 20 -10 -5 0 510 15 20 -10 -5 0 5 1015 20
20 20 20 20
inFgr 2N-0 Eo l -itd bn S10-2 e
f 10e . 10 10ig-
5-5 5 5 1-
0 0 -
C. -5 -5 - : -5 .;. -5
-10 . -10 - -10 -- -10-
-15 -15 --- 15 -15
-10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20 -10 -5 0 5 10 15 20
Equivalent Width Equivalent Width Equivalent Width Equivalent Width
Figure 2.12: Scatter plots of spectral slope vs MVIC E.W. based on the global maps shown
in Figure 2.4. Each subplot is a 10' latitude band from the global maps (the latitude range
of each subplot is given in the upper, right corner).
42
Influence of Topography
In addition to looking at latitudinal trends we also look at the relationships between
methane absorption (and spectral slope) and elevation using the digital elevation model
(DEM) from Schenk et al. (2016) and preforming a similar analysis to Figure 2.13. Based on
Figure 2.14 the average MVIC E.W. is highest for elevation above 2 km, for most of these
elevations the average MVIC E.W. is around 6 nm. Below 2 km the average MVIC E.W.
steeply drops to 2 nm then gradually declines to zero. Low elevations, below -3 km, also
show signs of methane absorption, with average MVIC E.W.'s around 2 nm.
Moore et al. (2018) found that while both methane and nitrogen precipitate at low eleva-
tions, at higher elevations the atmospheric temperature and pressure do not allow nitrogen
to condense so only methane will accumulate. The broad MVIC E.W.'s observed above 2 km
may be an indication that this region not only contains an abundance of methane but that
it is also purer (less N2 contaminated) than the methane found at lower elevations.
Spectral slope does not appear to be as dependent on elevation, with broad error-bars
throughout Figure 2.14 and averages around 0 for most elevations. The red and yellow
material is most likely the result of atmospheric haze that has settled on the surface and is
found in topographic highs and lows (Grundy et al., submitted). Pluto's coloration is most
likely being driven by other factors besides elevation. The one trend that can be identified
is that low elevations, those below -2 km, tend to have bluer spectral slopes; this includes
regions like Sputnik Planitia and the impression near the north pole. Sputnik Planitia is
a volatile-filled basin measuring approximately 750 x 1, 400 km (Moore et al., 2016). Haze
landing on Sputnik Planitia may be quickly buried by volatile sublimation and deposition
and the area may be undergoing solid state convection (McKinnon et al., 2016; Grundy et al.,
submitted). Most of Pluto's terrain below -2 km lies within Sputnik Planitia, where haze
is buried, which explains why these elevations show a bluer average than the rest of Pluto's
surface.
43
90 90
75 - 75
60 60
45- 45
30- 30
15- - 15
0- .
S -15 - - _15-
-30 - ,- -30-
-45- -45
-60- -60
-75 - -75-
-90 1 -901
-6 -4 -2 0 2 4 6 8 -10 -5 0 5 10 15 20
MVIC E.W. (nm) Spectral Slope (%reflectance/lOOnm)
Figure 2.13: Left: MVIC E.W. as a function of latitude based on the global maps presented
in Figure 2.4. Right: Spectral slope as a function of latitude based on the global maps
presented in Figure 2.4. The points represent the mean value for that range and the error
bars are the standard deviation. A subsampling correction has been applied to account for
the cylindrical projection.
The influence of topography can also be seen on a smaller scale in Figures 2.5, 2.7, 2.8,
2.9, and 2.10. Strong methane absorption is seen on the peaks and south facing slopes
of the Al-Idrisi Montes, with slightly weaker absorption in the adjacent, low-lying Sputnik
Planitia (Figure 2.5). In Figure 2.10 methane absorption only shows up on the highest
regions of Pioneer Terra. Figure 2.8 shows a chain of methane topped mountains sticking
out of the otherwise flat, red, and methane depleted Cthulhu. The craters and fossae in
Figures 2.7 and 2.9 also show a strong relationship between topography, color and methane
absorption. Many of these features have broad methane absorption on their rims or walls,
as does the floor of Elliot Crater, and for many their coloration does not match that of
the surrounding area. These trends do not hold for Pioneer Terra (Figure 2.10), however,
44
where the craters appear smoother, potentially from burial by atmospheric transport and
deposition or potentially cryovolcanic or glacial flow (Singer et al., 2016). Earle et al. (2018)
(see Chapter 5) found that while equatorial latitudes on Pluto are highly sensitive to run-
away albedo and maintain albedo-driven volatile deposition contrasts over long timescales,
polar latitudes will experience seasonal transport (with albedo having a minimal effect). This
could explain why, for the example regions shown here, small-scale features like craters and
fossae have a larger effect on color and methane absorption than they do at higher latitudes.
A more complete and detailed study of this potential trend is warranted but outside the
scope of this paper.
4
2
0
'U
0
-2 [
-4
'U
0
-2
-4
-4 -2 0 2 4 6 8 10 -10 -5 0 5 10
MVIC E.W. (nm) Spectral Slope (%reflectance/100nm)
Figure 2.14: Left: MVIC E.W. as a function of elevation based on the global maps presented
in Figure 2.4. Right: Spectral slope as a function of elevation based on the global maps
presented in Figure 2.4. The points represent the mean value for that range and the error
bars are the standard deviation.
45
U
S
I _
_ 3
~ - -- -
2.4.2 Slope-MVIC E.W. Units and Comparison with LEISA re-
sults
In addition to the MVIC channel, the Ralph instrument also contains the Linear Etalon
Imaging Spectral Array (LEISA) channel, a short-wavelength, 1.25 - 2.5pm IR, spectral
imager (Reuter et al., 2008) that has also been used to map the surface composition of Pluto
and its satellites (e.g. Grundy et al., 2016; Protopapa et al., 2017; Schmitt et al., 2017).
Given the low spectral resolution of the MVIC data and lack of laboratory measurements,
there is no way direct way to draw conclusions about grain size, abundance, dilution state,
etc. from MVIC date alone. However we can gain some insight by looking for correlations
between LEISA and MVIC results, leveraging the higher spectral resolution of LEISA and
higher spatial resolution and surface coverage of MVIC.
To aid in our interpretation of the spectral slope and MVIC E.W. maps, we divide Pluto's
surface into six categories based on that pair of parameters and how they correspond with
different regions on the LEISA maps presented in Protopapa et al. (2017) and Schmitt et al.
(2017). Figure 2.15 shows where each of these terrains is found on Pluto's surface, allowing
us to see which areas show similar colors and compositions to each other. The general
characteristics of each region have been determined through comparison with Ralph/LEISA
results in order to leverage LEISA's higher spectral resolution to decipher how different
methane properties manifest themselves in the MVIC maps (since the MVIC maps alone do
not have sufficient spectral resolution to distinguish between different grain sizes, dilution
states, etc.). To better understand the latitudinal constraints on each region, Figure 2.16
shows histograms of each region as a function of latitude.
In Figure 2.15 the areas with the strongest absorption in the 890 nm band are shown
in purple; most of these areas have neutral to blue spectral slopes. The equivalent width is
sensitive to not only the abundance but also other factors like grain size and mixing state.
MVIC alone does not provide enough spectral information to detangle these factors, but
by comparing our maps with those presented in Protopapa et al. (2017) and Schmitt et al.
46
(2017) we see that the areas in purple correlated with areas in the LEISA maps that are not
only methane rich, but also contain the purest methane. These areas are most abundant
at the equator and are found exclusively between 40'N and 40'S (Figure 2.16). On the
approach hemisphere (where digital elevation map coverage is available for comparison)
they correlate with higher elevation areas. This type of terrain is scattered throughout the
eastern side of Tombaugh Regio, where Schmitt et al. (2017) found strong spatial variability
between nitrogen and methane. Moore et al. (2018) identified this area as bladed terrain, a
distinctive landscape on Pluto formed from large methane deposits at low latitudes (30 N
and 300S) and high elevations (above 2 km), where nitrogen does not condense. Figure 2.15
shows additional purple regions around Pluto's equator on the non-encounter hemisphere,
indicating the possibility of additional bladed terrain. Since these particularly pure methane
deposits only seem to form at high elevations, this would indicate that these regions (which
are not covered by the digital elevation model) are likely to have elevations above 2 km.
Areas with bluer spectral slopes (value less than 0) and little (between 0 and 5 nm) or
no (less than 0 nm) methane absorption around the 890 nm band are shown in blue and
green, respectively, in Figure 2.15. Sputnik Planitia contains a mix of methane, nitrogen, and
carbon monoxide (Grundy et al., 2016; Protopapa et al., 2017; Schmitt et al., 2017). Schmitt
et al. (2017) reported that outside of Tombaugh Regio nitrogen was found concentrated
between 30'N and 60ON latitude with less uniform deposits between 60'N and 70'N, and
Protopapa et al. (2017) found a similar latitudinal trend. In Figure 2.15, most of the areas
found to have nitrogen with some methane mixed in appear in green, while the areas with
more methane than nitrogen appear in blue (or yellow, to be discussed below). Figure 2.16
shows that about 80% of the green terrain is concentrated between 30ON and 70ON latitude.
These terrains appear to be N2 ice-rich with the equivalent width of the 890 nm methane
band being driven by the concentration of methane. On the non-encounter hemisphere the
mid-northern latitudes (30 0N and 600N) are predominantly blue, however the lack of green
terrain at these longitudes may be driven more by artifacts of the calibration (as can be
47
seen by comparing the maps in Figures 2.2 and 2.3) than an actual absence of nitrogen.
Many of the blue areas in this region lay close to the cut-off between blue and green terrains
(such that shifting the cutoff between the two categories will change there classification), as
opposed to the purple and yellow regions on the non-encounter hemisphere which are not as
effected by minor changes to the Slope-MVIC E.W. unit boundaries.
Areas with intermediate methane absorption (MVIC E.W.s between 0 and 5nm) and
intermediate spectral slopes (between 0 and 10) are shown in yellow in Figure 2.15. On the
encounter hemisphere, yellow terrain is particularly common in two regions: a band just
north of Cthulhu and Lowell Regio (near Pluto's north pole). Protopapa et al. (2017) found
the area north of Cthulhu to be composed of both methane and tholins. Lowell Regio is both
methane-rich and contains a "gold material" which follows a unique mixing line from the
one between bulk Pluto colors and Cthulhu (Grundy et al., submitted; Olkin et al., 2017).
The terrain shown in yellow is scattered in additional areas across Pluto's non-encounter
hemisphere and does not seem to be as constrained by latitude or elevation as other terrains.
These regions most likely contain a mix of methane ice and tholins.
The least abundant terrain type in Figure 2.15 is shown in orange and has no methane
absorption (MVIC E.W.s less than Onm) and intermediate spectral slopes (between 0 and
10). Comparing the location of this terrain with the results of Protopapa et al. (2017) we
see these areas contain minimal methane ice and substantial tholin deposits (though not as
substantial as Cthulhu). The orange terrain is found in areas that Schmitt et al. (2017)
found to contain the strongest indication of H20 ice defined to optimize the separation from
the red material signature and methane containing ices.
48
0Ln
5)
-60
-90
0 30 60 90 120 150 180 210
Longitude (deg)
240 270 300 330 360
15- -
10
5
-5-
-10 
-~w
-15
-10 -5 0 5 10 15 20
Equivalent Width (nm)
Figure 2.15: Left: Map of Pluto's surface with mapped elements divided into six categories
based on MVIC E.W. and spectral slope Right: spectral slope vs MVIC E.W. with points
color coded based on MVIC E.W. and spectral slope cutoffs to group similar terrain types.
Pure methane rich
(associated w/ bladed terrain)
5 < E.W.
40 60 80
x of methane and tholins
0 20 40 60 80
Latitude (deq)
Methane rich
(seasonal and/or diluted w/ N2)
u.ut
0 < E.W. <= 50.07 S.S. < 0
0.06-
0.05
0.04
0.03
0.02
0.01
0.0-40 -20 0 20 40 60 80
Moderate tholin,
0.08 some methane
E.W. <= 00.07
0 < S.S. <= 10
0.06-
0.05-
0.04-
0.03
0.02 -
0.01-
-40 -20 0 20 40 60
Latitude (deq)
80
N2 (or CO)
rich w/ some methane
E.W. <= 00.07 S.S. < 0
0.06 -
0.05 -
0.04-
0.03
0.02
0.01 -
0.00-40 -20 0 20 40 60 80
Substantial tholin,
0.08 , little to no methane
E.W. <= 50.07.
10 < S.S.
0.06 -
0.05-
0.04 -
0.03
0.02
0.01
0.00
-40 -20 0 20 40 60 80
Latitude (deq)
Figure 2.16: Histograms of the relative frequency of the six different terrain types introduced
in Figure 2.15 as a function of latitude. Correction factors have been applied to account for
pixel widths changing as a function of latitude and the frequencies have been normalized to
the total mapped area.
49
90
60
30
IA
CU
-1'
-
0.07
.C 0.06
9 0.05
0.04
0.03
> 0.02
0.01
0.00
-4
0.08
. 0.07
.C 0.06
0.05
0.04
0.03
> 0.02
-4 001
0.00
-4
Mi
0 < E.W. <= 5
0 < S.S. <= 10
0 -20
The areas shown in red in Figure 2.15 have steep spectral slopes (of 10 or more) and show
little to no methane absorption. Like the purple terrain it is found exclusively between 40ON
and 40'S, with more than 98% of it concentrated between 30'N and 300S (Figure 2.16). On
the close approach hemisphere most of the red material is concentrated in Cthulhu. Cthulhu
is most likely composed of tholins, deposited from atmospheric haze and/or formed from
the irradiation of methane ice (Cruikshank et al., 2016). The presence of additional red
patches along Pluto's equator may indicate tholin-covered regions like Cthulhu (but smaller)
on Pluto's non-encounter hemisphere.
Comparing the results presented here with those from the Ralph/LEISA instrument gives
us further insight into Pluto's surface composition. The region between 30'N and 300S lati-
tude shows the broadest diversity of colors and compositions. Earle et al. (2018) (see Chapter
5 and discussed further in Chapter 6) show that these latitudes are more sensitive to runaway
albedo variations and can form and support stark albedo and volatile distribution contrasts
over million-year timescales better than the polar latitudes. This could explain why these
latitudes harbor both the reddest and most pure methane deposits on Pluto's surface, while
higher latitudes show fewer extremes and less diversity. The terrains near the equator, like
the in-filled Sputnik Planitia, heavily tholin covered Cthulhu, and unique bladed terrain,
are developed over million-year timescales. The polar terrains experience more seasonal ex-
tremes and are expected to undergo significant changes from volatile transport over seasonal
timescales, and thus cannot support the extreme red deposits and broad methane absorp-
tions (most likely from purer deposits and larger grain sizes) seen near the equator. There
is evidence for more bladed terrain as well as more dark tholin deposits like Cthulhu on
Pluto's non-encounter hemisphere. Pluto's more northern latitudes are more homogeneous
and do not encompass the same extremes as the equatorial latitudes. The intermediate lat-
itudes, between 30'N and 60'S, seem to be ice-rich, containing a mixture of both methane
50
and nitrogen, which makes the 890 nm band appear less broad. The north polar latitudes,
above 60'N, show mostly moderate methane absorption with some tholin mixed in places,
particularly within Lowell Regio.
2.5 Conclusions
We present here maps of the equivalent width of the 890 nm methane absorption band
and spectral slope across Pluto's surface as mapped by the Ralph/MVIC instrument. We
find Pluto's surface to show a diverse and complicated distribution of methane abundance
and colors. MVIC E.W. and spectral slope both show some latitudinal dependence. The
equatorial latitudes, between 30'N and 30'S, show a much broader diversity of colors and
equivalent widths.
MVIC E.W. also shows dependence on elevation, with most of the broadest MVIC E.W.
occurring above 2 km. This could be explained by the results of Moore et al. (2018),
who found that between 30'N and 300S and above 2 km methane will condense but it is
too warm for nitrogen to condense, making these deposits more pure than lower elevation
deposits where methane is often mixed with nitrogen. This dependence can also be seen
looking at smaller features on Pluto, like mountain tops and crater rims, many of which
show methane deposits. Spectral slope does not show as strong a dependence on elevation.
The reddening on Pluto's surface is most likely related to the settling of atmospheric haze
(which is a global process) or the formation of tholins in ice by irradiation from UV and/or
charged particles (Grundy et al., submitted; Cruikshank et al., 2016) and thus less sensitive
to elevation.
The maps presented here provide new insight into understanding Pluto's global methane
and color distribution, they also open the door for potential further detailed study of the
complicated relationship between Pluto's composition and geology. Additionally, Pluto's
current volatile distribution provides context and constraints for studying Pluto's long-term
seasonal evolution, as we will do in the next several chapters.
51
9
15
10
5
0
-5
110 115 120 125 130 135 140
Lonqitude(deg)
145
10
5
0
-5
110 115 120 125 130 135
Lonqitude(deg)
Elliot
I
140 145
crater
V
'tOcM
a 0km
110 115 120 125 130 135 140 145
Longitude(deg)
Figure 2.7: Box "C" in Figure 2.4. Cylindrical projections of Pluto's surface showing part
of Cthulhu containing Elliot crater (the large, complex crate in the upper right corner),
Virgil Fossa (the fossa that runs from Elliot crater to the lower left corner of the image),
and Beatrice Fossa (shorter and south of Virgil). Top: MVIC E.W. of the 890 nm methane
absorption band. Middle: spectral slope. Bottom: digital elevation model from (Schenk
et al., 2016), projected to match the resolution of the equivalent width and slope maps.
52
CP
-o
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
20.0
17.5
15.0
12.5
10.0
7.5
5.0
2.5
0.0
-2.5
-5.0
3.0
2.4
1.8
1.2
0.6
0.0
-0.6
-1.2
-1.8
-2.4
-3.0
r)
3
I
0
0
0
D
2
-o
~0
15
10
5
0
-5
IT
-5 -5 -5
0' 10
-CU -1 . 10
-15 -15 -15
Okm-
-20 -20 -20
40 142 144 146 148 150 140 142 144 146 148 150 140 142 144 146 148 150
Longitude(deg) Longitude(deg) Longitude(deg)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -5 -4 -3 -2 -1 0 1 2 3 4 5 -3.0-2.4-1.8-1.2-0.6 0.0 0.6 1.2 1.8 2.4 3.0
MVIC E.W. (nm) S.S. (%reflectance/100nm) Elevation (kin)
Figure 2.8: Box "D" in Figure 2.4. Cylindrical projections of Pluto's surface showing part
of Cthulhu containing a chain of methane frost covered mountains, informally known as
Enrique Montes. Left: MVIC E.W. of the 890 nm methane absorption band. Middle:
spectral slope. Right: digital elevation model from (Schenk et al., 2016), projected to
match the resolution of the equivalent width and slope maps. Note, this region is near
the edge of the DEM where the map transitions from using stereo imaging to using limb
shadowing to determine elevation, the seem running across the image from -3' to -17'
latitude is an artifact of this transition.
53
00
40 5.0
4.5
35 4.0
3.5
30 3.0 r
~2025 2.0 ..
1.5 3
20 1.0
0.5
15 0.0
115 120 125 130 135 140 145
40 Lo itude(de ) 20.0
17.5
35 15.0
-1 112.53
30 1.0 -
25 5.0
4- 2.5
20 0.0
-2.5 3
5 -5.0
115 120 125 130 135 140 145
Longitude(deq) .
foi a2.4
35 -1.8
1.2 2
(30 41 0.6 <
(U 40.0 
-
.25 -0.6
3 -- 1.2 3
20 -- 1.8
100km -2.4
15 L - I -- 3.0
115 120 125 130 135 140 145
Longitude(deg)
Figure 2.9: Box "E" in Figure 2.4. Cylindrical projections of Pluto's surface showing part of
Viking Terra, the region west of Sputnik Planitia and north of Cthulhu. Top: MVIC E.W.
of the 890 nm methane absorption band Middle: spectral slope Bottom: digital elevation
model from (Schenk et al., 2016), projected to match the resolution of the equivalent width
and slope maps.
54
175 180 185 190 195 200 205 210 215
Longitude(deg)
a .L. 5-Sr w '~~a -.a-
175 180 185 190 195 200 205 210 215
Longitude(deg)
e IA
Adr
ijtai
- r~ a
175 180 185 190 195 200
,W I
.1
-' --
205 210 215
75
70
65
60
3.0
2.4
1.8
1.2
0.6
0.0
-0.6
-1.2
-1.8
-2.4
-3.0
en
0)
5
0
3t
Longitude(deg)
Figure 2.10: Box "F" in Figure 2.4. Cylindrical projections of Pluto's surface showing part
of Pioneer Terra, the region north of Tombaugh Regio. Top: MVIC E.W. of the 890 nm
methane absorption band Middle: spectral slope Bottom: digital elevation model from
(Schenk et al., 2016), projected to match the resolution of the equivalent width and slope
maps.
55
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
5
4
3
2
1
0
-1
-2
-3
-4
-5
S
n
3
~
U,
3
55 -
170
75
70
65
60
a'
a)
-o
0)
V
55 E
170
75
70
65
60
a'
W)
r r t
100km
55 1
17 0
ell,.',W -I..
56
3Pluto's Insolation History and "Super
Seasons"
3.1 Introduction
This chapter is primarily based on work published in Earle and Binzel (2015), along with
work contributed to Binzel et al. (2017) and Stern et al. (2017).
Pluto's high obliquity (currently around 1190) varies by about 23' over a period of less
than 3 million years while Pluto's longitude of perihelion regresses 3600 over 3.7 million years
(Dobrovolskis et al., 1997; Spencer et al., 1997). As a result of this pair of orbital variations
Pluto's sub-solar latitude at perihelion has ranged between 53'S and 76'N over the past 3
million years (Figure 3.1). Pluto has a high orbital eccentricity (e ~ 0.25) which causes its
heliocentric distance to vary from less than 30AU out to almost 50AU, which leads to the
solar constant changing by a factor of - 3 over the course of its orbit (Spencer et al., 1997).
Insolation intensity and distribution is dependent on instantaneous heliocentric distance
and obliquity (Levine et al., 1977). Pluto's high eccentricity coupled with its changing obliq-
uity and sub-solar latitude at perihelion create substantial differences in insolation patterns
on Pluto when averaged over different time intervals (Binzel, 1990, 1992). Understanding
57
these patterns can provide important insight in interpreting surface features revealed by New
Horizons and understanding volatile transport on Pluto. Pluto's atmosphere is probably in
vapor pressure equilibrium with isothermal surface ice, so the surface atmospheric pressure
is controlled by the surface volatile temperature (Spencer et al., 1997; Hinson et al., 2018).
Insolation is one of the key inputs for volatile transport and atmospheric pressure models,
however most of the modeling done to date only focusses on short timescales during the
current epoch (Hansen and Paige, 1996; Young, 2013; Hansen et al., 2014). Given the mag-
nitude of Pluto's orbital variations (and consequently its insolation distribution) over million
year timescales, it could be expected that Pluto's volatile distribution, atmospherics pres-
sure and surface geology are impacted by these variations. Over the next several chapters
we explore Pluto's insolation history and its implications for Pluto's atmospheric pressure,
surface temperatures, and volatile distribution.
Before we discuss the implications of Pluto's insolation history in detail it is worth
acknowledging the instability of Pluto's orbit. Pluto's motion is found to be chaotic on
timescales of 10 to 20 million years (Sussman and Wisdom, 1988, 1992). We chose to focus
our work on timescales of less than three million years, as this is sufficiently long enough to
encompass the last two extrema for Pluto's sub-solar latitude at perihelion but short enough
to be well within the limit of Pluto's orbit being predictable.
3.2 Insolation Model
The work presented here is based on the model originally published in Earle and Binzel
(2015), but with a minor update to better correct for the Keplerian slowing of the orbital
velocity near aphelion (Nadeau and McGehee, 2017). The model determines the insolation
at the top of Pluto's atmosphere as a function of latitude and time. First, the timescales of
interest must be set and then the integration step size determined. For our purposes the size
of the time step varied based on the duration of interest and the time frame over which the
insolation was going to be averaged. Before the insolation can be calculated Pluto's position
58
aA)
CT
-0
a
0
(M
C
0
a)
4--0
a)
.
0
-j
t!
~0
Ln-
.4-
:3
-J
130
125
120
115
110
105
100
360
300
240
180
120
60
0
90
60
30
0
-30
-60
-90
3-
3.0 -2.5
3.0
I-
3-
3.0
-2.5
-2.5
-2.0
-2.0
-2.0
-1.5
Timi (Mvrc
-1.5
Timn (Mrcl
-1.5
Time (Myrs)
-1.0
-1.0
-1.0
-0.5 0.
-0.5 0.
