A set of orbital elements to fully represent the zonal harmonics around an oblate celestial body
Name
2010.12722.pdf
Description
Submitted version
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609.13 KB
Format
Adobe PDF
Checksum (MD5)
66fb1645f416d4add904847252df33e7
Author(s)
Arnas, David
Linares, Richard
Date Issued
2021
Journal
Monthly Notices of the Royal Astronomical Society
Publisher
Oxford University Press (OUP)
Citation
Arnas, David and Linares, Richard. 2021. "A set of orbital elements to fully represent the zonal harmonics around an oblate celestial body." Monthly Notices of the Royal Astronomical Society, 502 (3).
Version
Original manuscript
Abstract
ABSTRACT
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a linear system for the unperturbed problem and, in addition, a completely polynomial system when considering the perturbation produced by the zonal harmonics from the gravitational force of an oblate celestial body. These orbital elements present no singularities and are able to represent any kind of orbit, including elliptic, parabolic, and hyperbolic orbits. Moreover, an application to this formulation of the Poincaré–Lindstedt perturbation method is included to obtain an approximate first-order solution