-0.5
0
0
0.0
Figure 3.1: Top: Pluto's changing obliquity as a function of time over the past 3 million
years. Middle: Regression of Pluto's longitude of perihelion over the same interval. Bot-
tom: Pluto's resulting sub-solar latitude at perihelion as a function of time. As noted in the
text, possible long-term chaotic orbital variations occur over substantially longer timescales
than considered here. Calculations are based on the analysis of Dobrovolskis et al. (1997).
must be established for each time step. This is done by determining sub-solar latitude and
angle from perihelion as a function of time. Both of these values were calculated using
the orbital model of Pluto initially presented in Dobrovolskis and Harris (1983) and refined
in Dobrovolskis et al. (1997), which uses the time and corresponding eccentric anomaly to
calculate the angle from perihelion, phase angle, and angle between Pluto's longitude of
59
.........-...
- Extreme
Extreme N rthr
-Southern Iummrs
- SummersCurrent .
"Equinox"
perihelion to its vernal equinox, which in turn can then be used to calculate the sub-solar
latitude at any time (Dobrovolskis and Harris, 1983; Dobrovolskis et al., 1997). This process
is described in detail in Appendix A. This model well represents Pluto's orbit for time scales
of 10 million years, which is several times the length of our longest trial making this model
sufficiently accurate for our purposes (Dobrovolskis et al., 1997).
Once Pluto's geometric parameters have been calculated as a function of time, the helio-
centric distance and local hour angle at sunset must also be determined in order to calculate
the insolation for each time step and latitude. Since we know the shape of Pluto's orbit (from
its semi-major axis and eccentricity) we can determine instantaneous heliocentric distance r
using the angle from perihelion (which tells us where in its orbit Pluto falls at a given time).
The instantaneous heliocentric distance r is given by
- a(1 - e2 )
r = ( 2 (3.1)(1 + e cos 0)
where a is the semi-major axis, e the eccentricity, and 6 the angle from perihelion (Levine
et al., 1977).
For mapping insolation dependence onto the sphere of Pluto, we chose to use a 2' latitude
step, which converts to - 40 km between each planetary latitude location for each insolation
calculation. In order to determine the local hour angle at sunset h for each latitude we must
first consider two special cases where the sun will neither rise nor set at certain latitudes on
a given Pluto day. The first special case is for those latitudes that are in constant sunlight
during the Pluto day in question (in which case h = 7r). The second case is the opposite
scenario where the latitude is in shadow and receives no sunlight for the full Pluto day (in
which case h = 0). For all other scenarios the sun will set at some point during the Pluto
day and the local hour angle of sunset h is given by:
- sin # sin (
cos h = cs os6(3.2)
Cos 6 Cos
60
where q is the planetary latitude and 6 the latitude of the sub-solar point (Levine et al.,
1977). With a diurnal period of 6.38726 0.00007 days (Tholen and Buie, 1997) (which is
much shorter than its 248 year orbital period), Pluto can be considered a rapidly rotating
planet for the purpose of the insolation calculations presented here. This assumption and its
implications were studied in detail in Young (2012) which found that atmospheric buffering
dominates over diurnal timescales and restricts Nitrogen temperatures and surface pressure
variations to less than 0.2% over a single Pluto day. The insolation I for a given latitude q
on a rapidly rotating planet (where rotational period << orbital period) is given by
I(#) = (PSo/7r)(ae/r)2 [cos 6 cos q sin h + h sin 6 sin #] (3.3)
where P is Pluto's rotational period in minutes, So the solar constant at 1 AU, and a, is the
semi-major axis of the Earth's orbit (1 AU) (Levine et al., 1977). After the insolation has
been calculated at each latitude for all of the time steps, the average for each latitude can
be taken over the desired time interval.
3.3 Results
3.3.1 Diurnal Insolation
We initially set out to study how the insolation received above Pluto's atmosphere varies
when integrated over different epochs. For all comparisons we divide the total integration's
timescale by the interval. This provides "average insolation" values in units of ergs cm- 2 sI
received over each timescale so that time dependent latitudinal variations can be revealed
(next, in subsection 3.3.2 we will consider maximum diurnal insolation as a function of
latitude over various timescales). There are clear trends in how integrated insolation varies
with the time period over which it is averaged (Figure 3.2). We are particularly interested in
how insolation varies over different timescales leading up to the close approach of the Pluto
61
system by New Horizons, so for each of the timescales presented the average was taken
from the designated start date to mid-July 2015. These timescales are intended to inform
interpretation of surface composition and geology as revealed by New Horizons.
Over short timescales, ranging from a few days to a few decades, Pluto's average insolation
varies dramatically with latitude. For each of these short timescales, the maxima occurs at
one pole and minima at the other. The most extreme case occurs at the current orientation
where for a single Pluto day the average insolation values vary by more than 950 ergs cm-2
s-1 across Pluto's latitudes. At this time, Pluto experiences arctic summer, so the North
Pole and the entire region above 38'N latitude (including the 51ON sub-solar latitude) are
experiencing constant sunlight ("midnight sun") while the region below 380S latitude resides
in constant shadow and receives zero insolation during this period.
Another epoch of interest when considering how Pluto's surface may respond to changes
in insolation is the time since Pluto's surface was mapped based off data from observations
of a series of transit, occultation, and eclipse events between Pluto and Charon that occurred
from 1985 to 1990; referred to as the Mutual Events (Binzel et al., 1985). The late 1980s
also marked the passing of Pluto's most recent perihelion and equinox. As Pluto has moved
away from perihelion and into arctic summer since 1990 the average insolation has been
significantly higher in the northern region, peaking at the North Pole, which since 1990, has
received an average of over 650 ergs cm- 2 s-1. In contrast, at the southernmost latitudes,
Pluto has been receiving little or no insolation over the last two and a half decades.
Over slightly longer timescales of possible interest, such as the total time since Pluto was
discovered in 1930 (i.e. decadal scales), we still see this trend of the maximum insolation oc-
curring at one pole and the minimum at the other. However over this multi-decade timescale
the difference between the minimum and maximum is less dramatic and the trend is in the
opposite direction. From the time Pluto was discovered, the South Pole has averaged about
475 ergs cm-2 s-1 while the North Pole's average insolation has been less than half that.
62
I
90
60
30I
(U
-0
0
-30
-60
-go I
0 200 400 600 800 1000
Average Insolation (ergs/cm 2 s)
Figure 3.2: Average insolation at each latitude over varying timescales. The "One Pluto
Day" average is taken over a single Pluto day in mid-July 2015, when NASA's New Horizons
spacecraft flew through the Pluto system. All other averages are taken from the start time
indicated to mid-July 2015. "M.E." refers to the mutual events, a series of occultation and
eclipse events occurring between Pluto and Charon.
Over longer timescales, ranging from one Pluto orbit (248 Earth years) to millions of
years, Pluto's average insolation is symmetric across the equator, with the maxima occurring
at both poles in minima at or near the equator. Nadeau and McGehee (2017) and Hamilton
et al. (2016) have explained this symmetry by showing that the slowly changing aspect angle
at aphelion compensates for the greater heliocentric distance and balances out the pole-to-
pole accumulated insolation over a single orbit. This balancing results in far less dramatic
latitudinal variations over the longer timescales than those seen over the shorter timescales
described above.
63
One Pluto Day (2015)
Since M.E. (1990)
A Since Discovery (1930)
- One Full Orbit (1767)
-- - Past 0.9 Myrs
- -.Past 2.35 Myrs
-0
Over the single Pluto orbit (248 Earth years) leading up to the New Horizons fly-through
of the Pluto system, Pluto's poles have averaged 250 ergs cm- 2 S-1, the maximum average
over that time period. The minimum average insolation, of less than 216 ergs cm- 2 s-1,
occurs around 25'S and 25'N latitude. All of the latitudes between 35'S and 35'N receive
less than 220 ergs cm- 2 s-
We next consider two longer timescales over which Pluto's obliquity and longitude of
perihelion cycles become relevant. Over the past 0.9 million years Pluto's obliquity has gone
from its most horizontal, 1030 , to its current value of - 120'. As Pluto has undergone this
portion of its obliquity cycle it has averaged a minimum insolation of about 200 ergs cm-2
s-1 at its equator and maxima at each pole of 270 ergs cm--2 s-1. Averaging over an even
longer timescale of 2.35 million years, during which time Pluto's obliquity reaches both its
extrema, 103' and 126', Pluto's insolation begins to average out somewhere between that of
the current orbit and that of the 0.9 million years timescale. Over this longer timescale the
minimum average insolation still occurs at the equator, but is around 210 ergs cm 2 s-.
Again, the maxima are found at the poles, but with a value of 259 ergs cm- 2 s-1, placing
it almost exactly between values for the current orbit and 0.9 million years timescales. So
while the difference between the average insolation at Pluto's poles varies widely over short,
sub-Pluto year timescales, over longer timescales the poles average the same amount of
insolation, generally slightly greater than that of the equator.
3.3.2 Pluto's "Super Seasons"
Over the course of a Pluto orbit the average diurnal insolation is symmetric across the
equator. The location of the extrema and difference between them is largely dependent on
Pluto's obliquity cycles, described in section 3.1. Figure 3.3 (left) shows how the average
annual insolation over a single Pluto year varies with different epochs. As was discussed in
the previous section, over one Pluto year in the current epoch, the pole receive an average of
250 ergs cm- 2 s-I, while all of the latitudes between 35'S and 35'N receive less than 220
ergs cm- 2 s-1 and the minimum average insolation occurs around 25'S and 25'N latitude.
64
I
When Pluto's obliquity is closer to horizontal, the poles receive an average of close to 280
ergs cm-2 s-1 while the equator averages less than 200 ergs cm- 2 S- 1. At the other extrema,
when Pluto's obliquity is more vertical (up to 1260), the equator and poles average almost
the same amount of insolation over a Pluto year while the minima occur around 300S and
300N.
-- Current Orbit - - 0.9 Myrs Ago 2.35 Myrs Ago
280 1600
%I
260 1316 -
240 - 1032-
tu
'*'.E.-...c 220 '4 8-
E
~200 44
-90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90
Latitude (deg) Latitude (deg)
Figure 3.3: Left: Annual average insolation vs. latitude for a single Pluto year during three
different epochs. Right: Maximum diurnal insolation vs. latitude over a single Pluto year
during three different epochs.
Studying Pluto's insolation averaged over an orbital period does not give the full picture
of Pluto's insolation history because of Pluto's highly eccentric orbit and regressing longitude
of perihelion. Currently Pluto experiences equinox and perihelion around the same time, re-
sulting in both hemispheres experiencing fairly similar seasonal cycles. However, as Pluto's
orbit evolves and goes through phases where equinox and perihelion are further apart, each
hemisphere experiences very unique seasons. While both poles accumulate the same amount
of insolation over the course of one full Pluto orbit, whichever pole is tipped towards the
Sun at perihelion will experience a shorter, more intense summer. So the maximum diurnal
insolation at that pole will be significantly higher than the opposite pole, which will experi-
ence a longer, but less intense summer at aphelion. Figure 3.3 (right) shows the maximum
65
diurnal insolation reached at each latitude over a single Pluto year during the three epochs
being considered. 0.9 million years ago and 2.35 million years ago were selected for more
detailed study since there are the two most recent epochs when Pluto's sub-solar latitude at
perihelion was at extrema (Figure 3.1). Over the 0.9 million years ago epoch the sub-solar
latitude was high in the northern hemisphere at perihelion, resulting in a maximum diurnal
insolation of 1,600 ergs cm- 2 s-1. During that same epoch the southern hemisphere never
received more than 500 ergs cm- 2 s 1 . 2.35 million years ago the southern hemisphere ex-
perienced a less extreme version of this with the south pole (- 1, 200 ergs cm- 2 S1) more
than double the maximum diurnal insolation of the north pole (~ 470 ergs cm-2 s- 1).
1600 1
1400- Obliquity = 119 deg
1200-
1000-
800- 
. ,' -
600 - *f
400- 0
200 % %
L- - - - ---
1800 1850 1900 1950 2000
Year
2 1600 900
1400 Obliquity = 103 deg 
- 600
o 1200 - 1200- 300
a 1000- -
800 - - 0
600- 
- - -30c
400 
---- ---- ------ -90
.2 20---------------
n lt - = -*af. 0- 900
0 50 100 150 200
(J T-0.9 Myrs (years)
1600
1400- Obliquity = 126 deg
1200 -
1000 - , -
800 6000
400 
g
200
0 50 100 150 200
T-2.35 Myrs (years)
Figure 3.4: Diurnally averaged insolation over 1 Pluto orbit for select latitudes. Top: current
orbit. Middle: 0.9 million years ago. Bottom: 2.35 million years ago.
66
To look at this effect in greater detail we plot the insolation for select latitudes over the
three different epochs in Figure 3.4. The equator always receives diurnal insolation even as
Pluto's orbit evolves over million year timescales. Every single Pluto rotation the equator
received some insolation and never average more than 490 ergs cm- 2 s'. The poles receives
a far less even distribution of sunlight. During Pluto's current epoch, each pole spends
roughly half of Pluto's 248 year orbit in sunlight (and the other half in shadow, receiving
no insolation). During the peak of their summer season each pole averages around 1,000
ergs cm-2 s1 of insolation. Over the two historical epochs considered, Pluto experiences
what we refer to as "Super Seasons", where one hemisphere experiences a short, intense
summer and long winter, while the other experiences a short winter and long, less intense
summer. This can be seen most dramatically for the 0.9 million years ago epoch (Figure
3.4; middle). Over this epoch the north pole experienced a maximum diurnal insolation of
1,600 ergs cm-2 s- during its summer season and then spent more than 160 years at a
time in darkness, receiving no insolation. In contrast, during this same epoch the South
Pole received a maximum diurnal insolation of less than 500 ergs cm- 2 s- 1, but spent more
than 100 years at a time averaging over 350 ergs cm- 2 s- 1, and spent less than 90 years
at a time in darkness. The dramatically different insQlation patterns experienced over these
"Super Sesaon" Epochs have the potential to not only effect volatile transport during the
epochs themselves but also have a lingering effect on the surface geology and composition of
Pluto.
67
3.4 Discussion
3.4.1 Climate Zones
An additional consequence of Pluto's orbital variations are its unusual "climate zones",
which are defined and discussed in detail in Binzel et al. (2017). Here we will give a brief
overview of the "climate zones" and how they relate to Pluto's insolation history and "Super
Seasons". The zones we describe here are defined astronomically based on sub-solar latitudes
and do not incorporate atmospheric circulation.
Table 3.1: Pluto's climate zones defined by astronomical cycles. The number in brackets
denotes the percentage of total surface area covered by the specified range. Adapted from
Binzel et al. (2017).
Climate Defining Characteristics Current Maximum Permanent
Zone Range Range Range
Tropics Sun reaches overhead point during 60N to 60S 77N to 77S 53N to 53S
orbital year [87%] [97%] [80%]
Arctic Experiences periods of midnight Sun 30N to 90N 13N to 90N 37N to 90N
in summer and darkness in winter 30S to 90S 13S to 90S 37S to 90S
lasting one full rotation or more [50%] [78%] [40%]
Tropical Experiences both overhead sun and 30N to 60N 13N to 77N 37N to 53N
Arctic arctic seasons, during orbital year 30S to 60S 13S to 77S 37S to 53S
[37%] [75%] [20%]
Diurnal Day/night cycle occurs, each and ev- 30N to 30S 37N to 37S 13N to 13S
ery rotation, throughout orbital year [50%] [60%] [22%]
Polar Sun never reaches the overhead 60N to 90N 53N to 90N 77N to 90N
point at any time during the orbital 60S to 90S 53S to 90S 77S to 90S
year [13%] [20%] [3%]
Pluto's high obliquity means it lacks the temperate zones that cover much of Earth's
surface. Instead it features a zone unique to high obliquity planets that we refer to as
the "tropical arctic", which encompass mid-latitudes that experience overhead sun (like
the tropics) as well as periods of sunlight in summer or darkness in winter that last one
full rotation or more (like the arctic). Currently this region spans between roughly 30'N
to 60'N and 30'S to 60'S, but in the past had a maximum range of 13'N to 770N and
130S to 77'S, encompassing 3/4 of Pluto's surface area (Table 3.1). Pluto's large arctic
68
circles currently cover half the planet, reaching from each pole down to 30', and in the past
have extended as far down as 13' in each hemisphere. Currently 87% of Pluto is tropical,
meaning it experiences direct overhead sunlight at some point during Pluto's orbital year
as the subsolar point ranges from roughly 60'N to 60'S. The complement to Pluto's arctic
zone is its diurnal zone, the region near the equator which is not arctic and thus experiences
a day/night cycle for every single Pluto rotation. Currently this region covers half of Pluto's
surface and lies between 30'N to 30'S, but in the past it has covered as much as 60% of the
surface and as little as 22% (extending from only 130N to 13'S). Almost all of Pluto (97%)
has experienced direct sunlight at some point in the last few million years as the maximum
extent of the tropic region is 77'N to 77'S. The compliment of the tropics is the polar zone,
where the sun never reaches the overhead point during Pluto's orbital year.
Since climate zones and insolation are both dependent on obliquity, the ranges of Pluto's
climate zones fluctuate with its changing insolation patterns. When Pluto's tropic, arctic,
and tropical arctic zones are at their maximum range, Pluto's poles receive the maximum
annual average insolation and the equator the minimum with about 30% less average annual
insolation. At the other extrema, when the diurnal and polar zones are at their maximum
range, Pluto's equator receives the maximum annual insolation with the poles receiving
slightly less and the minima occurring near near 30'N and 300S. During these epochs Pluto's
insolation is more evenly distributed and the minimum and maximum annual insolation vary
by less than 10%.
In the always-diurnal zone (13 0N to 13'S) the maximum diurnal insolation varies by
less than 40% as Pluto undergoes its obliquity variations, where as always polar zone (77 N
to 90'N and 77'S to 900S) sees variations of 55% to more than 70%. The average annual
insolation in the alway diurnal zone varies by 12-15% and in the alway polar region it changes
by about 18%. The intermediate, alway tropical arctic zone (37'N to 53'N and 37'S to 53'S)
shows smaller variations of as little as 5% to less than 14%.
69
Binzel et al. (2017) includes a discussion of surface features, both geologic and composi-
tional, that correlate with climate zones. These correlations suggest climate zones may be
relevant to Pluto's surface morphology, but more detailed thermo-physical modeling of the
long-term evolution of the system is needed to confirm this. In the following chapters we
will perform thermal and volatile sublimation/deposition modeling to further explore these
corrections.
3.4.2 Past Epochs of Higher Atmospheric Pressure
Stern et al. (2017) suggests Pluto's "Super Seasons" may have produced higher atmo-
spheric pressures capable of supporting liquids on Pluto's surface and presents multiple lines
of geomorphological evidence consistent with higher pressure epochs in Pluto's past. For
Stern et al. (2017), we performed modeling of CH4 and N2 surface vapor pressure variations
over one Pluto orbit for Pluto's current epoch, as well as well as its last two "Super Season"
epochs, 0.9 and 2.35 Myrs ago. That model is presented here.
The model assumes either CH4 or N2 ice on Pluto's surface and uses a simple model to
account for first order surface albedo variations. Within the equatorial zone Tombaugh Regio
is included as a volatile rich region with an albedo of 0.6 extending from 45'N to 30'S with
a width of 450 in longitude. The remaining equatorial band is assumed to have no volatiles.
Trials were run with the poles extending to 60' and 45' latitude, and with emissivities
of 0.9 and 0.6 for each case to span the range of likely emissivities. The poles are modeled
for three different scenarios to span the parameter space: a high albedo where the poles are
fresh (0.6 albedo), an intermediate albedo where the poles are partially depleted of fresh
volatiles (0.3 albedo), and a low albedo (0.1 albedo) case representing a darker volatile base.
Within each trial the volatile spatial distribution, albedo, and emissivity are held static. The
surface pressure is calculated using a modified version of the energy balance equation given
in Trafton (1984) and described in detail in Earle et al. (2017b) and Chapter 4 of this thesis.
70
Polar Caps extending to 60' Polar Caps extedning to 450
Emissivity 0.6 Emissivity 0.9 Emissivity 0.6 Emissivity 0.9
102 10 o ' ' ' '' ' 10 2 10 2
10?10 10 I -1o -
S i 0 0 0 0
9 10 10? 10 101- 02 -2 110 -- 1 0-
18501900150200 50 1 501900150 200250 1 501900 1502000200104 1 0 15 20020
102 10 - 10 - 10
L).
0 0o 00 4'
10
0  
100 10 -
1 010 1 10 0, 1 10 4 10
100 104 -2 ,,, 104 10
10 104- 10 100
10 10 110 10 Poa 4'' io 0.
0 0 10 10 20 20 0 50 100 15O 200 250 0 50 100 150 200 250 0 50 100 150 200 250
r .10? r iog 10
C" 0 .
S10 100 10044- 104 0.
10 2~i -02 -7 10 2' 10~ 24
-4'
10 10 10'
different epochs. (Top row) Current epoch where perihelion occurs at "equinox" (Middle
row) The "Extreme Northern Summer" epoch occurring 0.9 Myrs ago where the subsolar
point is at high northern latitudes when Pluto reached perihelion. (Bottom row) The
"Extreme Southern Summer" epoch 2.35 Myrs ago, where the subsolar latitude is furthest
south at perihelion. Modeled with polar caps extending to 600 latitude (first and second
columns) and t45~ (third and fourth columns) and an emissivity of 0.6 (first and
third columns) and 0.9 (second and fourth columns). Perihelion is marked with a
black vertical dashed line in each plot. Adapted from Stern et al. (2017)
Here we focus on the N2 model results since Nitrogen most likely exerts the controlling
influence on atmospheric pressure (Summers et al., 1997; Hinson et al., 2018) and is more
sensitive to pressure variations over "Super Seasons". Model results are shown in Figures 3.5
and 3.6. The best match for the current atmospheric pressure on Pluto is the scenario with
polar caps extending to 45 , a polar cap albedo of 0.3, and emissivity of 0.9. Comparing
the atmospheric pressure over the current epoch (top rows of Figures 3.5 and 3.6) with
the diurnal insolation over this epoch (top plot in Figure 3.4), we see that pressure trends
with maximum diurnal insolation being received anywhere on Pluto rather than simply
71
Nitrogen with Polar Caps Extending to 75 and Emissivity = 0.6
102 Current Epoch
10 -
2 101
E101
9.93mbar
1.04mbar1850 1900 1950 2000 2050
Year
102 T-0 9 Myrs Epoch 28.21mbar
h"O, 128.64mbar
10 18.46mbar
C,)
1-2
104s
10 -
0 50 100 150 200 250
Orbital Cyde (Year)
10 T-2.35 Myrs Epoch 33.01mbar -
13.49mbar
1 0
_E 10
10,_
0 50 100 150 200 250
Orbital Cyde (Year)
Polar Albedo
- - 0.1 - 0.3 0.6
Figure 3.6: Model of atmospheric molecular nitrogen pressure over a single Pluto orbit at
three different epochs. (Top row) Current epoch where perihelion occurs at "equinox."
(Middle row) The "Extreme Northern Summer" epoch occurring 0.9 Myrs ago where the
subsolar point is at high northern latitudes at perihelion. (Bottom row) The "Extreme
Southern Summer" epoch occurring 2.35 Myrs ago, where the subsolar latitude is furthest
south at perihelion. These model polar caps extend to 750 latitude and have an emissivity
of 0.6. Adapted from Stern et al. (2017)
heliocentric distance (in which case we would expect atmospheric pressure to have peaked at
perihelion). The volatile distribution on Pluto may also play a role in the peak pressure being
offset from perihelion (Young, 2013). The peak pressure for various trials with the model
72
show differences of nearly two orders of magnitude. The trials run during Pluto's current
epoch (characterized by equinox and perihelion occurs close together) show the lowest peak
pressures. The highest peak pressures are seen in the trials during Pluto 0.9 million year ago
"Super Seasons" epoch, when the sub-solar latitude was high in the northern hemisphere
at perihelion. While more detailed modeling is needed to more precisely estimate the past
atmospheric pressures on Pluto, these models indicate that it is plausible that over Pluto's
past "Super Seasons" epochs it could have reached surface atmospheric pressures much higher
than its current value. This modeling also shows that the current epoch is near the minimum
atmospheric pressure state of the parameter space we covered.
Stern et al. (2017) goes on to present geomorphological evidence for past epochs of higher
pressure including features such as dendritic channels, cryovolcanism, wind streaks, and
a ponded, lake-like feature informally referred to as Alcyonia Lacus (Figure 3.7). While
some of these features may be explained by mechanisms other than higher atmospheric
pressure, it is unlikely that none of them formed from epochs of higher atmospheric pressure.
This observational evidence paired with the simple atmospheric pressure modeling suggest
Pluto's atmosphere and surface processes are substantially different during epochs of "Super
Seasons".
3.5 Conclusions
Pluto undergoes obliquity variations and longitude of perihelion regression on cycles of 3
million and 3.7 million years, respectively (Dobrovolskis et al., 1997). These cycles, coupled
with Pluto's high eccentricity (e ~ 0.25), create substantial differences in the insolation
patterns experienced on Pluto. When studying average insolation and comparing timescales
of days, years, centuries, and millennia we observe stark latitudinal dichotomies on shorter
timescales, and symmetry across the equator coupled with slight variations in the extrema on
timescales lasting one full orbit or more. When looking at insolation averaged over a single
Pluto orbit during the current epoch and two historical epochs (selected for their extreme
73
*7
Figure 3.7: Examples of geomorphological evidence for past epochs of higher atmospheric
pressure on Pluto. (a) Dendritic network northeast of Sputnik Planitia. (b) Other network
terrain to the northwest of Sputnik Planitia. (c) A 4km high, 150km wide feature infor-
mally named Wright Mons and likely cryovolvaniv. (d) Isolated ponded, lake-like feature
informally named Alycynonia Lacus. All scale bars are 30km and images are oriented with
north up unless otherwise noted. Images a-c are - 320m/pix from the PMVIC-LORRLCA
(MVIC) observation and image d if ~ 130m/pix from PMPAN_1 (LORRI). Adapted from
Stern et al. (2017)
sub-solar latitudes at perihelion), we see dramatic variations caused predominantly by Pluto
varying obliquity. We break things down a step further to look at the maximum diurnal
insolation reached at each latitude over these three epochs, as well as the diurnal insolation
74
for various latitudes over a single Pluto year during each epoch. From this analysis we see
Pluto undergoes epochs of "Super Seasons", where one pole receives a short, intense summer
followed by a prolong period of darkness, while the other pole received a short period of
winter darkness and longer but less intense summer.
Pluto's obliquity variations are also responsible for the oscillating limits of its "climate
zones" defined in Binzel et al. (2017). We see that over Pluto's obliquity cycles the maximum
diurnal insolation in the always diurnal zone varies by less than 40% while the always polar
zone undergoes variations of 55-70%. The always diurnal and always polar zones in general
show larger variations in average annual insolation than the intermediate, alway tropical
arctic zones.
Stern et al. (2017) shows the Pluto's "Super Seasons" may be responsible for past epochs
of significently higher pressure on Pluto. The modeling shows variations of peak atmospheric
pressure ranging almost two orders of magnitude, with the lowest peak atmospheric pressures
occurring during the current epoch. This provides preliminary evidence for Pluto's "Super
Seasons" effecting volatile transport, atmospheric pressure, and surface morphology. In the
following two Chapters we perform more detailed studies of Pluto's surface temperature
(Chapter 4) and volatile sublimation and deposition (Chapter 5) over the current epoch as
well as the two most recent "Super Season" epochs to explore how high obliquity and orbital
variations impact its surface evolution.
75
76
4Long-term Surface Temperature
Modeling of Pluto
4.1 Introduction
This chapter is based on work originally published in Earle et al. (2017b) as part of the
Icarus' Special Issue about The Pluto System inspired by NASA's New Horizons mission
flying through the Pluto system in July 2015.
NASA's New Horizons mission has provided a wealth of new data about the Pluto system,
including detailed surface geology and volatile distribution maps (Stern et al., 2015; Grundy
et al., 2016). The images of Pluto sent back by New Horizons also reveal striking latitudinal
and longitudinal albedo variations on Pluto's surface (Stern et al., 2015; Grundy et al.,
2016) bringing to high resolution the intriguing variegation originally revealed from Earth
through decades of mapping efforts (e.g. Buie and Tholen, 1989; Buie et al., 2010; Young
and Binzel, 1993; Grundy et al., 2013). These features provide new motivation for studying
surface temperature variations on Pluto both in the current epoch as well as over the past
77
few million years as Pluto's orbit has undergone variations creating dramatic differences
in Pluto's seasons over million year timescales, such as the "Super Seasons" described in
Chapter 3.
Here we set out to determine what effect Pluto's "Super Seasons" as well as Pluto's
albedo variations have on Pluto's surface temperatures. The impact on atmospheric pressure
and possible implications for surface morphology are addressed by Stern et al. (2015) (and
briefly discussed in Chapter 3, Section 3.4.2). In this work we focus on the asymmetric
surface temperature effects of Pluto's changing geometries as opposed to the effects of total
accumulated insolation. Nadeau and McGehee (2017) and Hamilton et al. (2016) show that
the Keplerian slowing of orbital velocity at aphelion compensates for the greater heliocentric
distance and balances out the pole-to-pole accumulated insolation over a single orbit. While
insolation is symmetric, here we find that maximum surface temperature, being a much more
instantaneous effect, proves to be both asymmetric and a greater driver of volatile transport
activity. Thus our focus on temperature modeling in the present work.
Previous work has already been done to model volatile transport on Pluto (and inherently
surface temperature). With the exception of Young et al. (2015)1, most of this work predates
the New Horizons' flyby of the Pluto system so their only observational constraints are
atmospheric measurements from occultation observations and lower resolution ground-based
albedo maps (Young, 2013; Olkin et al., 2015; Hansen et al., 2014). These works also all
focus on the current epoch. We try to build upon the previous work by making use of the
results from NASA's New Horizons mission as well as considering the long term variations
in Pluto's orbit and resultant "Super Seasons".
As previously mentioned, Pluto's orbit is believed to be chaotic on timescales of 10 to 20
million years (Sussman and Wisdom, 1988, 1992) so we choose to focus on timescales of 3
million years or less in order to stay well below the limit of Puto's orbit becoming chaotic.
'Since the publication of Earle et al. (2017b), additional post-encounter models have been published. In
Chapter 6 we discuss these models and compare them with the work presented here.
78
4.2 Methods
4.2.1 Local Temperature Model
A first step towards understanding seasonal surface temperatures is looking at the annual
insolation averages and how they vary over million year timescales. To do this we start
by calculating Pluto's orbit over the timescales of interest using the orbital model of Pluto
initially presented in Dobrovolskis and Harris (1983) and refined in Dobrovolskis et al. (1997)
(and described in Chapter 3, Section 3.2). This model well represents Pluto's orbit for time
scales of 10 Myrs, which is several times the length of our longest trial making this model
sufficiently accurate for our purposes (Dobrovolskis et al., 1997). This provides us with the
inputs necessary to calculate Pluto insolation as a function of latitude using the equations
found in Levine et al. (1977) and an updated orbitally symmetric model from Earle and Binzel
(2015) as guided by the analytic solution by Nadeau and McGehee (2017) and discussed by
Hamilton et al. (2016).
We choose to focus on three significant epochs in Pluto's orbital history. The first is
Pluto's current orbit, characterized by equinox and perihelion occurring close together. Sec-
ond is Pluto's orbital geometry 0.9 million years ago, characterized by Pluto's sub-solar point
at perihelion being high in the northern hemisphere; we call this "extreme northern summer"
The third epoch of interest is Pluto's orbital geometry 2.35 million years ago, characterized
by Pluto's sub-solar latitude at perihelion being low in the southern hemisphere; we call this
"extreme southern summer".
We begin comparing these epochs by examining the insolation averaged over one Pluto
orbit (Figure 4.1, top left panel). At the current epoch (blue, solid line) one Pluto orbit yields
insolation maxima at the poles and minima around 30' (Earle and Binzel, 2015). During
the epoch 0.9 million years ago (green, dashed line), the equator received a substantially
lower minimum value for its insolation while the poles received almost 1.5 times as much
insolation on average. For the epoch 2.35 million years ago, (purple, dotted line), a relatively
79
flat latitudinal insolation pattern emerges with the maximum occurring at the equator, with
additional local maxima at each pole, and minima just beyond 30. During the current
epoch, characterized by equinox occurring near perihelion and aphelion, both poles receive
relatively similar insolation patterns. However during past epochs when Pluto underwent
what we call "super seasons" one pole received more insolation over a shorter period of time
while the other received less insolation but for a longer stretch of time, creating asymmetries
in the maximum insolation as a function of latitude (Figure 4.1). These differences between
maximum insolation and duration of time over which it is received become relevant when
trying to model surface temperatures during different epochs.
While the average annual insolation and average surface temperature (Figure 4.1 top left
and bottom left, respectively) show pole-to-pole symmetry, the maximum local insolation
and surface temperatures reached show the asymmetries that we call "super seasons", as
discussed in Chapter 3. In order to calculate surface temperatures as a function of lati-
tude and albedo we use the 1-dimensional thermophysical model presented in Spencer et al.
(1989) (all temperatures calculated and presented herein are surface temperatures, unless
otherwise indicated). The Spencer model was designed to calculate surface and subsurface
temperatures on a rotating body as a function of local time and was originally written in
IDL, but here has been rewritten in Python and adapted for seasonal changes corresponding
to the varying sub-solar latitude and heliocentric distance.
The model determines heating in the surface layer by balancing thermal emission, inso-
lation, and conduction with the layer below. The middle layers are balanced by conduction
only from the layer above and below. The bottom layer is balanced by conduction with
the layer above and the lower boundary heat flux (Spencer et al., 1989). For the lower
boundary heat flux we use 2.5 ergs/cm2 s. We assume an emissivity of 0.9 based on Spencer
et al. (1989). For the other thermal parameters we used values for methane at 40 K given
in Spencer and Moore (1992); a heat capacity of 1.8 x 107 ergs/gK, density 0.52 g/cm 3,
thermal inertia 6.3 x 105 ergs/cm'-.sK.
80
-- Current Orbit - - 0.9 Myrs Ago 2.35 Myrs Ago
280
260
240
220
200
I-
0
Ln
C
2 44.1
T 43.2
E
12 42.3
'U
<41.4
40.51
-9 0 -60 -30 0 3
Latitude (deg)
1600, -
.2
0
E
E
1316 k
1032-
748-
464-
I 1 180L
30 60 90 -9
49.0
47.4
45.8
E- 45.8
E
S42.6
______1 41.010 60 90 -9
0
0
-60 -30 0
Latitude (deg
-60 -3 0 0 3
Latitude (deg)
30 60 90
I)
0 60 9 0
Figure 4.1: To explore temperature effects, we begin with Figure 3.3; repeated here as the top
two panels. Bottom Left: Average surface temperature over one Pluto orbit as a function
of latitude. Bottom Right: Maximum surface temperature reached at each latitude over
one Pluto orbit as a function of latitude. Blue, solid lines are over Pluto's current orbit.
Green, dashed lines over one Pluto orbit, 0.9 Myrs ago, and the purple, dotted line over one
Pluto orbit 2.35 Myrs ago. Note the changing y-axis scales. For the temperature profiles a
global albedo of 0.3 is assumed.
The original version of the model is designed to calculate local temperatures over times-
pans of a few rotations with a constant sub-solar latitude and heliocentric distance. We have
adapted the model for seasonal use by having it read in instantaneous heliocentric distances
81
1801 1
-90 -60 -30 0
Latitude (deg
45.0
4 -
4
4
4
4
4
4
4
4
44 I
.4
""I ~
4
4
4.. II
- '.,
- - -
-
4 
1
4
I
K I..
I
*
I
I
I
I
I
I
4
4 I
4 ~ I
4
4 'I,
4 I
4 1
4 ~
I I I -
and sub-solar latitude values calculated using the model from Dobrovolskis et al. (1997).
These values are then used to take into account how Pluto's geometry relative to the sun
changes throughout its orbit.
The model used here, of course, does have several limitations. The thermophysical pa-
rameters are not temperature dependent, thermal re-radiation is only from the surface layer,
and most importantly, volatiles are assumed to escape without re-condensing so that the
temperatures of volatile ices can vary over the surface (the global model is treated in section
4.2.3). Even with these limitations the model serves as a good starting point for under-
standing seasonal temperature variations on Pluto. For example with a homogeneous Pluto
(which assumes a global uniform albedo of 0.3) a substantial range of temperatures with
seasonally dependent asymmetrical latitude distributions become readily apparent (Figure
4.1, right column). Pluto is of course variegated; we address the non-uniform case below.
It should be noted that this model and its associated figures (e.g. Figure 4.2) should not
be interpreted as hard and fast results so much as a limiting case describing the absence
of volatile transport for exploratory comparison to an opposing limiting case that includes
volatile transport.
4.2.2 Pluto Albedo Model
In order to account for Pluto's albedo variations we have created a simplified albedo map
of Pluto (Figure 4.3) that takes into account several of the major albedo units on Pluto's
surface. We assume a static Pluto, in which the albedo units do not vary with time or with
solar zenith angle. To represent the region known as Tombaugh Regio, we assign an albedo
value of 0.6 to a patch 450 wide in longitude, and extending from -30' to 45' latitude.
Elsewhere between t25' latitude, we use a dark band with an albedo of 0.1 to represent
the region informally known as Cthulhu Regio. At all other locations an albedo of 0.3 is
assumed.
82
Current Orbit (Equinox at Perihelion)
1800 1850 1900 1950 2000
Year
T - 0.9 Myrs (Northern Summer at Perihelion)
-------------------- -
- ~ ~ ~ ~  ~ ~ ~ ~ ~ - - - - ---------------------------
48
46
C-
40
48
46
E 42
40
100 150 200
Time (from 0.9 Myrs Ago)
T - 2.35 Myrs (Southern Summer at Perihelion)
- -
50 100 150 200
Time (from 2.35 Myrs Ago)
Figure 4.2: Top: average daily surface temperatures over the past Pluto orbit.
average daily surface temperatures over one Pluto orbit, 0.9 million years ago.
average daily surface temperatures over one Pluto orbit, 2.35 million years ago.
hemisphere latitudes are indicated by dashed lines while, Northern hemisphere by
and the shaded region the "diurnal zone".
Middle:
Bottom:
Southern
solid lines
4.2.3 Global Model
Most of the time Pluto's atmosphere may be in surface temperature equilibrium with
surface frosts (Owen et al., 1993; Trafton, 1984). Along with our local model we also consider
a global temperature model for comparison. By looking at how the temperatures of the local
83
50
Uniform
Albedo = 0.3
- Lat: 90
- Lat: 45
- Lat: 13
Diurnal
-Zone
-- Lat: -13
- - Lat: -45
- - Lat: -90
2
L
a.
E
12
4E
4f
42
4;
40
0
0
90 Toy Model of Pluto
30
0 Alb =0.. Alb 0.1
_j -30
-60
-90- image Credit: NASA/JHUAPL/SwR1
Figure 4.3: Left: The simplified albedo map used for the local thermal modeling Right:
Cylindrical mosaic of Pluto. The latitude ranges for the simplified albedo map have been
estimated from the mosaic map of Pluto.
model compare with the instantaneous, global equilibrium temperatures we can get a better
understanding of which regions will most likely be losing volatiles and which will be gaining
volatile deposits.
Just as with the local model we start the global modeling using the heliocentric distance
and sub-solar latitude calculated based on Dobrovolskis et al. (1997). Again we assume an
emissivity of 0.9 based on Spencer et al. (1989). In order to avoid overlapping albedo regions
in the model we simplify our albedo map to include poles, with an albedo of 0.3, which
extend to 45' and a bright patch with albedo 0.6 which extends from -30' to 450 and is
450 wide in longitude. All other areas on the surface are assumed to be depleted of volatiles.
We can then calculate global temperatures based on the energy balance equations given in
Trafton (1984). However, equation 10 in Trafton (1984) appears to contain an extra factor
of A, which we removed. The original version also only accounts for polar caps as a volatile
reservoir, we have modified it to include Tombaugh Regio as a volatile region. Our modified
version of Trafton's energy balance equation is:
(ANP + Asp + ATR)cUT 4 = irF[(1 - ap)(A* p + A* p) + (1 - aTR)A*R] (4.1)
84
where c is the emissivity, 7rFO is the solar flux at Pluto, ai the albedo of the region, Ai the
area of the region, and A* the effective insolation area of the region. The subscript NP
denotes the north polar region, SP the south polar region, and TR the bright equatorial
region informally known as Tombaugh Regio (note: all features names are informal at this
time).
Trafton (1984) also provides the equations necessary to calculate A* for the polar regions.
If a pole is in shadow, A* = 0. If the pole is sunward facing and the sub-solar latitude (#)
is greater in magnitude than the colatitude of the polar cap boundary (0, or 7 - 0,) then
A* = r sin 3 q. For the in-between cases, where a pole is partially lit, the equation becomes
more complicated:
7r Cos A* = - - cos 0 cos2 # - cos 2  - cos2 # sin- Cos2 cos q5( tanq# +sn - secq5(42
+ sin # sin2 0c cos- 1  -tan + sin 2 ttan-a1 -n (4.2)
tall0 )c N/tan2 0c - tan2
Equation 2 is reproduced from Trafton's equation 13 (a full derivation can be found in
Trafton, 1984). The cos- 1 term is in the second quadrant when # > 0 and in the first
quadrant when # < 0. To calculate the contribution from the opposite hemisphere Trafton
(1984) uses -# instead of q.
We calculate A* for the northern and southern part of Tombaugh Regio separately (and
then add them). For each side we use the process described in the previous paragraph to
determine A* for the entire hemisphere as well as a cap reaching down to the extent of
Tombaugh Regio in that hemisphere. By subtracting A* of this cap from A* of the entire
hemisphere we are left with the latitudinal band on which Tombaugh Regio lies. We can
then divide this band, based on the longitudinal width of Tombaugh Regio, to get A* for
just Tombaugh Regio.
85
While this model provides us estimates of the global temperatures on Pluto that we
can compare to our local temperatures model, this model does have limitations. Most
notably, it does not take into account thermal inertia or internal heat flux. The temperatures
provided by the model are instantaneous, and as a result drop below most of our local model
temperatures when Pluto is at perihelion.
4.3 Results
4.3.1 Annual Temperature Patterns - Uniform Albedo Model
We start our discussion by looking at local surface temperature variations at select lat-
itudes over the course of one Pluto orbit for our three epochs of interest for the case of a
globally uniform albedo of 0.3 across the entire surface. Figure 4.2 shows temperature vari-
ations at the poles, 450, and in the "diurnal zone". We define the "diurnal zone" as the
area between -13' south and +13' north. This is the region on Pluto's surface that always
receives diurnal insolation as the obliquity varies over million year timescales (for further
discussion of the "diurnal zone", see Chapter 3 or Binzel et al. (2017)). All other regions
of Pluto have been been in the arctic (or antarctic) circle at some point in the past few
million years, experiencing extended periods of constant sunlight in "summer" and constant
darkness in "winter".
Looking at Figure 4.2 we see obvious latitudinal variations as well as two changing trends
between the three epochs: (1) the differences between polar, mid-latitude and equatorial
surface temperatures vary between epochs and (2) the surface temperature patterns of the
two hemispheres, specifically the poles, contrast within each epoch as well as when comparing
them between epochs.
The difference between polar, mid-latitude and equatorial local surface temperatures from
one epoch to the next are largely driven by how Pluto's obliquity (and as a result insolation
patterns) are changing over million-year timescales. This can be seen by comparing the
differences in Figure 4.2 with the insolation curves in Figure 4.1. Not surprisingly the areas
86
receiving the highest average insolation over the year also experience the warmest surface
temperatures. The interesting exception to this can be seen in the 2.35-million-year-ago
case. During this epoch the equator receives a higher average insolation, however since
it is in the "diurnal zone" the insolation is fairly evenly distributed throughout the year,
leading to steady surface temperatures that are generally lower than the peak polar surface
temperatures. This is caused by the poles receiving constant insolation as "midnight sun"
for part of the year. The diurnal zone surface temperatures are generally the most steady
(varying by only ~ 0.5K per year) while polar temperatures vary by 3 or more degrees
throughout the year.
The other variations are the contrasts between the hemispheres during each Pluto year
as well as the different epochs. These variations are driven primarily by variations in Pluto's
sub-solar latitude at perihelion coupled with its relatively high orbital eccentricity (e ~ 0.25).
During the current epoch, equinox and perihelion occur close together. As a consequence, the
north pole receives insolation from roughly the time Pluto passes perihelion until it reaches
aphelion while the south pole receives insolation from aphelion to perihelion. This results in
both poles having equal length dark seasons and summers of similar duration and intensity.
In contrast, 0.9 million years ago when Pluto's sub-solar latitude at perihelion was high in
the northern hemisphere (at ~ +760), the northern hemisphere received direct sunlight at
perihelion while the southern hemisphere received its most direct sunlight at aphelion where
the insolation flux is diminished by a factor of three. This results in what we are referring to
as "Super Seasons", where one pole receives a short, "hot" summer and long winter, while
the other receives a short winter and much longer, but less intense summer. A slightly less
dramatic version of these "Super Seasons" can be seen in the epoch 2.35 million years ago
when the sub-solar latitude at perihelion was ~ -53' leading to short-lived high local surface
temperatures in the southern hemisphere and a much longer, but lower temperature summer
in the northern hemisphere. We emphasize since the equatorial region always receives its
87
solar energy on a diurnal day/night cycle and never during an interval of continuous arctic
summer, the equatorial region does not experience any "Super Seasons" the way the poles
do.
4.3.2 Historical Temperature Extremes - Variegated Albedo Model
To get a more global view of trends on Pluto, and to incorporate Pluto's striking albedo
variations we ran the thermal model for various latitude and albedo combinations (based on
the simple albedo map we presented in section 2.3 and shown in Figure 4.3). From these
trials we were able to create minimum and maximum local surface temperature maps (Figure
4.4) to study how both albedo and latitude variations affect surface temperature extremes.
The effects of the "Super Seasons" discussed in the previous subsection can be seen in these
plots.
Figure 4.4 draws attention to the impact albedo variations have on surface temperature.
The bright, 0.6 albedo region, representing Tombaugh Regio stays cold (never rising above
~ 37K) while the darker, 0.1 albedo, Cthulhu Regio stays warmer (never falling below
~ 42.5K), even though these two regions are at comparable equatorial latitudes.
To get a better idea of long term extrema we took the information from the subplots
presented in Figure 4.4 and combined it to determine the absolute minimum and maximum
temperature reached at each latitude and albedo combination over the three epochs of in-
terest combined. These results can be seen in Figure 4.5. This emphasizes the contrast
between the bright region which generally never exceeds 40K and the rest of Pluto where
local surface temperatures never drop below 40K and reach almost 50K.
4.3.3 Comparison with Global Model
To better understand what regions we expect to be experiencing sublimation and de-
position we compare some of our local model results with the global temperature model
described in Section 2.3. Since the global model does not account for thermal inertia we can
88
90 Toy Model of Pluto
60 Alb - 0.3
30
0 . Alb = 0.6
00 
60
-30 
-
-60 Ab-0.3
-90
90
60-
30
0 - B
-30
-60-
-90
T - 0.9
Alb - 0-3
Alb = 0 6
AUb - 0.3
Current Orbit (Equinox at Perihelion)
90 Minimum Temperature Maximum Temperature
60 60
30 30
0
-30
-60
-90
60
30
0
-30
-60
An
(Northern Summer
0
-30
-60
-90
a Perih on)
60
30
0
-30
-60-
-90
48.0
46.5
45.0
'a
-o
(U
-J
T - 2.35 M(rs (Southern Summer at
60-
30f
0-
-30
-60.
-90
Figure 4.4: This figure compares Pluto's current orbit with its past super seasons. Left Col-
umn: The simple albedo map of Pluto used to make local surface temperature maps. Cen-
ter Column: The minimum temperature reached during the Pluto year for each latitude
and albedo combination on Pluto's surface. Right Column: The maximum temperature
reached during the Pluto year for each latitude and albedo combination. Top Row: The
current Pluto orbit. Middle Row: One Pluto orbit, 0.9 million years in the past. Bottom
Row: One Pluto orbit, 2.35 million years ago.
make more direct comparisons by comparing the global temperatures to the instantaneous
equilibrium temperatures calculated by the local model. We chose to focus on three specific
latitudes: the north pole (900), the equator (0), and the south pole (-90').
89
0n
W) U
90
60
30
S 0
-30
-60
-90
- Ab - 0.3
- Alb = 03
Aft -. 3
PeriIpJion)
60
30
0
-30
-60-
-90
.
-
- -
39.0
37.5
36.0
40.
s
Historical Extremes:
Past 2.35 Myrs
90 Toy Model of Pluto 90 Minimum Temperature 90 Maximum Temperature
48.0
60 - Alb = 0.3 60- 60- 46.5
30 - 30 - - 30 -45.0 M
43.5 3
- 4 Alb 0.6 e - 0 42.0 3
40.5 $
5J -30 
-30- 
-30- 39.0
-60 Alb = 0.3 -60- . .- - -6037.5
36.0
-90 -90 0
Figure 4.5: Left: The simple albedo model of Pluto initially introduced in section 2.2,
used for the local model. Middle: The minimum surface temperature reached at each
latitude and albedo combination over the three epochs of interest. Right: The maximum
surface temperature reached at each latitude and albedo combination over the three epochs
of interest.
Table 4.1: Minimum and maximum global temperature (K) reached for each epoch
Epoch Min T (K) Max T (K)
Current 24.4 37.7
0.9 Myrs Ago 27.5 45.0
2.35 Myrs Ago 27.5 38.4
For each of the latitudes and epochs of interest we compare the instantaneous local temper-
ature testing albedo values of 0.1, 0.3, and 0.6, with the global temperature over that same
time period (Figure 4.6). The minimum and maximum global temperature for each epoch
are also given in Table 1. Since there is no thermal inertia the equatorial temperatures will
vary considerably throughout a Pluto rotation, so here we just look at the mean equatorial
equilibrium temperature over each Pluto rotation. We see some obvious contrasts between
the polar and equatorial cases. The equatorial temperatures never vary by more than a
few degrees Kelvin while the polar temperatures show dramatic seasonal variations of 40K
or more. The global temperatures range between roughly 25 - 45K, showing the greatest
amplitude over the 0.9 myrs ago epoch when Pluto was near its minimum obliquity.
90
Lat - 90 deg
Ab
-A
1800 1850 1900 1950 2000
. .
- I
4
50 100 150 200 250
Time (years)
Lat = 0 deg
60 r
50 -
40-
20
20 -
1800 1850 1900 1950 2000
70
60
50
40
30
20
10
70
60
50
40
30
20
10
0
60
50
40
30
20
60
50
40
30
20
50 100 150 200 250
Time (years)
Figure 4.6: Comparison of instantaneous global temperatures to instantaneous local equilib-
rium temperatures for select latitudes and albedos. The columns are organized by latitude
with left: latitude 900, center: latitude 0', right: latitude -90'. The rows are organized
by epoch with top: the current Pluto orbit (where the time increment is Earth years), mid-
dle: one Pluto orbit, 0.9 Myrs ago, bottom: one Pluto orbit, 2.35 myrs ago. The global
temperatures are indicated by the solid, black lines, the albedo = 0.1 local cases are purple,
dashed lines, the albedo = 0.3 cases are blue, dot-dashed lines, and the albedo = 0.6 cases
are marked with green, dotted lines.
4.4 Discussion
When considering long-term insolation patterns on Pluto, the relative minimum at the
equator relative to the poles has been shown in several previous works (e.g. van Hemelrijck
(1982), Dobrovolskis (1989), and Spencer et al. (1997)) and illustrated at multiple epochs
by Earle and Binzel (2015). Thus if the minimum location served as the explanation for the
location of Tombaugh Regio (Hamilton et al., 2016) our analysis indicates Pluto would show a
bright equatorial band rather than a "spot". We argue that the equatorial region on Pluto is
a "preservation zone" for whatever is seeded there, where the preservation capability is driven
91
70
60
e 50
02
a 40
30
20
10
Lat -90 deg
A
000
- ,'.I
70
60
50
40
30
20
0-
o NZ
< U
2.
M'G
Ln
1800 1850 1900 1950 2000
70
0 50 100 150 200 251
70 -
0 50 100 150 200 25
60-
50
40-
30
20
10-
0
-a
-A
0 -0 50 100 150 200 2
I -g
-0 - -., -.
50
50 100 150
Time (years)
-. .. .
-
60-
50 -
20
10
200 2500
by the coupling of the local albedo with an always diurnal cycle (and never a continuous
arctic summer or winter), which we first showed qualitatively in Earle et al. (2015). Thus the
equatorial zone is optimized to be the region of maximum contrasts that allows the darkest
region (Cthulhu Regio) to abut directly the brightest region (Sputnik Planitia).
We find that once a region at the equator becomes bright it will become both the coldest
and most consistently available cold trap, making it a likely area for volatile deposition,
which in turn will refresh and brighten the surface. So for example, if Sputnik Planitia
formed from an impact basin, as suggested by Moore et al. (2016), the topographic low would
have initially attracted volatiles, creating a bright spot and triggering a strong feedback loop
of volatile deposition in that area. Surface composition maps show that Tombaugh Regio is
in fact volatile rich, showing high abundances of both N2 and CH4 (Grundy et al., 2016). In
contrast, Cthulhu regio does not show any volatile abundances (Grundy et al., 2016). Given
Cthulhu's low albedo and resulting higher local surface temperatures it could be expected
that once a region at the equator began to darken it would become consistently one of the
warmest regions of the planet and thus unlikely to gain any long term volatile accumulation,
leading to further darkening.
Another way of looking at this effect is to compare the instantaneous equilibrium tem-
peratures with the global temperatures, as we did in Figure 4.6. The polar temperatures
show dramatic seasonal variations, spending portions of the year well above and well below
the global temperatures. This suggest these regions will undergo cycles of deposition and
sublimation and their volatiles (or at least a portion of their volatiles) will be seasonal. This
effect persists for all of the albedo cases we tested, suggesting the polar regions are not
likely to experience albedo variations caused by strong feedback. The equator on the other
hand shows less seasonal variation, and remains close to the global temperature through-
out the epochs studied. Over most of the time periods studied the bright (albedo = 0.6)
equator temperatures are several degrees colder than the global temperature, it only briefly
gets above the global temperature, and never by more than a few degrees, indicating net
92
deposition is most likely occurring in bright equatorial regions. Such ongoing long-term net
deposition could be an important factor that keeps Tombaugh Regio's morphology appearing
'young' and crater-free. On the other hand, the dark (albedo = 0.1) equator temperatures
are generally higher than global temperatures, and only dip below the global temperatures
for brief periods during each orbit. If all of the volatiles migrate away from a region, the
bare surface will no longer be cooled by sublimation and a significant amount of seasonal
cooling will need to take place before seasonally transient frosts can be deposited (Trafton,
1984). Taking this into consideration, it is very likely that dark, equatorial regions are gen-
erally bare of volatiles, any volatiles deposited are most likely minimal and seasonal. These
comparisons show further evidence for "runaway" albedo variations at the equator and more
stable, and spatially consistent albedos in the polar regions.
Thus the fact that the brightest and darkest regions on Pluto co-exist at the same latitude
demonstrate that it is not the insolation minimum that drives the survival of Pluto's "cold
icy heart". Rather it is the diurnal zone that allows self-preservation of an albedo extreme
that gets seeded therein. To understand this phenomenon further we looked at the difference
between the absolute maximum and absolute minimum local surface temperature reached
at each latitude over the three epochs of interest, to see how much temperature variation
each latitude experiences (Figure 4.7). We find that regardless of albedo, the variations in
the equatorial and midlatitude region stay small, less than 3.5K. Moving away from the
midlatitudes and towards the poles the variation in temperature increases. This effect is
more dramatic in the northern hemisphere where the variation at the north pole is between
4.3 and 7.5K depending on the albedo. The stability of temperatures in the equatorial band
independent of albedo makes it likely that once seeded, albedo variations in the equatorial
region will be able to survive million-year or longer timescales while the polar region will be
more susceptible to changing albedos.
93
Variations in Historical
Temperature Extremes
3 4 5
Temperature Variation (K)
I- - Alb = 0.6 - Alb = 0.3 1 Alb = 0.1I
Figure 4.7: Latitude on Pluto vs. the variation between the minimum and maximum tem-
perature reached at that latitude considered over the three epochs of interest: the current
orbit, 0.9 myrs ago, and 2.35 myrs ago. The red, dashed line uses an albedo of 0.6, the blue,
solid line an albedo of 0.3, and the green, dotted line an albedo of 0.1
4.5 Conclusions
After performing thermal modeling to study surface temperature variations on Pluto as
a function of latitude and albedo we see stark contrasts in the surface temperatures of high
albedo regions (like Sputnik Planitia) and low albedo regions (like Cthulhu Regio) near the
equator. Once seeded, a bright region at the equator will become the coldest cold trap on
Pluto's surface, making it a likely location for further bright, fresh volatile deposition. In
contrast, once an equatorial region begins to darken, its lower albedo will help it stay warm,
94
90
60 1-
301-
-o
a)
-o
4-'
-J
01
-30
1UI
4a
4*
-60 1-
-90L
0 1 2 6 7 8
making it an unlikely place for long term volatile deposits to form. We see that even with
Pluto's varying orbit, the bright, volatile rich Tombaugh Regio should be able to survive on
million-year timescales. This also appears to be a unique characteristic of Pluto's equatorial
region, and we don't expect such stark albedo variations would be able to survive in the
polar regions. We will explore this effect and its latitudinal constraints in more detail in
Chapter 5.
The New Horizons observations are allowing for the development of better albedo maps
of Pluto. As these maps become available we will be able to take a more detailed look at
the local surface temperature variations across Pluto's surface. The first look presented here
already points to some interesting results, including the survival of Tombaugh Regio over
million-year timescales.
95
96
5Albedo Matters: Understanding
Runaway Albedo Variations on Pluto
5.1 Introduction
Most of the work in this chapter was originally published in Earle et al. (2018).
The images sent back from New Horizons show in high resolution the stark latitudinal
and longitudinal albedo and surface volatile variations originally discovered from decades
of Earth-based mapping efforts (e.g. Buie and Tholen, 1989; Buie et al., 2010; Young and
Binzel, 1993; Grundy et al., 2013). While the latitudinal variations could be explained by
prior volatile transport models (e.g. Hansen and Paige, 1996; Young, 2013; Spencer et al.,
1997), these models do not address the dramatic longitudinal contrasts observed. It has been
shown that on Saturn's moon Iapetus, albedo differences are capable of triggering runaway
global migration of water ice which would explain the moon's extreme albedo dichotomy
(Spencer and Denk, 2010). It has been suggested that Pluto's surface may also be sensitive
to "runaway" albedo variations which create and maintain its longitudinal contrasts (Earle
et al., 2015, 2017b; Hamilton et al., 2016). We use the term "runaway" as a moniker for
"strong feedback loop", remaining consistent with how it is used in Spencer and Denk (2010);
97
Earle et al. (2017b); and Hamilton et al. (2016). Here we perform a detailed study of this
effect over both the current epoch and past "Super Season" epochs to explore its effectiveness,
latitudinal dependence, and sensitivity to Pluto's orbital variations.
As discussed in chapters 3 and 4, Pluto's varying high obliquity and regressing longitude
of perihelion combine to create to create epochs of "Super Seasons" on Pluto, where one
pole is oriented most directly at the Sun at perihelion and thereby experiences a short,
intense summer and subsequent long duration, dark "arctic" winter. Figure 5.1 shows the
diurnal insolation for select latitudes over the last Pluto orbital year (top) compared to the
diurnal insolation for those latitudes during an orbital year occurring at the last two "Super
Season" epochs (middle and bottom). These calculations are based on the equations for
Pluto's orbit presented in Dobrovolskis et al. (1997), which represent Pluto's orbit well for
timescales of 10 million years. Since we are focused on timescales of less than 10 million
years and looking for general trends instead of strictly quantifying volatile distributions, this
accuracy is sufficient for our work. Obliquity is an important driver in the orbitally averaged
annual insolation for each latitude, as shown in Figure 5.2. Thus as Pluto's obliquity varies
we would expect Pluto's volatile transport to also change. It has already been suggested
that conditions on Pluto during these "Super Season" epochs could vary substantially from
Pluto's current environment (e.g. Stern et al., 2017; Earle et al., 2017b; Binzel et al., 2017,
also see Chapters 3 and 4), however most of the previous volatile transport models only
consider short timescales during the current epoch, keeping Pluto's obliquity fixed to explore
its effectiveness as a function of latitude.
Here we present a simple volatile sublimation and deposition model as a first step towards
exploring the long-term relationship between albedo, latitude, and volatile sublimation and
deposition when Milankovitch-like obliquity cycles are included. In considering all of these
effects, we particularly focus on obtaining a quantitative understanding of possible runaway
albedo and volatile distribution variations on Pluto's surface. We look at these relationships
not only during Pluto's current epoch, but also over several of Pluto's past "Super Season"
98
1600
1400
1200
1000
800
600
400
200
0
1600
1400
1200
1000
800
600
400
200
0
1600
1400
1200
1000
800
600
400
200
Obliquity = 119 deg
-
%
1800 1850 1900 1950 2000
Year
- Obliquity =103 deg 
-
" - - - - - - "" - - - - -- .
0 50 100 150 200
T-0.9 Myrs (years)
Obliquity = 126 deg
--
-0
d- 
-
-
0 50 100 150 200
T-2.35 Myrs (years)
Figure 5.1: Diurnally averaged insolation over 1 Pluto orbit for select latitudes. Top:
orbit. Middle: 0.9 Myrs ago. Bottom: 2.35 Myrs ago.
epochs. We purposefully chose a simple model to allow for quick computations and to
minimize the number of assumptions that have to be made about parameters, such as thermal
inertia; parameters that are still not well known for Pluto's surface. Given the simplicity
of the model, our results are focussed on the qualitative relationships and do not make any
effort to predict specific quantities of transport.
We use separate models to look at the behavior of Nitrogen and Methane, two of the
most abundant volatiles on Pluto (Cruikshank et al., 1976; Cruikshank and Silvaggio, 1980;
Clark et al., 1986; Owen et al., 1993; Grundy et al., 2016). Pluto's surface ice probably con-
99
0
0
M
.2
- 900
- 600
--- 30
-
0
- - 30
- - -600
- - 90
current
90
60
Obliquity
30 - -
1570
1350CU-0-
M ~ - 1260
- 1200
-30- 103
- 90
-60-
-90
0 50 100 150 200 250 300
Annual Average (ergs/cm 2 S)
Figure 5.2: Annually averaged insolation (over one Pluto orbit) as a function of latitude for
various obliquity values. For reference, we also show obliquity values for some additional
cases (0', 900, 157 , and 1350), which are not reached during Pluto's current obliquity cycle.
sists mostly of methane and nitrogen in solid state solution, with vapor pressures different
from those of the individual ices (Trafton, 2015). Again, to avoid assumptions and keep the
computations efficient, we chose to use separate models for each species for this initial eval-
uation. We consider albedo variations as a possible mechanism for creating and maintaining
the stark longitudinal albedo and volatile distribution contrasts seen around Pluto's equator.
For completeness, we explore quantitatively runaway albedo and volatile distributions at all
latitudes. To assess the process of albedo feedback, this model assigns albedos to different
regions on Pluto to see how volatile sublimation and deposition will respond to albedo vari-
ations, for example darkening from photochemistry (Cruikshank et al., 2016; Wong et al.,
2017) or brightening from fresh deposits in an impact basin like Sputnik Planitia (Schenk
100
et al., 2015; Moore et al., 2016). We explore how long such albedo features would be able
to survive given Pluto's orbital variations and "Super Seasons" and how sensitive different
latitudes on Pluto are to runaway albedo and volatile distribution variations.
5.2 Methods
5.2.1 Basic Model
To start we created a simple sublimation and deposition model based on the work done for
Triton in Spencer (1990). The model assumes all surface ice is in thermal equilibrium. Since
we are focussed on patterns over long timescales, we use diurnally averaged insolation so
the volatile equilibrium temperature varies with seasons, not over the diurnal cycle. Young
(2012) explore the implications of this assumption in detail and found that atmospheric
buffering dominates over diurnal timescales and restricts nitrogen temperature and surface
pressure variations to less than 0.2% over a Pluto day. We purposefully chose a simple
sublimation and deposition model, to allow us to focus on the role albedo plays in volatile
transport over long timescales, while limiting the number of assumptions that must be made
about parameters that are still not well known for Pluto, such as thermal inertia. The
lack of thermal inertia and diurnally averaged insolation mean we are essentially assuming
infinite thermal inertia or effective atmospheric buffering over diurnal timescales and zero
thermal inertia over seasonal timescales. The implications of not including thermal inertia
are discussed in subsection 5.4.3. The model is initiated with an even ice distribution, and is
run for approximately 10,000 years (40 Pluto orbits) to give the volatiles a chance to reach
a steady state for the epoch in question. For the simplest version of the model, the variables
considered are the initial ice mass per area, the albedo of the ice, the albedo of the substrate,
and the emissivity of the ice and substrate.
101
Global volatile temperatures are calculated by balancing insolation and thermal radiation
averaged over the exposed volatiles. By rearranging equation 1 of Spencer (1990) to solve
for the volatile temperature (T,) we get:
T ( f (1 - A)S(O)F(O)da 1/4 (5.1)
Ea f F(O)da
where E is the emissivity, a the Stefan-Boltzmann constant, F describes the ice coverage as
a function of latitude 6, S is diurnally averaged insolation, A bolometric albedo and f da is
integration with respect to the surface area of the object. From here we can calculate the
net mass sublimation rate as a function of latitude (rm(6)) using:
.(0) = ((1 - A)S(O) - EaT(5.2)
L
where is L is the latent heat of sublimation from Brown and Ziegler (1980). If the ice
mass load at a given latitude drops to zero, that region is considered to be "ice free" (with
F(O) = 0) and the local temperature is calculated by balancing the local diurnally-averaged
insolation and radiation:
T 0O = (1 - Asub)S(0) 1/4
E01
where A,,b is the albedo of the substrate. If the local temperature drops below the global ice
temperature in a given area, then ice will start condensing on that area again. All the trials
shown here use a substrate emissivity of 1.0 and an ice emissivity of 0.9 unless otherwise
stated (Stansberry et al., 1996; Stansberry and Yelle, 1999).
5.2.2 Nitrogen Model
The focus of this paper is to study how albedo will affect volatile transport over time. In
order to do this we set up a simple test case where Pluto's surface is divided longitudinally
into three sections (each 120 degrees wide in longitude and stretching from pole to pole).
Each section is assigned a different ice albedo value (0.1, 0.3, or 0.6), and the substrate is
102
assumed to be dark (albedo = 0.1). The trials start with nitrogen distributed evenly across
Pluto's surface. As the model runs the nitrogen is able to redistribute between sections.
Within each of the sections the nitrogen ice keeps the same albedo throughout the run. We
assume the nitrogen ice is essentially clear (Duxbury et al., 1997) and that its albedo is
being driven by external circumstances, while for the variable ice albedo model described in
the next section we allow the albedo of each section to change over time. We acknowledge
that there are circumstances that could potentially lead to the clear nitrogen ice driving the
surface albedo, for example solar gardening or scattering at ce - /N 2 transition fronts could
lead to a bright albedo while precipitating dust and haze or cosmic rays altering impurities
in the ice could darken the Nitrogen (Duxbury et al., 1997; Grundy and Stansberry, 2000).
However, we chose not try to address these complex processes with this simple model.
5.2.3 Variable Ice Albedo Model
The variable ice albedo model builds on the nitrogen model described above with a few
modifications. For example, we use the latent heat of sublimation of methane (instead of
nitrogen) (based on Brown and Ziegler, 1980). The model is initiated, as described above,
with three different albedo sections and an even ice distribution. However, unlike the nitrogen
model, the methane albedo is allowed to vary as ice sublimates and deposits.
Based on the rate of hydrocarbon deposition from Wong et al. (2017) and assuming it
takes roughly 0.005 g/cm 2 of irradiated hydrocarbons to darken the surface (Stern et al.,
1988), we assume that Pluto's surface darkens by about 3.2 x 10-5 per year. Once the
albedo in the model falls to 0.5, we assume no further darkening. If fresh ice is deposited on
a dark layer, the model tracks the mass load of the fresh layer and should that fresh layer be
depleted by sublimation, the albedo in that area will drop back down to that of the exposed,
underlying dark layer.
103
As fresh ice is deposited the albedo increases by 0.5 for the first 0.5 g/cm 2 of methane
deposited, and then by 0.1 per each additional g/cm 2 after that, until a maximum albedo of
0.85 is reached. These are rough estimates of how albedo varies with ice age and mass load,
further laboratory measurements of the reflectance of methane ice and production of tholins
could improve this model.
5.3 Results
5.3.1 Nitrogen Model Results
The nitrogen model was run with Pluto divided longitudinally into thirds with a different
albedo assigned to each third (as described in subsection 5.2.2). Various emissivities (between
0.6 and 0.9) and initial ice mass loads (between 10 g/cm 2 and 1, 000 g/cm 2) were tested and
the results of a typical trial are shown in Figures 5.3 and 5.4, where the initial ice mass load
was 10 g/cm2 and the ice overlaid a dark, 0.1 albedo, substrate. Figure 5.3 shows how the
ice mass load changed over the final Pluto year for each albedo section over each of the three
epochs of interest, while Figure 5.4 shows snapshots of Pluto's Nitrogen distribution at four
different times over the last orbit leading up to the New Horizons close approach in July
2015. For cases like this one, where the nitrogen layer is thin enough for the substrate to be
exposed in areas experiencing significant sublimation, we find a number of trends dependent
on albedo and epoch. The poles experience orbit seasonal polar caps extending as far as
300 in each hemisphere more or less regardless of ice albedo and epoch. The results at the
mid and equatorial latitudes are far more dependent on the ice albedo and epoch. If the
equatorial latitudes are dark (0.1 albedo) or moderate (0.3 albedo) they quickly lose their
volatiles during all three epochs. However, if these same areas are bright (0.6 albedo) they
become a cold trap, and gain nitrogen.
The extent and depth of nitrogen accumulation is variable based on the epoch (obliquity
and longitude of perihelion). During the current epoch (top row in Figure 5.3), over the
10,000 year trial a nitrogen layer reaching mass loads over 40 g/cm2 in some places, builds
104
Alb = 0.1
Emissivity = 0.9 and Initial Mass/Area = 10.0g/cm2
nn Alb = 0.3 an Alb = 0.6
0 0 0__ 
_
-30 -30 .- 30
-60 e---60 
- 42.
-090 900
1800 1850 1900 1950 2000 1800 1850 1900 1950 2000 1800 1850 1900 1950 2000
'tar arer
600
-60 60-
-30- Q80 --30 -) 0uu
-60 - -60-
5 10 1 200 -90 90
5 0 5 20 0 50 100 150 200 0 50 100 150 200
Time (years) Time (years) Time (ears)
50 100 150
Time (years)
200
0.800
50 100 150
Time (years)
200
28.000
36.00
~ ____20.000
- 236.00
50 100 150 200
Time (years)
Figure 5.3: Nitrogen mass load as a function of latitude over the last Pluto year of a 40 Pluto
year (~ 10, 000 Earth year) trial for three different epochs in Pluto's orbital evolution, each
started with an even, lOg/cm 2 distribution of nitrogen. Each row is a different epoch, and the
three columns represent each of the thirds the surface has been divided into longitudinally,
with a different ice albedo assigned to each. The polar latitudes generally show seasonal ice
deposits, regardless of albedo. While the mid and equatorial latitudes are strongly albedo
dependent, with the bright (0.6 albedo) region building up a large equatorial deposit while the
dark (0.1 albedo) and intermediate (0.3 albedo) regions lose all of their equatorial nitrogen.
up between 45'N and 45*S. For the 0.9Myrs ago epoch (middle row in Figure 5.3), where
Pluto's obliquity is around 103' and the North Pole experiences short, intense summers and
long, dark winters, the band of equatorial deposition is much narrower and thicker. At
the equator more than 70 g/cm 2 of nitrogen accumulate, but the deposition site is much
narrower, only extending between roughly 30'N and 30'S. 2.35 Myrs ago, Pluto's obliquity
was around 126' and its South pole pointed towards the Sun at aphelion. Over this epoch
105
90
0'
0
0'
@1
~0
a'
0
m
-I
0 .2
05 4
.0 -10
60
30
0
-30
-60
-90 0
90
60
30
0
-30
-60
-90
0'
Z
0
,a
U
(U
'0 0.800
n. oo -
, - u - 4
f{ Ia 60
30
0
-30
-60
go
70
60
50
z
40
CT
20
10
initial
mass/area
0
%a
1829 1891 1953 2015
30
27
24
21
15 27
12
9 L
61
3_
0
Figure 5.4: Nitrogen mass load for the three different albedo regions, shown at 4 different
times in the past Pluto year, including 2015 (right) when NASA's New Horizons spacecraft
flew through the Pluto system.
(bottom row in Figure 5.3), nitrogen is broadly distributed over the entire high albedo
region, with the thickest (45 g/cm2 ) deposits falling around 45'N and 45'S. The polar
regions maintain ice year-round but the mass load varies seasonally. The equator maintains
a thin layer of ice with very little seasonal variation.
Figure 5.4 shows an alternative visualization of the results presented in Figure 5.3. Here,
the nitrogen mass load for each albedo is shown at four different quarters of a Pluto year up
to and including 2015, when the New Horizons spacecraft made its close approach through
the Pluto system. The polar cap is fairly uniform across all three albedo regions and shifts
seasonally from the South to the North pole. At the time of the New Horizons encounter, the
Northern hemisphere was entering into summer. According to the model, the north polar
cap was in the process of migrating south, with darker, northern areas potentially already
being depleted of volatiles, while brighter areas may still maintain some deposits. The model
also predicts darker, equatorial regions will be completely nitrogen depleted, while a bright,
equatorial region would have the potential to trap a majority of the surface nitrogen. This
representation also makes it easier to see the migration within the bright, equatorial trap,
where some nitrogen is exchanged seasonally between 30'N and 30'S.
106
Emissivity = 0.9 and Initial Mass/Area = 10.Og/cm 2
Alb = 0.1 Alb = 0.3 90
60
30
0
-30
C"
0
LO)
0
0m
C4
-4
27
0
'a
-P
a,
S,
\
-0-0
16.oo 016,00o -
50 100 150 200
Time (years)
60
30
0
-30
-60
8.000
50 100 150 200
Time (years)
Alb = 0.6
1800 1850 1900 1950 2000
Year
50 100 150 200
Time (years)
16.000
50 100 150 200
Time (years)
Figure 5.5: Methane mass load as a function of latitude over the last Pluto year of a 40 Pluto
year (~ 10, 000 Earth year) trial for three different epochs in Pluto's orbital evolution, each
started with an even, 10 g/cm 2 distribution of Methane. Each row is a different epoch, and
the three columns represent each of the thirds the surface has been divided into longitudinally,
with a different ice albedo assigned to each. Again, the polar latitudes show less albedo
sensitivity than the mid and equatorial latitudes. The asymmetric bands are dependent on
the starting conditions of the model, occurring in whichever hemisphere experiences winter
first when the model begins running (further demonstrating the persistence of bright deposits
near the equator).
5.3.2 Methane (variable albedo) Model Results
The results of the variable ice albedo model (Figure 5.5) are very sensitive to the rate
at which the albedo varies (which is not well known), and the point in the seasonal cycle at
which the model run begins. In particular the asymmetric banding is a function of which
hemisphere experiences winter first (i.e. starting the model half a Pluto year earlier or later
107
90
60
30
0
-30
90
-6 0-30
40
-0-90 1-90
1800 1850 1900 1950 2000 1800 1850 1900 1950 2000
90 Nar 90 90
60 60 o660
30 - 30 30
0 . 0
-- 30 30 -30
-60 -60 -6
-90 -0 50 100 150 200 0 50 100 150 200
90
60
30
130
90
60
30
0
-30
-60
-90
20
0
a.
10
initial
mass/area
0
016.000
i -jtj , - i -
Time Nvears) dirt Time Nvears)
-60
16.000 16.00o
will switch the banding to the other hemisphere). The width and mass load of the banding
is also strongly driven by the rate at which the albedo varies. These latitudes are so albedo
sensitive that a single season of sublimation and darkening or bright, fresh ice deposition
can trigger the albedo to runaway.
There are still a number of interesting trends displayed by this model. As with the
nitrogen model, the poles experience seasonal deposits, but here they show the possibility
of more permanent deposits building up in past epochs (see bottom row of Figure 5.5). The
bright region (0.6 starting albedo) shows very similar results to the nitrogen model but with
slightly broader latitudinal coverage (compare the last columns of Figures 5.3 and 5.5).
Unique to the variable ice albedo model, are the mid-latitude deposits in the dark (0.1
starting albedo) and intermediate (0.3 starting albedo) regions. While these bands are very
sensitive to the conditions of the model, their existence does show us that at mid-latitudes,
a bright ice deposit could trap enough methane to survive seasons of sublimation.
5.3.3 Low-obliquity Model Results
For comparison we ran several nitrogen models for some general cases not specific to
Pluto (with a starting ice mass load of 10 g/cm2 ) for the current Pluto epoch, but with
Pluto's obliquity changed (Figure 5.6). With an obliquity of 1570, comparable to Earth's
23.5' but retrograde, all of the nitrogen is quickly sublimated away from the equatorial
latitudes to form polar caps. Most of the nitrogen goes to the bright (0.6 albedo) polar
region, forming caps extending down to around 45'N and 45'S. The intermediate (0.3
albedo) region developed smaller, thinner, permanent polar caps and a small amount of
nitrogen is exchanged seasonally between the poles of the dark (0.1 albedo) region.
An obliquity of 135' was considered as an intermediate case (Figure 5.6, middle row).
Again, all of the nitrogen at the equator was quickly sublimated away. The dark (0.1 albedo)
and intermediate (0.3 albedo) regions both develop seasonal polar caps. The bright region
develops large polar caps extending to 20'N and 20'S, with seasonal variations in mass load.
108
Emissivity = 0.9 and Initial Mass/Area = lOg/cm 2
Alb = 0.1
0 - 0060
30
0
-- 30
-60
A-oA
1800 1850 1900 1950
Year
2000
00
40.
1800 1850 1900 1950 2000
*ar
0
1800 1850 1900 1950 2000
Yar
60
30
0
-30
-60
60
30
0
-30
-60
Alb = 0.390
60
30
0
-30
-.60
-90
1800 1850
too
1950 2000
0.8 
0 
-
1900 1950 2000
Nar
0.8 0,
..
4.001
1800 1850 1900 1950 2000
Year
1800 1850 1900 1950 2000
Yar
60
50.0(
30 -_________
0-
-30 JUUV10.000
-60 -
1800 1850 1900 1950 2000
Momr
90 
- . - 1 .0
90
60 2000
30 _5
0
25.000 25.01
-30
-60 3.0
-Qfl
1800 1850 1900 1950 2000
Year
Figure 5.6: Nitrogen mass load as a function of latitude over the last Pluto year of a 40
Pluto year (~ 10, 000 Earth year) trial each started with an even, lOg/cm 2 distribution of
nitrogen. Each row is a different obliquity (Pluto's current longitude of perihelion is used
for all three trials), and the three columns represent each of the thirds the surface has been
divided into longitudinally, with a different ice albedo assigned to each.
The final case, with an obliquity of 1260, is the limit of Pluto obliquity. The dark and
intermediate albedo regions develop seasonal polar caps very similar to the 1350 case. The
bright region develops deposits around 35'N and 35'S that vary in width over the seasonal
cycle, all the other latitudes in this region maintain a thinner, but consistent nitrogen layer.
109
0)
t:
0
1800 1850 1900
Nar
-QP k\N
90- Alb = 0.6
60 __
30
0
-30 --30 25,000
79ot
90do
in 0f 30
30
.2 0
00
fir% -3
-J
0
60
30
0
-30
-60
-90
- . - 'W",
100
90
80
70
z60
50 ET
30
40
30
20
10
0
nA
nn
-0 ? -O'
5.4 Discussion
The results of both the nitrogen model (section 5.3.1) and variable ice albedo model (sec-
tion 5.3.2) quantitatively show that Pluto's equatorial and mid-latitudes are more sensitive
to runaway volatile distribution and albedo variations than the polar latitudes.
For most parameters the poles experience seasonally exchanged volatile deposits. Since
most of the deposition occurs when the pole is in shadow, the albedo has very little effect on
the rate or quantity of deposition. It will however have a small effect on the speed at which
the deposit sublimates away, with brighter regions staying volatile covered slightly longer
once exposed to sunlight.
The mid and equatorial latitudes were far more sensitive to albedo variations and run-
away volatile distribution and albedo effects. Since Pluto has a high obliquity, its mid and
equatorial latitudes receive less annually averaged insolation than its poles (Figure 5.2),
these regions also don't receive prolonged (multi-year) periods of shadow and sunlight like
the poles do (Figure 5.1). This combination creates conditions where the albedo of the sur-
face drives whether volatiles are being deposited or sublimated from a given area, giving rise
to the strong feedback effects. Once an area near the equator becomes dark, it will become
too warm to maintain volatile deposits. Conversely, if an area becomes bright, it will become
a cold trap and rapidly attract further deposition.
Given the mid and equatorial latitudes sensitivity to albedo variations, once seeded, we
would expect longitudinal albedo contrasts to be able to survive at these latitudes over
multimillion year timescales. Broad features like the dark, volatile depleted Cthulhu Reggio
(informal name), and bright, volatile rich Tombaugh Reggio should be able to persist in
their current general state even over Pluto's super season cycles. Although there may be
some variation within these broad features over the obliquity cycle, for example, we would
expect to see some changes within Sputnik Planitia (the left side of Tombaugh Reggio,
believed to be a volatile filled impact basin) (Schenk et al., 2015; Moore et al., 2016) . As
Pluto's obliquity varies, the bright, equatorial latitude receiving the most volatile deposition
110
shifts. Over the current epoch we would expect deposition over the entire latitudinal range
of Sputnik Planitia. When Pluto's obliquity reaches 103', its closest to 90' (last experienced
0.9 Myrs ago), we would expect deposition to be most concentrated around the equatorial
part of Sputnik Planitia, and possibly some sublimation at its northern most extent. At
Pluto's other obliquity extreme (126 , last experienced 2.35 Myrs ago) we would expect
deposition at the higher latitudes of Sputnik Planitia (centered around 40 N) and little to
no sublimation and deposition near the equator.
5.4.1 Low Obliquity Trials
The latitudinal extent of the "runaway zone" is coupled strongly with obliquity. To fur-
ther explore this relationship we performed several trials with different obliquities (presented
in section 5.3.3). For Earth-like (157 ) and even moderate (135') obliquities, where the poles
receive less annually averaged insolation than the equator (Figure 5.2), the equatorial lati-
tudes will lose all of their volatiles, while the polar latitudes will be somewhat susceptible
to albedo variations, with the permanence and extent of the polar caps being albedo depen-
dent. For Pluto's most vertical obliquity, 1260 , the insolation minima are actually around
35 0N and 350S (Figure 5.2), and trials show this as a transitional case, where the poles
and equator are minimally effected by albedo while bands centered around 35'N and 35'S
experience mild runaway albedo and volatile distribution variations.
The most dramatic variations are seen in the T - 0.9 Myrs trials (e.g. Figure 5.3; middle
row). During this epoch, Pluto's obliquity was close to horizontal (1030) and it was expe-
riencing "Super Seasons". This means Pluto's equatorial region was not only receiving the
minimum annually averaged insolation (Figure 5.2), but it was also receiving a very con-
sistent amount of diurnal insolation while the polar latitudes experienced dramatic diurnal
insolation variations (Figure 5.1).
We propose this combination of minimum annually averaged insolation and minimal
difference in diurnal insolation over an orbit creates conditions for runaway albedo and
volatile distribution variations. Earle et al. (2017b) shows that instantaneous temperatures
111
at the equator are generally close (within 15K) to the global ice temperature, with the albedo
driving the local, instantaneous temperature above or below the global ice temperature,
which in turn supports runaway albedo variations. The poles' decades-long periods of shadow
and sunlight keep their instantaneous temperatures further from the global ice temperature
(with variations of more than 30K), with the albedo having very little effect of whether
the local temperature is above or below the global temperature (thus limiting the feedback
effects). Minimum annually averaged insolation keeps the area cold enough for volatiles to be
deposited, while steady, diurnal insolation keeps the instantaneous local temperature close
enough to the global average ice temperature that albedo plays an important role in whether
volatiles are being deposited or sublimated.
To better quantify this behavior, we calculate the relative difference between the maxi-
mum nitrogen mass load reached over the last Pluto year in the bright (0.6) and dark (0.1)
albedo regions (Figure 5.7). Values close to zero indicate little to no albedo sensitivity, while
value close to one indicate runaway albedo variations. From this analysis we see that for
low obliquity planets, the extent of the polar caps is albedo dependent, but the equatorial
region is not sensitive to albedo differences (since it experiences the highest average annual
insolation and does not have prolonged periods of sunlight and shadow, the volatiles will
migrate away from the equator regardless of albedo). However for higher obliquity planets,
like Pluto, the equator is the most albedo sensitive region and the poles show less albedo
sensitivity.
Pluto's range of obliquities makes its equatorial latitudes sensitive to runaway albedo
and volatile distribution variations and able to (once seeded) maintain longitudinal albedo
contrasts over long (multi-millions year) timescales. Because of their prolonged (decade,
and even century timescale) exposure to darkness and sunlight, Pluto's poles are far less
sensitive to feedback effects, experience mostly seasonal volatile deposits, and are unlikely
to be able to harbor longitudinal albedo variations over long (multi-orbit) timescales. The
mid-latitudes are generally sensitive to runaway variations, although their sensitivity varies
112
90
601
30
GJ
-o
0
.301
-60
-901
0.0 0.2 0.4 0.6 0.8 1.0
Albedo Sensitivity
Figure 5.7: Albedo sensitivity based on the relative difference between the maximum nitrogen
mass load reached over the last Pluto year in the bright (0.6) and dark (0.1) albedo regions
for various obliquities. Pluto's actual obliquity varies between 1030 and 126' (and is currently
around 1200), and additional obliquity values are shown for comparison.
strongly with the obliquity (particularly for the variable ice albedo model, where ice albedo
varied with freshness and mass load, these latitudes were very sensitive to not only the
obliquity but also the starting season of the model). Thus it is difficult to determine the
expected end result for these latitudes from this simple model.
5.4.2 Comparison with Observations
Based on the model we would expect to see some lingering volatiles near the North
pole at the time of the New Horizons' close-approach to Pluto. At equatorial latitudes,
we would expect the volatile distribution to be strongly correlated with the albedo. As
113
. -.
Obliquity
-
0
1570
1350
126
- 1200
1030
900
previously mentioned (section 5.4.1), the limitations of the model make it difficult to predict
the outcome for the mid-latitudes, but most likely, they would be volatile covered, with
some correlation between albedo and volatile deposition (but not as strongly correlated
at the equator). Furthermore, the results of the model suggest that longitudinal albedo
and volatile deposit variations can survive over long (multi-million year) timescales at the
equator, but the poles should not be able to support such extreme, longitudinal variations
and should be more uniform.
Comparison of composition maps from Protopapa et al. (2017); Schmitt et al. (2017);
Earle et al. (submitted) and Chapter 2 with the preliminary Bond albedo map presented in
Buratti et al. (2017) (see their Figure 5) show Pluto's equator is mostly dark and devoid
of volatiles with the major exception being Tombaugh Regio, the bright region near the
anti-Charon that is volatile rich, showing signs of containing nitrogen, methane, and carbon
monoxide. The region from 30'S to 30'N shows the greatest diversity of both albedos
and volatile abundances and Earle et al. (submitted) shows there is a strong correlation
between methane abundance and albedo throughout this region, as we would expect from
our model. From 30'N towards the pole the albedo and volatile distribution become more
homogeneous, with some latitudinal variations but very little longitudinal contrast, which
again is consistent with what we would expect from the model. Schmitt et al. (2017) found
nitrogen rich ice occurs mostly in 30' -60'N (and less uniformly in the 60' - 70'N range) but
above these latitudes only methane rich ice exists. Based on our model, during the current
epoch we would expect most nitrogen to be drawn to high albedo areas between 60'S and
60'N latitude, while methane would be more evenly distributed between equatorial latitudes
and the seasonally exchanged polar caps.
It is worth noting that this model focuses specifically on albedo and volatile distribution
and does not account for topography and geology which can also be contributing factors.
Geology can effect the change in albedo of a particular region, for example, possible solid
state convection in Sputnik Planitia could be burying haze particles, preventing them from
114
accumulating and darkening the surface of Sputnik Planitia the way they do in other ar-
eas (McKinnon et al., 2016; Grundy et al., submitted). Topography will also play a roll
in volatile transport, and it has been suggested that over time areas with low elevations
should slowly fill with volatiles (Trafton and Stansberry, 2015; Bertrand and Forget, 2016).
Counter examples can also be found across Pluto's surface indicating other effects, such as
insolation discrepancies, albedo variations, and local slopes, may take precedence on some
timescales (Lewis et al., 2017). A more comprehensive study of the relationship between
surface topography and volatile distribution could serve to better calibrate the effectiveness
of runaway albedo variations versus topographic effects for more detailed future modeling.
5.4.3 Consideration of Thermal Inertia
As previously mentioned, this model does not account for thermal inertia, and thus does
not try to make quantitative assertions about Pluto's volatile transport, but rather explore
how Pluto's unique orbit and orbital evolution may create regions sensitive to runaway albedo
variations, and thus the stark, longitudinal albedo contrast observed on Pluto.
The volatile transport parameter searches conducted by Hansen and Paige (1996), Young
(2013), and Hansen et al. (2014) found that increased thermal inertia will generally keep the
temperatures closer to the annual average, increase heating and cooling times (and thus lead
to slower deposition and sublimation of polar caps) and could lead to zonal banding (which
was also sensitive to other model parameters). The thermal inertia of Pluto's surface is
currently not well constrained, particularly over seasonal timescales, and while it is important
for detailed volatile transport study, based on past results its absence in this model should
not effect the general and strictly qualitative conclusions we are drawing from the model.
The values of thermal inertia that have been calculated from observations are between 20 -
30Jm-2 s1 /2K 1 , which is lower than would be expected for compact ice, and are discussed
in detail in Lellouch et al. (2000, 2011, 2016).
115
5.5 Conclusions
Pluto's high obliquity creates a unique set of conditions that make its equator and mid-
latitudes highly sensitive to runaway albedo and volatile distribution variations. Quantita-
tively we find the combination of minimal annually averaged diurnal insolation and minimal
difference in diurnal insolation over an orbit makes these latitudes capable of maintaining
stark, longitudinal albedo and volatile abundance variations (like those observed by New
Horizons) over long timescales. Large-scale longitudinal contrasts like the dark, volatile-
depleted, Cthulhu Regio (informal name), and bright, volatile-rich Tombaugh Regio, should
be able to co-exist at the same latitudes even over Pluto's "Super Season" cycles (which
occur roughly every 1.5Myrs). However, we do not expect Pluto's polar latitudes to be able
to support these kinds of longitudinal albedo and volatile abundance variations because of
their prolonged (decades) periods of continuous sunlight and darkness.
These results help us to better understand the longitudinal contrasts observed by New
Horizons and Hubble (Stern et al., 2015; Buie and Tholen, 1989; Buie et al., 2010; Grundy
and Buie, 2001; Grundy et al., 2013) as well as draw attention to the need for more careful
consideration of how ice albedo and its variation is considered in future volatile transport
models. Further radiative transfer simulations and lab studies of the reflectance of nitrogen
and methane ice, and how it varies with mass load and freshness will also aid in this effort.
116
6Pluto: Context and Conclusions
6.1 Context for Pluto Results
The work presented in this thesis is just a subset of the roughly 60 papers published about
Pluto and its satellites in the first 2 years since the New Horizons spacecraft flew through
the Pluto system. The wealth of new data provided by NASA's New Horizons mission has
lead to rapid advancement in the study of the Pluto system. In this section we provide some
context for the thesis work presented here relative to the full range of work being done on
the Pluto system in recent years.
Earle and Binzel (2015) was written and published before New Horizons reached the
Pluto system. The primary purpose of this paper was to serve as a resource during encounter.
This paper calculated Pluto's insolation history over varying timescales leading up to the
encounter and was used to interpret data as it was returned from the spacecraft and helped
guide preliminary science results. The work done for this paper also became the inspiration
and foundation for many of the post-encounter models including Earle et al. (2017b), Earle
et al. (2018), Binzel et al. (2017), Stern et al. (2017), and Bertrand et al. (2018).
117
The temperature modeling presented in Earle et al. (2017b) (Chapter 4) was the first
post-encounter paper to address volatile transport. It was published as part of the Icarus
Special Issue about the Pluto System, as were Binzel et al. (2017) (Climate Zones) and
Stern et al. (2017) (past epochs of higher atmospheric pressure). Since then additional time
and more detailed analysis and processing of the New Horizons data has allowed for more
detailed modeling of Pluto's volatile transport, like the model used to study albedo feedback
in Earle et al. (2018) (Chapter 5) and the global circulation modeling presented in Bertrand
and Forget (2016), Forget et al. (2017), and Bertrand et al. (2018).
Of the global circulation modeling papers, Bertrand et al. (2018) is the only one to con-
sider timescales over which Pluto's obliquity variations become relevant, thus making it the
most relevant to the work presented here. Bertrand's paper presents numerical simulations
of volatile transport on Pluto with a model designed to simulate the nitrogen cycle over
million year timescales, assuming all nitrogen ice has an albedo of 0.7 (and not including
methane or carbon monoxide in the model) and taking into account the changes in obliquity,
sub-solar longitude at perihelion, and eccentricity. During high-obliquity periods which in-
duce intense polar summers they find intense sublimation rates in the northern part of the
ice sheet in Sputnik Planitia, where as low-obliquity periods favor sublimation in the center
of Sputnik Planitia and condensation at the north and south extremities. In some of their
trials perennial nitrogen deposits formed at the mid-latitudes (but not the equator, which
remained volatile free).
The results of Bertrand et al. (2018) are in general agreement with what we would expect
based on the modeling presented in Earle et al. (2018) (Chapter 5). Based on Figure 5.3
we would expect Sputnik Planitia (since it is a high albedo area) to experience deposition
near the equator and sublimation from its northern and southern extrema 0.9 million years
ago, the last time Pluto's obliquity was nearly perpendicular. Where as 2.35 million years
ago, when the obliquity was low, we would expect more deposition at the northern and
southern limits of Sputnik Planitia, similar to the findings of Bertrand et al. (2018). Based
118
on our variable albedo model shown in Figure 5.5 (which uses methane instead of nitrogen),
we expect perennial volatile bands at midlatitudes will form if the presence of volatiles in
those areas increases the albedo (where as polar deposits will remain seasonal regardless of
albedo). Bertrand et al. (2018) found similar bands in some of their trials, and also suggested
that (while not considered in their model) albedo and presence of methane may drive the
existence and survival of mid-latitude nitrogen deposits outside Sputnik Planitia. Both Earle
et al. (2017b) and Bertrand et al. (2018) agree that further detailed modeling is needed to
fully understand how surface ices evolve on Pluto.
While it is the first result presented in this thesis and was started during the 2015
encounter, Earle et al. (submitted) (Chapter 2) is actually the most recent of the papers to
be published due to the time it took for all of the New Horizons' MVIC images of Pluto to be
sent back from the spacecraft and properly calibrated. Preliminary results of the MVIC E.W.
maps were presented in Grundy et al. (2016) and Moore et al. (2018). Interpretation of the
maps presented in Earle et al. (submitted) has been aided by results from the New Horizons
LEISA instrument presented in Grundy et al. (2016); Schmitt et al. (2017) and Protopapa
et al. (2017). The low spectral resolution of MVIC and lack of available laboratory data
in the low temperature regime at Pluto makes it difficult to make direct conclusions about
abundance, purity, or grain size based on the MVIC data alone. However, comparison with
LEISA data (which has lower spatial resolution but higher spectral resolution and covers
a different wavelength range) makes it possible to infer these properties and then leverage
MVIC's higher spatial resolution and more complete spatial coverage. Moore et al. (2018)
has already used the MVIC E.W. global map to suggest the possibility of additional bladed
terrain on the non-encounter hemisphere, showing that further detailed analysis of these
maps could aid in understanding the relationship between geology and composition and
interpreting the lower-resolution data from the non-encounter hemisphere of Pluto.
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6.2 Summary of Pluto Conclusions
Pluto's equatorial latitudes show a broader diversity of colors and
methane distribution than its polar latitudes
The maps presented in Chapter 2 (originally published in Earle et al. (submitted)) show
in a new light a broad diversity of terrains across Pluto's surface using MVIC E.W. and
spectral slope. We confirm other studies of Pluto's surface from New Horizons (e.g. Grundy
et al., 2016; Protopapa et al., 2017; Schmitt et al., 2017) as well as pre-encounter studies
performed by Hubble (e.g. Grundy and Buie, 2001; Buie et al., 2010; Grundy et al., 2013) and
maps created from Mutual Events data (Young and Binzel, 1993). The MVIC data used to
produce the maps in Chapter 2 provides the highest spatial resolution for compositional maps
yet achieved and better coverage than the LEISA instrument used for the other New Horizons
surface composition studies. From this more complete coverage we are able to determine
that the most extreme terrains on Pluto (reddest spectral slope, broadest MVIC E.W., etc.),
all occur exclusively along the equator in the latitude band between 30'S and 300 N. This
region contains the most volatile depleted (and tholin rich) terrains, as well some of the
purest methane deposits and areas with a mix of methane, nitrogen, and carbon-monoxide
ices. Buratti et al. (2017) also shows this latitude range containing both the upper and lower
limit of albedo values found on Pluto's surface, further attesting to the uniqueness of this
region. These physical data help guide and constrain the modeling efforts.
Pluto's orbital variations create substantial changes in Pluto's sea-
sonal cycles, including creating epochs of "Super Seasons"
Pluto undergoes obliquity variations and longitude of perihelion regression on cycles of 3
million and 3.7 million years, respectively (Dobrovolskis et al., 1997). These cycles, coupled
with Pluto's high eccentricity (e ~ 0.25), create substantial differences in the insolation
patterns experienced on Pluto, as seen in Chapter 3. One consequence of these cycles are
120
epochs of "Super Seasons" on Pluto, where one pole receives a short, intense summer followed
by a prolong period of continuous darkness, while the other pole received a short period of
winter darkness and longer but less intense summer.
Pluto's "Super Seasons" epochs have the potential to strongly impact its volatile distri-
bution and surface evolution. Analysis performed for this thesis (Chapter 3) and presented
within Stern et al. (2017) suggests these epochs may even be able to trigger periods of sub-
stantially higher atmospheric pressure on Pluto and possibly even support liquid nitrogen
on Pluto's surface, which would explain a handful of unusual surface features (examples of
which can be seen in Figure 3.7). Bertrand et al. (2018) performs more detailed atmospheric
pressure modeling which finds surface pressures above 100 Pa are unlikely to occur and
suggests that the surface features are instead the result of past liquid flow at the base of
massive nitrogen glaciers. Despite arguing against the higher pressures suggested by Stern
et al. (2017), Bertrand et al. (2018) still supports the significance of Pluto's orbital varia-
tions as a driver of Pluto's surface evolution and volatile transport. Further consequences
of these orbital variations are explored in detail in Chapters 4 and 5, with their conclusions
summarized below.
Pluto's high obliquity supports strong feedback loops creating stark
albedo contrasts
The surface temperature modeling performed in Chapter 4 (originally published in Earle
et al. (2017b)) provided an early indication that Pluto's equatorial and mid-latitudes were
more sensitive to albedo variations than polar latitudes. At equatorial latitudes the surface
temperature is strongly driven by the albedo of the surface, regardless of the global average
temperature. In comparison, polar latitudes will dip well below the global average in winter
and reach well above it in summer regardless of their albedo (particularly during "Super
Season" epochs).
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A simple volatile sublimation and deposition model is used in Chapter 5 (originally
published in Earle et al. (2018)) to study how Pluto's surface volatiles respond to albedo
differences, exploring these processes in greater detail over the current epoch as well as past
"Super Season" epochs. We find Pluto's high obliquity creates unique conditions that make
its equator and mid-latitudes highly sensitive to albedo feedback effects, resulting in them
being able to maintain stark, longitudinal albedo and volatile abundance variations over long
timescales. We do not expect Pluto's polar latitudes to be able to support these kinds of
longitudinal albedo and volatile abundance variations because of their prolonged (decades)
periods of continuous sunlight and darkness. We conclude that Pluto's poles experience
seasonal volatile deposits, the extent of which is driven more by seasonal epoch than albedo.
Albedo is an important driver in Pluto's volatile distribution and
surface evolution
The modeling performed in Chapters 4 and 5 shows that Pluto's high obliquity makes
its equatorial latitudes susceptible to feedback loops which create stark albedo and volatile
contrasts (as detailed above). Therefore we would expect Pluto's surface to show a great
deal of diversity near the equator and be more homogeneous towards the poles. Chapter 2
analyzes data from New Horizons, and concludes the region between 30'S and 30'N shows
the broadest diversity of colors and surface compositions, while Pluto's more northern lat-
itudes are more homogeneous and do not encompass the same extremes. The agreement
between the modeling and observations suggests that albedo is in fact an important driver
of Pluto's surface volatile distribution. Particularly since pre-encounter volatile transport
models, which used a more simplified treatment of albedo, could not explain these longitudi-
nal contrasts (e.g. Hansen and Paige, 1996; Young, 2013; Spencer et al., 1997). This suggests
that future volatile transport modeling should use a more careful treatment of albedo and
would benefit from further radiative transfer and lab studies of the reflectance of nitrogen
and methane (and how it varies with mass load and freshness) to more accurately model
how the albedo of volatile ice will vary.
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6.3 Pluto Future Work
The next steps for building upon the results presented here for Pluto would be a detailed,
quantitative study of the methane maps presented in Earle et al. (submitted) (Chapter 2),
followed by a detailed volatile transport study. These are outlined, in turn below.
A visual study of the methane abundance and spectral slope maps presented in Earle
et al. (submitted) (Chapter 2) reveals a complex relationship between geologic features, such
as craters, fossae, and mountain tops, that appear to be latitudinally dependent. However,
further work is needed to quantify these relationships. The maps could be used to quantify
the methane abundance and spectral slope of each crater's floor, walls, and rim which could
then be catalogued and studied as a function of latitude as well as geologic region. The
deposits and colors around fossae and mountain tops could also be explored as a function
of elevation, latitude, and insolation angle during the time of the New Horizons encounter.
Quantifying these relationships would improve our understanding of the surface evolution of
Pluto (and other volatile-rich objects), and also provide useful input for volatile transport
models and constraining the timescales over which surface processes occur on Pluto.
A volatile transport study could build upon the work presented in Earle et al. (2018)
(Chapter 5), using the constraints determined from the quantitative study of the MVIC
maps. Since Earle et al. (2018) was a preliminary study of Pluto's sensitivity to albedo
variations over the current epoch as well as past "Super Season" epochs, the model used is
a simple sublimation/deposition model that does not account for factors that are still not
well constrained for Pluto, such as thermal inertia. Volatile transport models done before
New Horizons' encounter of the Pluto system account for thermal inertia but don't take
into consideration Pluto's topography and often used a very simple treatment of albedo
variations (e.g. Hansen and Paige, 1996; Young, 2013; Spencer et al., 1997). Thus previous
models are limited in explaining Pluto's striking longitudinal contrasts. They also focus on
shorter timescales with Pluto's current obliquity and longitude of perihelion. Given that
many geologic features are expected to form and evolve over timescales of millions of years
123
or more, it can be expected that Pluto's "Super Season" epochs play a role in its surface
evolution and are important to consider while studying the relationships between geology
and composition. By combining the numerical methods laid out in Young (2017) with the
albedo variations developed for Earle et al. (2018) a more rigorous, post-encounter study of
volatile transport on Pluto could be completed. This would break down into two parts: first
a parameter search to best match the constraints of the current epoch, then a study of how
volatile transport varies as Pluto undergoes its extreme Milankovid cycles.
124
'7
Apophis and the "Smart Marbles"
Package
Preface
This chapter aims to provide a more complete understanding of the NASA Project Life-
cycle. I started graduate school two years before the New Horizons mission flew through
the Pluto system, thus my involvement with the mission has been limited to the the data
collection and analysis phase. For this final chapter we look ahead to a possible next step in
small body spacecraft exploration, a mission concept to study the asteroid Apophis during
its 2029 close approach to Earth. This provides an opportunity to start back at the begin-
ning of the NASA Project Lifecycle with a Pre-phase A concept study, to see how missions
go from being a rough idea to a spacecraft design and concept of operations.
The NASA Project Lifecycle begins with the space mission engineering process. For a
need-based mission, like the one proposed for Apophis, Wertz (2015) divides space mission
engineering into 14 steps, fitting into 4 broad processes: (1) defining objectives and con-
straints, (2) defining alternative mission concepts or designs, (3) evaluating the alternative
125
mission concepts, and (4) defining and allocating system requirements. Space mission engi-
neering is an interactive process, during which each of these broad processes gets repeated
as requirements and methods of achieving them get refined with each iteration.
This chapter explores a novel hardware concept for studying seismic activity on small
planetary bodies, the "Smart Marbles" package, to enhance the scientific potential of a
mission to Apophis. This hardware package is designed to be part of an Apophis mission
for which the space mission engineering process was begun as part of MIT's 12.43/16.83
Space Systems Engineering course during the Spring semester of 2017. MIT 12.43/16.83
Space Systems Engineering (2017) is the result of the first iteration of the space mission
engineering process and provides a rough concept for the mission. Given the time constraints
of the course, we had to abandon one of the science goals of the mission related to performing
seismology on small solar system bodies. Here we perform the next iteration of the mission
design process and revisit this science goal. We take a closer look at the scientific motivation
for achieving it, the measurement requirements, and evaluate hardware options, including
proposing a new hardware concept (Earle et al., 2017a), all in the context of the proposed
missions system requirements.
This chapter begins with an introduction to Apophis and the scientific motivation for
studying it (Section 7.1). Section 7.2 introduces the SET mission as it was designed by
12.43/16.83 Space Systems Engineering and highlights the additional scientific goals related
to seismology we aim to accomplish through further development of the design, defining the
objectives and constraints for this next iteration of the space mission engineering process.
Next, Section 7.3 defines alternative mission concepts (which are evaluated in appendix B).
From this process we rule out pre-existing hardware options and determine the need for
development of a new hardware concept. In Section 7.4 we consider the scientific motivation
in greater detail in order to further refine the science objectives and propose a preliminary
design for a novel hardware concept. We then consider how it would fit into the system
126
requirements for the proposed mission and how, if successful, it would enhance the mission
objectives of the originally proposed mission. Finally, we present our conclusions from this
process and the next steps for continuing the development process in Section 7.5.
7.1 Introduction
The asteroid 99942 Apophis (originally 2004 MN 4 ) is one of 1,9011 known potentially
hazardous asteroids (its properties are summarized in Table 7.1). It's believed to be in a slow
tumbling rotation state and have an elongated shape with a mean diameter between 365 and
389 meters and a mass between 4.4 and 6.2 x 1010 kg (M6ller et al., 2014). It precesses faster
than in rotates, with periods of 27.38 0.07 hrs and 263 6 hrs respectively (Pravec et al.,
2014). With a bond albedo between 0.10 and 0.17 and Sq spectral classification (resembling
LL ordinary chondrite meteorites), Apophis shows a strong resemblance to Itokawa, the
asteroid studied by JAXA's Hayabusa mission (Pravec et al., 2014; Binzel et al., 2009).
Apophis is currently in a slightly inclined Aten orbit with a period of 0.89 years.
Table 7.1: Summary of Apophis Properties
Property Value Reference
Mean Diameter 365 - 389 m Miller et al. (2014)
Mass Estimate 4.4 - 6.2 x 1010 kg M6ller et al. (2014)
Shape Elongated, asymmetric, possibly bifurcated Brozovik et al. (2018)
Rotation State Slow, tumbling M6ller et al. (2014)
Orbital Period 0.89 yrs Pravec et al. (2014)
Rotation Rate 263 6 hrs Pravec et al. (2014)
Precession Rate 27.38 t 0.07 hrs Pravec et al. (2014)
Bond Albedo 0.10 - 0.17 Pravec et al. (2014)
Spectral Type Sq-class Binzel et al. (2009)
Meteorite Analog LL ordinary chondrite Binzel et al. (2009)
Most significantly, Apophis will be passing between 5.6 and 6.3 Re of Earth's center on
Friday, April 13th, 2029. It is estimated that approaches this close by an objects this large
occurs on average intervals of 800 years or more (Giorgini et al., 2008), making this a rare
'This number was retrieved from NASA/JPL's Center for Near Earth Object Studies
(cneos.jpl.nasa.gov/stats/totals.html) and is accurate as of 4/27/18
127
event. Apophis' 2029 close approach to Earth offers a unique opportunity to study 'live' how
planetary tidal forces impact the shapes, spin states, surface geology, and internal structure
of large asteroids.
In recent decades, our understanding of asteroids has been transformed from points of
light to geological worlds owing to modern spacecraft exploration and state-of-the-art radar
and telescopic investigations. Yet their internal geophysical structures remain largely un-
known. Understanding the strength and internal integrity of asteroids is not just a matter of
scientific curiosity, it is a practical imperative for advancing knowledge for planetary defense
against the eventuality of an asteroid impact. Nature is providing the experiment for us in
the form of Apophis' 2029 approach to within about 30,000 km of Earth's surface (passing
inside Earth's geosynchronous satellite ring). This rare event provides the opportunity for
internal geophysical study as well as a chance to test current hypothesis on the effects of
tidal forces on asteroids.
A growing body of theoretical studies (Farnocchia et al., 2015; Keane and Matsuyama,
2015; Nesvorn' et al., 2005; Richardson et al., 1998; Scheeres et al., 2005, 2000; Souchay
et al., 2014; Yu et al., 2014) and physical evidence (Binzel et al., 2010; Miyamoto et al.,
2007), for tidal forces altering the shapes, spins, and surfaces of near-Earth asteroids all point
to these Earth-asteroid interactions being as fundamental to the asteroid hazard problem
as impact studies themselves. Numerical studies have predicted possible tidal distortion
(Richardson et al., 1998) or small, localized landslides triggered by tidal interactions (Keane
and Matsuyama, 2015; Yu et al., 2014) during Apophis' close approach to Earth. Evidence of
landslides have already been observed on the asteroid Itokawa (which is in the same spectral
class as Apophis and has a similar bond albedo) (Miyamoto et al., 2007) and resurfacing from
seismic shaking induced by tidal forces from near-planet encounters has been suggested as an
explanation for the unexpectedly high number of 'unweathered' asteroids in the near-Earth
object population (Nesvornf et al., 2005; Binzel et al., 2010).
128
There is a significant and growing body of evidence for Earth's tidal effects influencing
encountering objects, however there is still a great deal of uncertainty over the physical out-
comes of such encounters. Studying in detail how Apophis responds to Earth's tidal torques
during its 2029 close approach will provide an unparalleled opportunity for interpreting
strength and internal structure of a potentially hazardous asteroid, revealing the physical
process of Earth-asteroid tidal interactions, and could potentially capture 'live' tidally in-
duced activity occurring on the surface. These results would not only be a giant leap forward
for asteroid science but would also improve out understanding of solar system formation and
inform asteroid hazard assessment and mitigation strategies.
Within the context of it being unlikely that our spacefaring civilization would not mount
an effort to take advantage of measuring and monitoring this extraordinary "natural ex-
periment", MIT's 12.43/16.83 Space Systems Engineering during the Spring semester of
2017 designed the Surface Evaluation and Tomography (SET2 ) mission. The SET mission
uses a suite of high-heritage instruments mounted on a commercially available bus to study
Apophis before, during, and after its 2029 close approach to the Earth. In addition to the
scientific objectives surrounding the near-Earth approach, SET will also monitor and decode
the coupling of rotation and thermal cycling resulting in Yarkovsky drift3 .
An Apophis mission, like SET, also has great potential for engaging the public. The
science objectives of SET, particularly its contributions to asteroid hazard assessment and
mitigation strategies, are areas of research with great relevance to the general population.
Additionally, Apophis will be visible to the naked eye during its 2029 encounter, which is
certain to draw public interest and provide ample education and public outreach opportu-
nities. The SET mission study performed at MIT has already gained public interest and
2 The asteroid Apophis is named after the Egyptian god of chaos and evil. In Egyptian mythology, the
god Set is sent on his solar boat to thwart Apophis.
3Yarkovsky drift is caused by uneven temperatures across the surface of small (meter to ten-kilometer)
objects resulting in changes to their orbits.
129
has been featured in several popular science publications including Astronomy4, Space.com5 ,
SpaceFlightInsider.com , and MIT News 7, showing the potential an Apophis mission has to
capture the public's attention.
While the SET mission as it was originally proposed is capable of fulfilling a robust set
of science objectives, due to the time and resource constraints of the class, we were unable
to identify a way of making the mission capable of directly studying tidally induced seismic
shaking on Apophis. In this chapter, we perform the next iteration of the space mission engi-
neering process and revisit this abandoned science objective, consider the motivation behind
fulfilling it, and consider possible hardware options. We determine the best path forward is
development of the "Smart Marbles" package, a network of uncoupled accelerometers that
will be able to measure seismic shaking on Apophis with broad coverage and low cost and
risk. If successful, "Smart Marbles" will not only allow the mission to address additional
science goals related to seismic shaking, but it will also enhance its ability to address existing
science goals.
7.2 The SET Mission
This section reviews the SET Mission as designed as part of MIT's 12.43/16.83 Space
Systems Engineering during the Spring semester of 2017 in order to provide context for the
development of "Smart Marbles" (complete details can be found in MIT 12.43/16.83 Space
Systems Engineering (2017)). A. Earle served as the Lead Project Scientist for this study.
Here we show how Mission Objective 2 had to be modified because of the time and resource
constraints of the class. The goal of this iteration of the space mission engineering processes
is to restore this objective to fulfill its original goals and enhance the science outcome of the
mission through development of new instrumentation, like the "Smart Marbles" package.
'Nicole Kiefert. MIT students propose Apophis asteroid mission: After working hard to design a space-
craft, the students presented their ideas to NASA scientists. Astronomy.com. June 2017.
'Samantha Mathewson. MIT Students Design Mission to Huge Asteroid Apophis. Space.com. June 2017.
6 Bart Leahy. MIT Students Studying Mission to Asteroid Apophis. SpaceFlightInsider.com. June 2017.
7Meg Murphy. Project Apophis: Space Systems Engineering students design a close-range mis- sion to a
giant asteroid that will fly by Earth in 2029. MIT News. May 2017.
130
7.2.1 Mission Objectives
The SET Mission was designed around three mission objectives chosen to optimize the
scientific impact of the mission as well as inform asteroid mitigation strategies (Table 7.2).
Mission Objective 1: General Characteristics
The first mission objective encompasses the surface geology and mapping goals of the
mission. It includes characterizing Apophis' bulk properties, including: mass, volume, bulk
density, surface topography and composition. It also improves upon ground-based measure-
ments of Apophis' shape, size, spin state, and rotation rate. The designed investigation
starts with an initial survey before Apophis' close approach to Earth, continues throughout
the flyby event and concludes with a survey after the event (see subsection 7.2.3 for more
details). By observing these properties before, during, and after Apophis' close approach to
Earth the SET mission looks for signs of tidally induced deformation or seismic resurfacing,
as well as changes in spin state or rotation rate. A detailed study of Apophis' surface geology
and composition will also help with understanding its geologic and dynamical history.
Mission Objective 2: Internal Structure
The second SET mission objective focuses on understanding the internal structure of
Apophis through characterization before and after the asteroid's close approach to Earth.
The strength and cohesion of the interior can be determined from observations of Apophis'
interior structure and how it responds to the tidal torques from the Earth encounter event.
This information is useful for general asteroid studies and has implications for impact scenario
modeling and planetary defense.
Originally the SET mission's original concept sought to monitor Apophis' interior struc-
ture and any tidally induced seismic activity throughout its close approach to Earth. How-
ever, due to the time and resource constraints of 12.43/16.83 Space Systems Engineering,
it was ultimately decided to remove "during" from this mission objective and settle for just
taking interior measurements before and after the encounter. This limits the science of the
mission to monitoring seismic activity strong enough to induce observable surface changes
131
or changes to the organization of the interior structure. The goal of the "Smart Marbles"
package (Section 7.4) is to allow seismic measurements (and thus inference of the interior
structure) throughout the encounter phase of the mission to enhance the science outcomes of
the mission and better understand how tidal torques effect potentially hazardous asteroids.
Mission Objective 3: Orbit Characterization
The final SET mission objective focussed on studying the process of Yarkovsky drift.
Post-encounter the spacecraft continues to monitor Apophis until the next ground track-
ing opportunity in 2036. These synoptic measurements of position, rotation, and thermal
emission are intended to decode the coupling of rotation and thermal cycling resulting in
Yarkovsky drift. This can not only improve the future orbit determination for Apophis, but
it can also improve orbit determination for other potentially hazardous asteroids.
7.2.2 Instrumentation and Spacecraft Overview
The original design for the SET mission includes four scientific instruments for fulfilling
the mission objectives and science goals. The mission design provides a robust instrument
suite, while keeping cost and risk low, by choosing heritage instruments (with instruments
based on those flown on or designed for New Horizons, OSIRIS-REx, Mars Reconnaissance
Orbiter, and the Lucy Mission). A heritage bus was also chosen, with the selection of the
LEOStar-3 bus for the spacecraft (Figure 7.1). The LEOStar-3 is manufactured by Orbital
ATK and was used for the Dawn and Deep Space 1 missions. The nominal instrument suite
is described below and each instrument's contributions to fulfilling the science goals of the
is summarized in Table 7.2.
LOng Range Reconnaissance Imager (LORRI)
The first instrument designed to start science operations at Apophis is LORRI, the LOng
Range Reconnaissance Imager. LORRI is based on the instrument by the same name flown on
New Horizons (and planned for the Lucy mission), and consists of a 20.8 cm Ritchey-Chretien
telescope with a 1, 028 x 1, 028 pixel panchromatic CCD imager, giving it a 0.290 x 0.290
132
Table 7.2: Original Science Traceability Matrix for the SET Mission to Apophis
Top Level Mission Science Goal Science Measurement Requirement Primary Secondary
Requirement instrument Instrument
Survey Apophis' surface structure and Ralph-
Surface Mapping shape to learn about geology of mid-sized LORRI MVIC
M.O.1 - Characterize (before, during, (100's of meter diameter) asteroids (pan)
Apophis' shape, size, and atter Earth Survey Apophis' shape before and after Ralph- LORRI/Ralphdensity, surface encounter) encounter to determine the impact of MVIC(pan) LEISAtopography and tidal torque on an asteroid's shape
CUiipiUSiUiUi, fOLad1Uii Measure Apophis' spin state and
rate, and spin state rotations rate before and after encounter Ralph- LORRI/Ralph
to understand how tidal torques impact MVIC(pan) LEISA
the dynamics of a potentially hazardous
asteroid
Image Apophis' surface before, during,
and after the encounter at sufficient Ralph-
resolution to observe possible land slides LORRI MVIC
and other surface responses to tidal (pan)
torques
Map Apophis' surface with filters to allow Ralph- Ralph-Surface for color imaging and broad band MVIC LEISAComposition spectroscopy (color)
Mapping (betore, Spectral mapping of Apophis' surface to
during, and after look at compositional heterogeneities and
Earth encounter) better refine Apophis' spectral class with Ralph- Ralph-
higher resolution and broader wavelength LEISA MVIC(color)
coverage than achievable with
ground-based observations
Perform surface composition and color
surveys both before and after encounter Ralph
to look for tidally induced resurfacing
During encounter observe Apophis' Ralph-
surface with color filters at sufficient time MVIC Ralph-
and spatial resolution to observe tidally (color) LEISA
induced resurfacing
M.O.2 - Characterize Map Apophis' interior (before and after
internal structure Internal Structure encounter) to interpret the strength and RRTbefore and after internal structure of a potentially
near-Earth event hazardous asteroid
M.O.3 - Characterize
Apophis' orbit, Post-encounter monitoring to decode the
accounting for the Yarkovsky Effect coupling of rotation and thermal cycling TES LORRI/Ralph
influencing factors of resulting in Tarkovsky drift
the Yarkovsky Effect
Science Measurements Objectives highlighted in blue are significant for understanding how a potentially hazardous asteroid
responds to tidal torques
field of view (Cheng et al., 2008). During the approach phase LORRI is designed to be
the first instrument to resolve Apophis and take images to improve upon ground-based
measurements of Apophis' rotation rate, spin state, and shape while also monitoring the
area around the asteroid for potential hazards. Once the spacecraft is in orbit around the
asteroid, LORRI becomes responsible for high-resolution surface imaging, with an expected
resolution of 0.0099 m/pixel at a distance of 2 km from the surface.
133
Figure 7.1: CAD
Model of SET
spacecraft layout.
The instruments
are all located
at the top of
the spacecraft to
allow them to
be used simul-
taneously. The
RRT antenna
and solar panels
fold and are
deployed after
launch. (Image
credit: Amy
Vanderhout and
MIT 12.43/16.83
Space Systems
Engineering
(2017)).
Solar Panels
Instruments RRT
'Dipole
Antenna
Communications -
Antenna
18.6 M
Ralph
The Ralph instrument also has heritage on New Horizons and Lucy and consists of
a panchromatic and color imager (MVIC) and a spectral imager (LEISA). Chapter 2 of
this thesis presented some of the results from the New Horizons version of this instrument.
Multi-spectral Visible Imaging Camera (MVIC) consists of 7 independent CCD ar-
rays on a single substrate to produce panchromatic and colored images. Each CCD has a
5.7 x 0.037' field-of-view, but they are able to produce images with a much wider field-of-
view by operating in time delay integration (TDI) mode (Reuter et al., 2008). Once SET is
in orbit, MVIC becomes responsible for the broad panchromatic imaging, color and broad
band spectrometry mapping. These maps can be used to look for evidence of seismic resur-
facing induced by tidal torques from the Earth. Linear Etalon Imaging Spectral Array
(LEISA) is a wedged filter infra-red spectral imager that creates spatially resolved spectral
maps. LEISA is a scanning imaging instrument, that makes use of a special filter over which
the wavelength varies in one direction (Reuter et al., 2008). For SET the plan is to have
134
. 4
LEISA cover the 0.45 - 4.0pm wavelength range, with a spatial resolution of 60.8prad and
a 0.90 x 0.9' field-of-view. LEISA can map the surface composition of Apophis, search for
compositional heterogeneities, and reveal surface composition changes triggered by Apophis'
tidal interaction with the Earth.
Radio Reflection Tomography Instrument (RRT)
The RRT instrument designed for SET consists of a 10 m dipole antenna and electronics
box for signal generation and power amplification, it is based on SHARAD instrument flown
on the Mars Reconnaissance Orbiter (Putzig et al., 2009). The antenna is to be folded for
launch and then deployed using the elastic properties of the encasing tube. The instrument
maps the internal structure by recording the echoes of transmitted low-frequency radio waves
and using them to measure differences in dielectric properties of materials in the asteroid.
The RRT instrument will have a transmission frequency of 20 MHz and a bandwidth of
5 MHz. This bandwidth is designed to provide a spatial resolution of approximately 20 m
(assuming a refractive index similar to Itokawa). This resolution is sufficient for detecting
fragments roughly the size of the Chelyabinsk meteoroid (which struck Russia in 2013),
which is significant from a planetary protection perspective.
Thermal Emission Spectrometer (TES)
TES is based on the OTES instrument flown on OSIRIS-REx and consists of a telescope,
interferometer assembly, electronics, and support structure (Christensen et al., 2017). The
instrument achieves its spectral range by implementing an interferometer, beam splitter,
and moving mirror assembly. TES operates in the spectral range of 6 - 100 Am to map
mineralogical and thermophysical properties. At a distance of 2 km from the surface its single
detector with a 8 mrad field-of-view can see an area roughly 16m x 16m. TES can provide
insight into Apophis' mineralogy, globally map the material distribution, and determine
regolith physical properties based on diurnal temperature measurements (Christensen et al.,
2017). By combining thermal measurements from TES with imaging and ground-based radar
135
tracking we will be able to better understand the coupling of thermal cycling and rotation
which results in Yarkovsky drift. This can not only improve future predictions for Apophis'
orbit, but can also inform predictions for other potentially hazardous asteroids.
7.2.3 Concept of Operations
The SET -mission concept has a six week launch window starting in August of 2026
(with a back-up launch window in August of 2027). The concept of operations, including
rough instrument usage plan, is outlined in Figure 7.2. The instruments are planned to
be turned on and calibrated as the spacecraft leaves the Earth's sphere of influence and
uses solar electric propulsion to gradually change planes and match its orbit with Apophis'.
The spacecraft will rendezvous with Apophis at its aphelion in March 2028, giving it more
than a year to complete its initial survey of Apophis. Once the initial survey is complete
the spacecraft transfers to a leader-follower configuration 20 km ahead of Apophis before
its close approach to Earth on April 13th, 2029. This position provides favorable viewing
geometry while also keeping the spacecraft at a safe distance during the close approach to
Earth. After the Earth flyby event the spacecraft performs another survey before entering
the long term observation phase. The spacecraft continues to formation fly with Apophis for
at least 7 years to study the Yarkovsky effect before finally performing an exit burn to leave
Apophis' sphere of influence and enter its own heliocentric orbit (compliant with planetary
protection constraints).
7.3 Trade Space for Measuring Surface Activity
For this thesis work, the objective is to enhance the original SET mission design (pro-
posed by MIT's 12.43/16.83 Space Systems Engineering) with the addition of an instrument
to study seismic effects and interior structure during Apophis' close approach to Earth.
Taking this next step requires defining alternative mission concepts (and then evaluating
them). After considering both contact and non-contact options, including both pre-existing
technology (with novel implementation in some cases) and concepts that are still under de-
136
A1
2
4
5
6
7
8
9
10
ugust 2026 March, 2028
Turn On/Test
instrumentation
48 Days (16)
30 Days (10)
April 13 2029
96 Days (32)
60
2
Launch
Plane Change and Phasing Orbits
Approach I (20,000 km to 2 km)
Terminator Orbit I (2km)
Approach I (2 km to 500m)
Terminator Orbit 11 (500 m)
Transfer to Leader-Follower Position
Leader-Follower (20 km)
Approach I1 (20 km to 2 km)
Terminator Orbit III (2km)
Approach IV (2 km to 500m)
Terminator Orbit IV (500 m)
Long Term Observation Position
End of Mission Safe Depart*
Payload Usage Key
LORRI B&W Imaging -
LEISA Spectra RALPH
MVIC Color lmaging RALP
TES Thermal Emission Spec.
RRT Interior Structure --- --......
Ranging Primnarily 
_ngin_ Prir__
Figure 7.2: Proposed timeline of operations for the SET mission (Image credit: Max Vanatta
and MIT 12.43/16.83 Space Systems Engineering (2017))
velopment, six possible concepts are identified here. Each of the concepts are evaluated
based on how well they would be able to meet the scientific needs of the mission (particu-
larly coverage during the actual encounter phase), as well as other factors like heritage and
technology readiness, cost, risk, and whether or not the quantity of data produced would be
manageable. Table 7.3 summarizes the results of this analysis and the complete details can
be found in Appendix B.
After defining and evaluating alternative mission concepts, we determined that while the
"Smart Marbles" concept still has a low technology readiness level (TRL) rating by NASA
standards and requires further testing and development, it shows the most promising science
possibilities while still keeping risk and cost low and the data rate manageable. There is
also a clear path forward for further research and development that fits within the timeline
necessary to be spaceflight ready in time for a mission like SET to study the 2029 Apophis
close-approach (see subsection 7.4.3 and Earle et al. (2017a)).
137
)ays (20)
Table 7.3: Trade Space for Measuring Surface Activity. "TRL" refers to NASA's technology
readiness levels (see Appendix B for more details). "I.S.C." is for instantaneous surface
coverage possible during the encounter phase of the mission. "M.D.O." means manageable
data output, indicating whether or not the amount of data produced could easily be stored
on the spacecraft and sent back to Earth.
Concept Risk TRL I.S.C. M.D.O. Other Concerns
RRT/RTT Low 9 n/a Yes Can't observing during the encounter
Imaging Options Low 9* < 50% No *Cameras like this have flown before,
but not used in this way
Lander/Rover High 9 Minimal Yes Low success rate, high cost, requires
multiple units, political concerns
Doppler Laser Low 1 Minimal Yes Still a long way from being flight
Vibrometer ready
"Dumb Marbles" Low 9* < 50% No Requires better imaging, runs into
same problems as imaging options
*Artificial markers like this have been
implemented before, but not for seis-
mic studies
"Smart Marbles" Low 2 100% Yes Needs further development and test-
ing
7.4 "Smart Marbles"
Now that we have determined that "Smart Marbles" appear as a promising path forward
for enhancing the scientific capabilities of an Apophis mission, like SET, here I revisit the
science motivation for their development and further constrain the objectives and rational
for their design. From here we can begin formulating a preliminary design and determine
how it fits in with the rest of the SET mission design. We consider both how resources would
be needed to allocate the new instrumentation as well as how it would be able to enhance
the mission objectives and science outcomes of the mission.
7.4.1 Science Motivation
There is currently a large and growing body of evidence for seismic shaking
interactions from close encounters with planets effecting the surface evolution of
however these processes are still not well understood (e.g. Scheeres et al., 2015;
et al., 2015, and references therein). The primary science objective of "Smart
and tidal
asteroids,
Murdoch
Marbles"
138
is to provide a method of studying these effects, particularly in the context of the 2029
close-approach of Apophis, with better coverage, lower-cost, and lower-risk than traditional
landing packages.
Previous space missions that have studied asteroids in detail have provided a wealth of
new data to suggest seismic shaking occurs on asteroids and effects their surface evolution.
Thomas and Robinson (2005) provided the first evidence for seismic shaking as an asteroid
surface shaping process, when they suggested it as a mechanism for explaining the varying
crater densities observed an Eros. Specifically, they showed the formation of a relatively
young crater had resulted in the removal of craters up to 0.5 km over almost 40% of Eros'
surface within a particular straight line distance through the asteroid to the crater site
(and that these erasures could not be explained by burial by ejecta). Since then additional
evidence for seismic movement of regolith has been observed on Eros and other bodies, for
example signs of movement of material away from topographic highs on Eros and signs of
regolith migration on Lutetia (Murdoch et al., 2015, and references therein). The distribution
of craters and surface material on Itokawa (which shows has a similar albedo, size, and
spectral class as Apophis) also shows evidence of regolith migration and crater removal from
seismic shaking (Miyamoto et al., 2007; Murdoch et al., 2015).
According to Nesvornf et al. (2005), near-Earth asteroids undergo planetary encounters
more frequently than mutual collisions, suggesting tidal effects may play a substantial role
in the evolution of these bodies. Binzel et al. (2010) and Nesvornf et al. (2010) have both
suggested that seismic processes induced by recent planetary encounters may account for the
presence of 'unweathered' Q-type asteroids. In a most extreme case, the effects of planetary
tidal interactions were directly observed in the early 1990's when the comet Shoemaker-Levy
9 was pulled apart by (and later impacted) Jupiter (Weaver et al., 1994, 1995). In addition to
observational evidence, simulations have also shown the potential for tidal forces to impact
near-Earth asteroids. Richardson et al. (1998) showed that Earth's tidal forces can distort
139
and disrupt Earth crossing asteroids with weak, 'rubble-pile' structures. Simulations also
suggest near-Earth encounters may account for the odd shapes and rotation rates of some
near-Earth asteroids (Bottke et al., 1999).
Thus far most of what we know about the effects of tidal forces and seismic shaking on
asteroids is based on simulations and observational evidence suggestive of these processes
having occurred. The 2029 close approach of Apophis provides us with a 'live' experiment
by which to test and constrain our theories and dramatically improve our understanding of
near-Earth asteroids and the processes that shape them. There is currently much speculation
about what could happen during Apophis' close approach to Earth. Keane and Matsuyama
(2015) and Yu et al. (2014) both predicted that landslides on Apophis would most likely
be small, localized events widely distributed across the surface of Apophis. Observing these
events would provide useful constraints on this mechanism and the bulk properties of regolith.
More recent work by Brozovid et al. (2018) suggest Apophis may have a bi-oblate shape with
higher angles of repose than the convex shape assumed for the previous work, which could
show more dramatic changes than previously predicted. It has also been suggested that
Earth's tidal torques may change Apophis' rotation rate and spin state during its 2029
close-approach (Souchay et al., 2014).
The SET mission was designed to study the 2029 close-approach of Apophis as efficiently
as possible using pre-existing hardware. High resolution, color, and spectral imagers will
be able to detect changes to Apophis' surface composition and geology induced by the
encounter, and the RRT instrument will be able to map the interior structure before and
after the encounter and look for major changes. Given that the field-of-view is limited by
illumination and spacecraft viewing geometry it is unlikely that the imaging instruments will
be able to observe landslides or other small scale changes in action. The existing instrument
suite offers robust science capabilities and will be able to answer many important science
questions related to potentially hazardous asteroids and near-planet encounters however it
will not be able to directly measure seismic shaking. Taking seismic measurements at many
140
points on the surface of a near-Earth asteroid like Apophis would provide information about
the asteroid's internal structure, porosity, properties of its regolith, and would constrain
the effects of tidal torques on near-Earth objects. All areas of research that are of great
scientific interest as well as important for informing potentially hazardous asteroid mitigation
strategies. For this reason we set out to develop the "Smart Marbles" package to provide
a low-risk, low-cost, high spatial coverage method for studying seismic shaking on small,
airless, planetary bodies.
7.4.2 Science Objectives and Rationale
Ultimately the development of 'Smart Marbles' will require dedicated, detailed simu-
lations, but for our preliminary design we derive our science objectives based on previous
planetary seismology experiments and simulations.
A network of several planetary seismometers were placed on the Moon during the Apollo
program and have been used to determine the timing and location of moon-quakes, the inter-
nal structure of the Moon, and the properties of each layer (Goins et al., 1981; Nakamura and
Koyama, 1982). Thus far the Apollo lunar seismometers are the only planetary instrument
to record seismic data with clear evidence of an interior signal, however seismometers have
been deployed on Mars in the past and the Mars InSight mission plans to deploy a seismic
package that has shown a great deal of success during testing on Earth (Panning et al., 2015).
Viking 2 was equipped with a 3-axis, short period seismometer, which was unsuccessful in
obtaining measurements pertaining the Mars' interior but was able to determine that the
natural background noise on Mars was low, with the primary source being wind (something
we will not need to contend with on airless bodies like Apophis), it also determined the noise
could be reduced by a factor of 10' on future missions by removing the seismometer from
the lander (Anderson et al., 1977).
While seismometers are yet to be deployed on asteroids a slew of concept studies and
mission proposals have supported their feasibility and scientific impact (e.g. Scheeres et al.,
2003; Pavone et al., 2013; Anderson et al., 2014; Murdoch et al., 2014). Murdoch et al. (2014)
141
found that the seismic signal from an asteroid being struck at 6 km/s by a 10 g impactor was
dominated by waves in the 10-100 Hz range. Richardson et al. (2004) also studied simulated
impact induced seismic shaking (on asteroids with diameters between 1- 100 km) and found
seismograms generally had frequency spectrum between 1 - 100 Hz with a peak between
10 - 20 Hz. Walker et al. (2006) demonstrated that tools presently exist to make seismology
a method of determining interior discriminating information for irregular bodies, in their
simulations they successfully used seismology to distinguish between different geometries
and identify major features (such as regions and sound speeds).
On Earth there is already some precedence for using uncoupled accelerometer networks to
detect seismic activity, in particular using the accelerometers in smartphones and computers
to determine the time and location of seismic events (Kong et al., 2016; Han et al., 2017).
However, in addition to designing an accelerometer instrument that can survive the space
environment, launch, and deployment, a slew of other concerns arise when considering the use
of uncoupled seismometers on airless, low-gravity bodies like Apophis. The acceleration due
to gravity on kilometer sized asteroids (slightly larger than Apophis) if they have an elongated
shape can be on the order of 10-2 - 10-4 M/s 2 with variations of a factor of 2 across the
asteroid's surface (Tancredi et al., 2012), making it difficult to predict exactly what 'Smart
Marbles' will encounter at Apophis given the current level of uncertainty in Apophis' shape.
Furthermore, Tancredi et al. (2012) found that a particle layer shocked from below would
produce the lift of particles at the surface, which can acquire vertical velocities comparable
to the surface escape velocity in very low-gravity environments. Given the uncertainty over
exactly how Apophis will respond to Earth's tidal torques we can not completely rule out
the possibility of surface instruments being lofted (or less likely, completely ejected). This
is one of the motivations for the redundancy of the 'Smart Marbles' package, if one or even
several marbles are lofted or ejected it will not compromise the science goals of the mission.
Additionally, lofted 'marbles' are not a lost cause. Tracking the ballistic path of such marbles
can determine the strength of the seismic wave which caused the movement (Scheeres et al.,
142
2015). However, we still acknowledge this is an area of concern that warrants further detailed
study (particularly before making a final decision about the form the 'Smart Marbles' will
take).
Based on previous planetary seismic studies and simulations we have determined a pre-
liminary set of science objectives for the "Smart Marbles" package that will be refined with
further dedicated modeling. Currently, "Smart Marbles" are being designed to measure ac-
celerations up to 0.5m/s2 with a sensitivity of 0.0001m/s 2 and frequency range of 1--100 Hz.
This covers the range of seismic activity we might expect to see on an asteroid like Apophis
and provides sufficient sensitivity to differentiate interior structures and properties.
7.4.3 "Smart Marbles" Design Overview
The 'Smart Marbles' package is still under development and the complete details of the
design plan can be found in Earle et al. (2017a). Here we provide a quick overview of the
current design for context. The goal of the 'Smart Marbles' project is to provide scientific
capabilities that are not possible with non-contact remote sensing instruments while offering
broader coverage, lower risk, and a more cost efficient design than previously flown landing
packages. This is accomplished by leveraging simplicity and redundancy. Each individual
marble is based on a simple design with simple components (in some cases implemented in
innovative ways), making them cost efficient to design and build and low risk to operate.
Deploying 10's to 100's of marbles provides better coverage than traditional landing packages
and further decreases the risk. Marbles will be equipped with both marble-to-marble and
marble-to-spacecraft communications capabilities (adding another layer of redundancy) so
the failure of a single component (or even a whole marble) will have minimal effect the data
quality and ability to accomplish mission objectives.
For the purposes of Earle et al. (2017a) three different architecture concepts are under
consideration: spheres, beanbags, and cubes (Figure 7.3). All three architectures share sev-
eral common components and specifications. They all include a battery for power, controller,
and communications (both marble-to-marble and marble-to-spacecraft). Given the uncer-
143
Architecture Concepts
Spherical Marble Concept
Spacecraft
Dar ~Other Marbles
Pros:
- Simplicity of form allows the marbles to easily act as
markers of known physical properties even if the
electronics go dead.
- Rigid overall form allows for a single accelerometer
package to be used
Cons:
- The rigid marb;le could bounce off hard portions of
the asteroid (the portions giving the best seismic
readings)
Unfolding Cube Concept
Figure 7.3: Architecture concepts being considered for 'Smart Marbles'. Further details
about each of these architectures can be found in Earle et al. (2017a) (Image credit: Max
Vanatta).
tainty in the intensity of seismic activity expected, we have chosen to outfit each marble
with multiple accelerometers to cover a frequencies between 1 - 100Hz with sensitivities of
0.00001 - 1g. The marbles will likely use piezoelectric or MEMS type sensors which are
currently undergoing large technological improvements creating increased feasibility for this
type of application (Murdoch et al., 2015; Goldstein et al., 2006).
In all cases we expect each individual marble to be about 2 - 5 cm in diameter (diameter
of closed cube) and have a mass of roughly 100 - 500 g. The small size and mass of each indi-
vidual unit makes it possible to adapt the total volume and mass of the system based on the
scientific needs of the mission and resource availability. Given that Apophis makes repeated
close-approaches to Earth (with the next one predicted for 2036) substantially disrupting its
144
To Be Investigated
Beanbag Concept
Cons:
- The dampening means multiple accelerometers must
be used
Cons:
- Deployment can be risky
- Dust can cover and reduce the solar cell efficacy
- This architecture is far more complex than the
beanbag or spherical marble
Spacecraft Spacecraft
A AOther Marbles . Other Marbles
* -- -- --- --
A.& ~ . AlA_________
to
I IUA.A,
Pros: Pros:
- Banbg frm ampnsthe impact and would - The solar cells could allow for 1000+ houra of
inelaaticafly abaorb the majority of the impact forces operariona
damping the amplitude of each successive bounce. - The large surface area can reduce the chances the
- Hentage from Haysbusa I/TI markers sensors are knocked off the aurface
- Sensors rear directly on the surface - Urge unfolded area could be inlaid with a longer
- Mass is adjustable with type and quantity of 'beans' antenna
orbit carries significant risk (and potential political ramifications) if it is perturbed onto a
path that intersects Earth's orbit. Even assuming the maximum mass of 500 g and a package
of 500 units, the total mass being deployed at Apophis would be about 250 kg, which is only
4 x 10~' of Apophis' mass. Furthermore this mass would be soft landed, and distributed
across Apophis' surface, further minimizing the influence on Apophis' orbit. This is a "worst
case scenario" given that we will most likely use fewer marbles and the mass estimate used
here is the upper limit (this total mass is also well above the current payload mass limit for
the SET mission).
The exact architecture will be determined through further development and refinement
of mission objectives in order to more precisely weigh the pros and cons of each option. For
example, refined knowledge of power needs, battery capabilities, and accelerometer costs will
inform decisions. Spheres require the fewest accelerometers per marble, making them the
best choice if accelerometer price becomes a driving factor. Cubes have the largest surface
area making them best suited for the addition of solar panels if necessary (and giving them
the largest surface contact area). Beanbags are simple, have some heritage with the Hayabusa
mission (Yoshimitsu et al., 2009), and are best suited for absorbing the impact but require
several accelerometers and would be difficult to outfit with solar panels.
7.4.4 Mission Integration
Now that we have determined the measurements objectives for "Smart Marbles" and
developed a preliminary design concept, the next step is to consider how the package will fit
into the SET mission, including how resources will be allocated to support it as well as how
it will impact the potential science outcome of the mission.
First we consider the available resources on the SET mission to support "Smart Mar-
bles". The current concept of operations (see subsection 7.2.3) has the spacecraft arriving at
Apophis more than a year before the close approach to Earth. Currently the pre-encounter
observing plan includes ample margin (on the order of several months), some of which can
be used for "Smart Marbles" deployment. Even if the "marbles" are soft landed (using only
145
the acceleration from Apophis' gravity field) from the larger orbital distance of 2 km, it will
only take about 11.5 hrs for a "marble" to make it from the spacecraft to Apophis, so the
several months of margin available should be more than enough time for deployment.
We also must consider how much room is available on the spacecraft to accommodate
the "Smart Marbles" package, both in terms of volume and mass. The current design
uses less than half the available volume for the science payload, with room for additional
instrumentation of about 112 cm x 112 cm x 64 cm in volume. With the worst case scenario
of each "marble" occupying a 10cm x 10cm x 10cm area, this would place a limit of around
725 "marbles". However, slight reductions in radius or improved packing (for example if each
"marble" is a sphere instead of a cube) would make is possible to fit thousands of marbles.
Mass will most likely be a more limiting factor than volume. Currently, the spacecraft can
accommodate an additional 69.5 kg of scientific instrumentation. This means the spacecraft
could accommodate between 140 and 700 "marbles" depending on the mass of the final
design. However this does not account for the mass of the container and launch mechanism,
so more realistic upper limit is probably around 500 marbles. Assuming Apophis is spherical,
this would mean an average distance of about 28 m between "marbles" (with only 100
"marbles" deployed this would increase to 62 m). This preliminary analysis suggests the
"Smart Marbles" package will be able to achieve sufficient surface coverage while remaining
within the resource availability of the originally proposed SET mission, thus not requiring
significant modification or redesign of the original mission.
While "Smart Marbles" will not require the design of the spacecraft or concept of op-
erations to be substantially redesigned, they will have a significant impact on the scientific
outcomes of the mission. Table 7.4 shows how "Smart Marbles" would enhance the Science
Traceability Matrix (Tables 7.2) for the SET mission, by both adding the potential for new
science goals as well as enhancing the missions ability to fulfill preexisting science measure-
ment objectives. Most notably, M.O. 2 has been rewritten to not only include "during"
(the original motivation for this project) but also include characterizing the seismic response
146
Table 7.4: Updated Science Traceability Matrix (original shown in Table 7.2) for the SET
Mission to Apophis enhanced by the addition of "Smart Marbles"
Top Levele on Science Goal Science Measurement Requirement Instru nt ISecondary
Survey Apophis' surface structure and Ralph-
Surface Mapping shape to learn about geology of mid-sized LORRI MVIC
M.0.1 - Characterize (before, during, (100's of meter diameter) asteroids (pan)
Apophis' shape, size, and after Earth Survey Apophis' shape before, Ralph-
density, surface encounter) during, and after encounter to MVIC(pan)/ LORRI/Ralph
topography and determine the impact of tidal "Smart LEISA
composition, rotation torque on an asteroid's shape Marbles"
iate, adlu hp111 Suae Measure Apophis' spin state and
rotations rate before and after encounter Ralph- LORRI/Ralphto understand how tidal torques impact MVIC(pan) LEISA
the dynamics of a potentially hazardous
asteroid
Image Apophis' surface before, during,
and after the encounter at sufficient LORRI/ Ralph-
resolution to observe possible land "Smart MVIC
slides and other surface responses to Marbles" (pan)
tidal torques
Map Apophis' surface with filters to allow Ralph- Ralph-
Surface for color imaging and broad band MVIC Ralph
Composition spectroscopy (color) LEISA
Mapping (before, pectral mapping of Apophis' surface to
during, and after look at compositional heterogeneities and
Earth encounter) better refine Apophis' spectral class with Ralph- Ralph-
higher resolution and broader wavelength LEISA MVIC(color)
coverage than achievable with
ground-based observations
Perform surface composition and color
surveys both before and after encounter Ralph
to look for tidally induced resurfacing
During encounter observe Apophis' Ralph-
surface with color filters at sufficient time Ralph LEISA
and spatial resolution to observe tidally color) "Smart
induced resurfacing Marbles"
Measure seismic shaking before,
during, and after the near-Earth
event with sufficient sensitivity and "Smart
M.O.2 - Characterize Seismic Shaking coverage to differentiate interior Marbles"internal structure and structure and properties and
seismic response to determine significance of tidal
tidal torques before, interactions for evolution of a PHA
during, and after the Map Apophis' interior to interpret the "Smart
near-Earth event Internal Structure strength and internal structure of a RRT Marbles"
_______ -__Characterizepotentially hazardous asteroid
M\.O.3 - Characterize
Apophis' orbit, Post-encounter monitoring to decode the
accounting for the Yarkovsky Effect coupling of rotation and thermal cycling TES LORRI/Ralph
influencing factors of resulting in Yarkovsky drift
the Yarkovsky Effect IIII
Science Measurement Requirements highlighted in blue are significant for understanding how a potentially hazardous
asteroid responds to tidal torques
Changes made possible by the "Smart Marbles" package are highlighted in purple, with specific changes to Science
Measurement Requirements written in bold font
147
4
to tidal torques. By landing "Smart Marbles" on Apophis' surface before the encounter to
acquire baseline measurements we will be able to determine if and at what distance range
tidal torques induce seismic shaking on Apophis. Additionally, "Smart Marbles" will be
able to enhance the science outcomes of some of the imaging goals. The network aspect of
"Smart Marbles" means that in addition to providing seismic information they will also be
able to provide measurements pertaining to Apophis' shape, and track if and how it changes
during the near-Earth encounter. The surface motion data provided will also enhance our
understanding of the physical processes at work if landslides or resurfacing is observed by
the imaging and spectral instruments.
7.5 Conclusions and Future Work
This chapter reviewed the SET mission and performs the next iteration of the space
mission engineering process to both advance the mission design and serve as an opportunity
to learn about the early stages of the NASA mission lifecycle. We identified the need for
the mission to include instrumentation capable of directly measuring tidally induced seismic
shaking and determined that existing hardware could not meet the scientific needs of the
mission while also keeping the cost and risk reasonable. This served as our motivation for
developing the "Smart Marbles" package, a network of uncoupled accelerometers designed to
measure seismic shaking at a lower cost and with less risk than traditional landing packages.
Based on previous studies of planetary seismology we were able to determine this concept
is feasible and formulate a preliminary set of design requirements. If "Smart Marbles" are
successfully developed they will not only allow the SET mission to fulfill additional science
goals, they will also enhance its ability to address existing science goals, like understanding
the mechanism behind tidally induced resurfacing if it occurs.
Now that we've done a basic feasibility study of "Smart Marbles" and identified the scien-
tific motivation for their further development, the next major step in the development process
is performing simulations to model exactly how uncoupled accelerometers will respond in a
148
low gravity environment like the surface of Apophis, and refine the design requirements that
need to be met to achieve the desired scientific outcomes of measuring seismic waves and
inferring interior structure. These simulations will also inform decisions related to archi-
tecture, size, weight, power, and coverage (in terms of number of "marbles" deployed) and
allow the next iteration of defining and allocating system requirements. The first step will
be simulating how "marbles" respond to seismic shaking, including determining the condi-
tions under which they may be lofted or ejected from the surface given the low-gravity of
asteroid surfaces. The next step will be adding complexity to the model to determine the
sensors' sensitivity to discerning interior structure and effective coverage limits of each indi-
vidual "marble". Simulations of impact induced seismic shaking on asteroids have already
been performed by Murdoch et al. (2014) and Richardson et al. (2004). Walker et al. (2006)
demonstrated that tools presently exist to make seismology a method of determining interior
discriminating information for irregular bodies, in their simulations they successfully used
seismology to distinguish between different geometries and identify major features (such as
regions and sound speeds). The scientific potential of "Smart Marbles" is not restricted
to an Apophis mission, they could be used on any airless planetary body to study seismic
shaking, whether it be tidally or impact induced.
149
150
Appendices
151

Appendix A
Calculating Pluto's Obliquity
Variations using Dobrovolskis et al.
(1997)
The purpose of this appendix is to give a detailed description of how we calculate Pluto's ec-
centricity, angle from perihelion (or true anomaly), and sub-solar latitude over long timescales
for use in the insolation calculations described in subsection 3.2 and used throughout the
Pluto sections of this thesis. These calculations are based on the equations presented in
Dobrovolskis et al. (1997), referred to herein as "Dobro". We also compare the assumed
physical parameters used by Dobro with the precise results of New Horizons and their effect
on the timescales discussed in Chapters 3, 4, 5, and 6.
The equations lend themselves to working in terms of eccentric anomaly (E), so the
first step is to determine the eccentric anomaly range over which you want to calculate
the parameters and the step size (which varies based on how the total time over which
the calculations are going to be run). Once the eccentric anomalies have been determined,
they can be used to calculate the approximate times (,r) over which the parameters will be
calculated using:
r = E x (T/360.) (A.1)
153
Where T is the orbital period of Pluto in Earth years. Next we use Dobro's equation 12 to
define and calculate 4, a parameter that will be used throughout these computations:
4 = 72.80 + 9 1.O0 Tmyrs (A.2)
Where Tmyrs is T converted to millions of years. From here we can calculate the eccentricity
of Pluto's orbit (e) using equation 8 from Dobro:
e = 0.244 + 0.022 cos (0) + 0.0005 cos (34) (A.3)
Next we calculate the mean anomaly (M), which is derived from the eccentric anomaly and
eccentricity, using:
M = E - e sin(E) (A.4)
Mean anomaly is the angle from perihelion which a body would have if it moved in a circular
orbit, with constant speed, in the same orbital period as the actual body in its elliptical
orbit. It is mathematically convenient since since it varies linearly with time, and is used
here to determine the time (t) steps that will be used for the rest of the calculations:
t = M(T/360.) (A.5)
The next step is to use the eccentric anomaly and eccentricity to calculate the true anomaly
(v), which is the angle at the primary focus between the direction of perihelion and the
object's position, and is given by:
v = 2 arctan = tan - (A.6)
S1 -e 2
154
At this point we have the eccentricity (e) and angle from perihelion (v) of Pluto for all of
our times (t), the last thing we have to calculate is the sub-solar latitude as a function of
time. To do this, first we calculate the longitude of Pluto's spin angular momentum vector
(#) using Dobro's equation 20:
# = 19.50 + 130.20 tmyrs (A.7)
where tmyrS is the times t converted to million years. From q the component of Pluto's
unit spin vector aligned toward Pluto's orbit normal (Z) can be calculated using Dobro's
equation 23:
Z = -0.442 - 0.184 sin (A.8)
The obliquity of Pluto (0) is simply arccos Z by equation 15 in Dobro. Next we recalculate 0,
this time using t instead of T. We use 4 and # to calculate the angle between the longitude
of perihelion and the vernal equinox (X) from Dobro's equation 24:
X = # - 24.0'sin4' (A.9)
Finally we can calculate the sub-solar latitude (6) as a function of time using v, X, and Z
which have all been calculated as functions of time t:
6 = arcsin( 1 - Z 2 sin (v - X)) (A.10)
Now that we have Pluto's eccentricity (e), angle from perihelion (v), and sub-solar latitude
(6) all as functions of our set of times (t) we are able to use the equations from Levine et al.
(1977) to calculate insolation incident on the top of Pluto's atmosphere as a function of time
and latitude (as described in subsection 3.2).
155
Note that between these two sets of calculations we switch some of our parameter symbols
so that the equations stay consistent with how they were originally published. In particular
the angle from perihelion is represented by v in this appendix and 0 in subsection 3.2, and in
this appendix q5 is used to represent the longitude of Pluto's spin angular momentum vector,
but in subsection 3.2 it represents the latitude for which the insolation is being calculated.
Table A.1: Comparison of Pluto system parameters used in Dobrovolskis et al. (1997) and
reported in Stern et al. (2015)
Parameter Symbol(units) Dobrovoiskis Stern (2015) % Diff(1997)
Pluto mass mP (g) 1.27 x 1025 1.303 x 1025 2.6
Charon Mass me (g) 1.5 x 1024 1.587 x 1024 5.6
Pluto Radius Rp (km) 1,180 1, 187 0.6
Charon Radius R, (km) 620 606 2.3
Semi-major Axis a (km) 19,405 19,596 1.0
Principle moments A 7.329 x 1030 7.577 x 1030 3.3
of inertia B = C 5.187 x 1032 5.508 x 1032 6.0
Precessional H 0.493 0.493 0.000Constant
It is also worth acknowledging that theses calculations are from Dobrovolskis et al. (1997),
which is now more than two decades old and based on work originally presented in Dobrovol-
skis and Harris (1983). During that time our knowledge of the Pluto system has improved
dramatically. However the differences between the values used for Dobrovolskis et al. (1997)
and those reported in Stern et al. (2015) are minimal (Table A.1), with a difference of less
than 1% for the semi-major axis of Charon's orbit and Pluto's radius, and a difference of
less than 3% for Charon's radius and the combined mass of the two. The differences in these
measured parameters result in differences of roughly 3% and 6% for the moment of inertia
along the semi-major axis through the center of both bodies (A) and the moments of inertia
through along the axes perpendicular to A (B and C), respectively. Where A, B, and C are
defined as:
A = 0.4miR2 + 0.4mcR 2 (A.11)
156
B = C = A + a2 mPmC (A.12)
mp + m
Despite these small differences the precession constant, H, which is defined as:
H = (A. 13)
2C
is the same for both the values presented in Dobrovolskis et al. (1997) and Stern et al. (2015).
The precession constant is a dimensionless measure of the planets oblateness used to predict
long-term behavior, for Pluto it is determined mostly by the large aspect ratio of the system
(thus was accurate before other parameters of the system were well known). From H we can
calculate a using equation 2 in Dobro:
= 3 2 (1 - e2 )- 3/ 2 H (A.14)2 N
where n is Pluto's orbital mean motion around the sun and N is Pluto's rotation rate (or
Charon's mean motion rate). Alpha then gives us the change in Pluto's obliquity (0) and
angular momentum vector (q) over time using Dobro's equations 13 and 14:
do - siniCos + sin# 
-" (A.15)
dt dt .dt
= -a cos o - cosi d + sin i sin # cot 0 + cos # cot d (A.16)dt (dt dt (dt
where i is the inclination and Q is the longitude of the ascending node. From here Dobro
converts to cartesian coordinates (to make integrating more efficient). The derivatives in
cartesian coordinates (according to Dobro's equations 16, 17, and 18) are:
dX = aY Z Y Cos i Zsini d (A.17)
dt y dt -s dt
( ) = -CXZ - X cos i )+ Z (di) (A.18)
dt (dt dt
157
(dZ\ .Cd
= Xsini - Y(di) (A.19)
Sdt )(dt dt
By integrating and then using equation Dobro's equation 20 (Equation A.7 above) and
equation 19 (0 = 115.50 + 11.8 sin #) we get Dobro's equation 21(A.9 above), 22 (Y =
0.884 sin(19.50 + 130.2't) - 0.088), and 23 (equations A.8 above). Pluto's eccentricity, and
Pluto and Charon's orbital mean motions were well known at the time of Dobro's calcu-
lations, and updates to the system's parameters provided by Stern et al. (2015) have not
changed the value of H thus changes to alpha and the dependent equations above are negli-
gible. Furthermore since we are looking at long term trends, tiny variations in the orbit (if
they occurred) would not have a significant impact on our results.
158
Appendix B
Detailed Exploration of the Trade
Space for Measuring Surface Activity
Before designing the "Smart Marbles" concept described in Chapter 7, we considered several
alternative architectures to try to search for signs of tidally induced seismic activity dur-
ing Apophis' close approach to Earth. In addition to considering the scientific potential of
each concept we also considered factors such as risk, cost, technology readiness level (TRL),
and whether or not the date rate was manageable. We employed NASA's standards for
determining the technology readiness level of each concept (Figure B.1). Most of the op-
tions we considered already had heritage and a TRL of 9, however we also considered some
other technologies that are still early in their development and yet to be space flown. Our
assessment of risk encompassed factors including success of previous missions using similar
technology, the level of difficulty associated with operating the instrumentation (and landing
if applicable), and the likelihood and science impact of component failures.
Through this analysis and consideration of the entire trade space for measuring surface
activity, we ultimately determined that "Smart Marbles" warranted further development
because of their high scientific potential in a low cost, low risk package.
159
TRL 9
-Actual system "flight provenM through successful mission operations
TRL 8
eActual system completed and 'flight qualified' through test and
denmuntration (ground or space)
TRL 7fSystem prototype demonstration in a space environment
TRL 6
*System/subsystem model or prototype demonstration in a relevant
environment (groundor space)
TRL 5
*Component and/or breadboard validation in relevant environment
TRL4
-TR L 3
*Analytical and experimental critical function a or characteristicproof-of-
concept
Figure B. 1: NASA's Technology Readiness Level (TRL) definitions. A TRL number is
obtained once the description in the diagram has been achieved. (Image credit: NASA)
B.1 RRT/RTT
For the purpose of the SET Mission designed by the 12.43/16.83 Space Systems Engi-
neering Spring 2017 class, a Radio Reflection Tomography (RRT) instrument was selected
to measure the interior strucutre of Aphophis before and after it's close approach to the
Earth. This sort of instrument offers several advantages for measuring interior structurer
but also has limitations which ultimately lead to redefining the science mission objectives
for the SET Mission for the purposes of 12.43/16.83 Space Systems Engineering
160
RRT (Radio Reflection Tomogrpahy) and RTT (Radio Transmission Tomography) in-
struments send radio waves towards an object and then measure the reflection (RRT) or
transmission (RTT) of the waves after they have interacted with the object. Using inver-
sion and modeling techniques the received signal can be used to determine the complete
3-D interior structure of an asteroid. Simulations indicate this technique is sensitive to in-
terior cracks, void spaces and variations in composition and density of the interior for a
wide range of target structures (however it is not sensitive to whether block interstices are
void or regolith filled) (Safaeinili et al., 2002; Grimm et al., 2015). Since RRT instruments
are measuring reflections, the transmitter and receiver can both be mounted on the same
spacecraft. The simplicity and cost savings of only requiring a single spacecraft was a ma-
jor motivation in selecting an RRT instrument instead of an RTT instrument for the SET
Mission. However, it is worth acknowledging that Grimm et al. (2015) found the use of two
spacecraft and RTT capabilities has been shown to dramatically improve the recovery of
subsurface structure. That study also found that the velocity model has to be close to the
true distribution to focus the echo on the boundaries of the internal blocks (something we
will discuss more at the end of this subsection).
Both RRT and RTT instruments have successfully been flown on planetary missions
(qualifying them as TRL 9 by NASA standards). The COmet Nucleus Sounding Experi-
ment by Radio Transmission (CONSERT) instrument (RTT) on the Rosetta Mission made
use of transmitters and receivers on both the Rosetta spacecraft and the Philae lander.
Comet 67P, the target of the Rosetta Mission, has a radius of roughly ten times that of
Apophis. Propagation through the smaller lobe of the nucleus was successfully achieved and
analysis showed a decrease in the dielectric constant with depth, most likely from a decrease
in the dust-to-ice ratio or increase in porosity (Ciarletti et al., 2015). RRT instruments
have been used at Mars, including Mars Reconisicence Orbiter's (MRO) SHAllow RADar
(SHARAD) instrument and its predecessor, the Mars Advanced Radar for Subsurface and
161
Ionosphere Sounding (MARSIS) instrument on Mars Express. SHARAD made use of a wider
transmission band width to achieve higher resolution to profile subsurface ice layers down to
hundreds of meters in the Martian subsurface (Seu et al., 2007).
For the SET Mission, as described in MIT 12.43/16.83 Space Systems Engineering (2017),
an RRT instrument is planned, that will have a transmission frequency of 20MHz and a
bandwidth of 5MHz. For a reflective index similar to Itokawa this would result in a spatial
resolution of roughly 8.5m, and worst case scenario a resolution of 20m. In addition to its
proven heritage, one benefit of using an RRT instrument on a mission to Apophis is that
it is not dependent on seismic activity to determine interior structure, so in the event that
tidal forces from the Earth are not strong enough to trigger seismic events on Apophis it
will still be possible to learn about Apophis' interior structure. However, it is expected
to take about 30 days to fully map the interior of Apophis. The field-of-view, spatial and
time resolution of an RRT instrument are not sufficient to measure seismic effects from tidal
forces, thus the RRT will not be able to accomplish the same science goals as the proposed
"Smart Marbles" concept. The two would have compliment each other nicely on an Apophis
mission, since the RRT could provide interior structure information regardless of the results
of the tidal interaction and the "Smart Marbles" package can provide information about
tidal interactions, and assuming seismic activity does occur, could provide guidance for the
RRT models to focus the echo boundaries.
B.2 Imaging Options
For imaging options we consider using a high-frequency, high-resolution camera mounted
on a spacecraft like SET, as well as Earth-based radar (which can achieve higher spacial
resolution than Earth-based imaging). The obvious appeal of these options is that they do
not require any physical contact with the asteroid, making them lower cost and lower risk
than any kind of landing package. In the case of Earth-based radar observations the necessary
equipment already exists and does not require a spacecraft mission. However this option does
162
depend on the necessary facilities remaining operational until 2029 or new comparable (or
better) facilities being online by then. A high-frequency, high-resolution imaging instrument
on a mission like SET could study Apophis' surface during its close approach to Earth and
look surface changes, while it would require a spacecraft it would also be able to achieve
much higher spatial and time resolution than Earth-based radar observations.
Earth-based radar observations have already been used to constrain Apophis' shape, size,
and spin state, and Apophis will be observable from Goldstone from mid-March to mid-April
of 2029 and from Arecibo starting April 14th, 2029 (the day after Apophis' close approach to
Earth) and continuing until late-May (Brozovid et al., 2018). By transmitting using the 34m
DDS-13 antenna at Goldstone it will be possible to image Apophis to 1.875 meters/pixel in
2029 (Brozovid et al., 2018). These observations would make it possible to look for changes
in Apophis' spin state, by comparing measurement from before and after close approach,
and would be able to look for changes in Apophis' shape and surface morphology to several
meters scale. This method is also limited by its field of view, since only one side of Apophis
is visible from Earth at a time. While these observation do offer promising scientific results
(Brozovi6 et al., 2018), they can not compete with the resolution possible from spacecraft-
based imaging, and will not be able to directly measure seismic activity like "Smart Marbles".
For these reasons we find Earth-based radar to be worth while scientific pursuit, both in its
own right and as a compliment to a spacecraft mission, but it is unable to address the science
questions we plan to explore with "Smart Marbles".
A high-frequency, high-resolution imager on a mission like SET would be able to observe
Apophis' surface with higher spatial and time resolution than ground-based radar. However,
like ground based observations it is limited by its field of view, assuming a mission with a
single spacecraft it would only be able to view about half of Apophis' surface at a time (po-
tentially even less depending on the geometry of the spacecraft, asteroid, and sun). Another
major limitation of this method is the high data volume it produces. We start by estimating
the data output of an instrument with resolution and an observing cadence that would not
163
be sufficient to measure seismic activity itself, but would be able to observe its side effects,
like localized landslides, regolith sorting, and changes to shape and surface topography, in
detail. To accomplish this we would need a resolution of around 0.1 m/pixel and a CCD
of roughly 5, 000 x 5, 000 pixels to be able to image the full disc at the same time. This
estimate is based on Apophis' long axis having a lower bonds of 450 meters (Brozovi6 et al.,
2018) and assuming moderately good position knowledge and spacecraft pointing. With a
sensitivity of 8 bits/pixel each image would be 0.2 Gbits. We assume an observing cadence
of 5 images/second (given that we are only looking for the side effects of seismic activity,
not the waves themselves) over the 30 hr encounter phase of Apophis' close approach to the
Earth (which only spans the length of time the Apophis is within 1 lunar distance of the
Earth). This would produce roughly 108 Tbits of data, two orders of magnitude more than
the 3 Tbits of storage planned for the SET mission (which would also be needed to store data
from other instruments and spacecraft housekeeping data). Not only would the spacecraft
need to be able to store that much data but at some point it would need to be sent back
to Earth. Using a Ka-band communications, and assuming a downlink speed of 6 Mbps, a
reasonable estimate for a distance of 0.15 AU (Slobin, 2015), it would take more than 200
days worth of dedicated downlink time to transfer that much data to Earth. This time could
be dramatically reduced using laser communications, which could cut the downlink time to
around 100 hours, but currently have no deep space heritage (NASA, 2015). This shows
that high-frequency, high-resolution imaging options are plagued by three major challenges
(1) creating a large format CCD with fast read out times, (2) storing very large quantities
of data on the spacecraft, and (3) downlinking such a large quantity of data. In addition
to these major design challenges such an instrument would have a limited field of view and
would not be able to directly detect seismic activity, only its consequences (assuming tidal
forces are substantial enough to trigger such effects). Given the challenges associated with
designing and operating a high-frequency, high-resolution imager and the limited scientific
payoff, we chose to not pursue this option any further.
164
B.3 Lander/Rover
Among the mission architectures explored in 12.43/16.83 Space Systems Engineering
was the possibility of including a landing package or rover with a seismometer as part of the
SET Mission. While the scientific potential of such packages is promising, they tend to be
very high cost and high risk, with a less than 30% success rate for launched seismometers
(Lognonn6, 2005, and references therein). It is also difficult to couple a seismometer to a
planetary surface (Goldstein et al., 2006), adding to the cost, risk, and complexity of such
missions. Numerical computations based on the asteroid Eros show seismology can differ-
entiate interior structures in small bodies, however it requires measurements from multiple
points on the object's surface (Walker et al., 2006). In addition to not providing enough
data to infer interior structure, a single seismometer has the potential to miss events since
waves do not propagate well through regolith (Purnell, 1986) and surface changes on Apophis
are expected to be small, localized events (Yu et al., 2014; Keane and Matsuyama, 2015).
Additionally, landing anything of substantial mass on the asteroid, that could conceivably
perturb its orbit, poses political concerns given how close it comes to the Earth at regular
intervals. Anything that could increase the risk of future impacts or alter where impacts
occur would have major political, ethical, and planetary defense ramifications.
B.4 Laser Doppler Vibrometer
In addition to the heritage based options described above we also explored the possi-
bility of studying Apophis' surface during its close approach to Earth using Laser Doppler
Vibrometers, technology not yet used in spaceflight. Laser Doppler Vibrometers measure
the doppler shifts a laser beam reflected of a surface to determine the motion of the surface.
This technique is appealing for studying Apophis since it does not require physical contact
with the asteroid's surface (thus making it simpler and lower risk than landing packages)
and ideally would be able to measure seismic vibrations at several points on the asteroid's
surface (which could then be used to infer interior structure).
165
Laser Doppler Vibrometers have been developed for applications such as non-destructive
testing of aircraft parts (Kilpatrick and Markov, 2008) and buried land-mine detection (Lal
et al., 2006). However, these instruments offer a limited field-of-view (and being mounted on
the spacecraft further restricts the field-of-view to the spacecraft facing side of Apophis) and
their high sensitivity and precise nature pose serious challenges for becoming flight qualified
and successfully operating on a spacecraft. While further development of this technology
could one day make it more spaceflight compatible, given the current challenges it is unlikely
it would be ready for mission use by the mid 2020's (when an Apophis bound mission would
need to launch to observe Apophis during the 2029 close approach to Earth).
B.5 "Dumb Marbles"
In addition to the "Smart Marbles" package we also considered whether or not we could
go even simpler (and cheaper) and deploy a collection of highly reflective objects of known
mass, shape, volume, and surface friction across the surface of Apophis, without any instru-
mentation or communication capabilities. We would try to study Apophis' surface changes
and seismic activity through imaging of the "Dumb Marbles". The properties of asteroid
regolith are still not well understood and the dynamics of granular material in the small-
body gravitational environment is vital for interpreting their surface geology (Murdoch et al.,
2015). We would attempt to gain a better understanding of the surface processes on Apophis
(as well as seismic activity and thus internal structure) by deploying 10's to 100's of easily
observable test "particles" of known properties across its surface. There is some technological
precedence for this, the Hayabusa mission deployed a highly reflective target marker on the
asteroid Itokawa. However, Hayabusa's target marker served as an artificial landmark and
was used purely for navigation and spacecraft guidance purposes (Yoshimitsu et al., 2009).
The SET mission as proposed in MIT 12.43/16.83 Space Systems Engineering (2017)
will carry an instrument modeled after the LORRI instrument on New Horizons and Lucy
for its high resolution imaging. As it currently stands this is the instrument best suited
166
for monitoring the "Dumb Marbles" once they have been deployed on Apophis' surface,
thus the spatial resolution and time between LORRI images sets the limit on the spatial
and frequency resolution limits on this package. At a distance of 2 km (the spacecraft
distance planned for the surveys of Apophis' surface before and after its close approach to
Earth) LORRI will be able to observe Apophis' surface at a resolution of 0.0099 m/pixel.
However, at this distance LORRI is only able to image a fraction of Apophis' surface at a
time, thus limiting the effective spatial coverage of the hardware package. During the actual
encounter phase, the spacecraft will be in a leader-follower configuration with the asteroid
at a distance of 20 km, giving LORRI much lower spatial resolution (but better coverage).
In addition to the limited coverage and resolution, the imaging speed of LORRI is too
slow to measure seismic vibrations, it would only be capable of witnessing their effects, like
landslides. Trying to modify or replace LORRI to improve coverage, resolution, or imaging
frequency will quickly run into the same challenges encountered with high-resolution, high-
frequency imaging options (described in subsection B.2).
While there are some scientific benefits to having test "particles" of known properties
deployed on an asteroid, the limited spatial and time resolution and coverage possible with
simple "marbles" (incapable of taking their own measurements and communicating with the
parent spacecraft) makes the potential science, particularly in terms of measuring seismic
activity (and inferring internal structure), minimal. "Smart Marbles" will also serve as test
"particles" of known properties, but with the addition of accelerometers and communications
capabilities will be able to fulfill more science objectives.
167
168
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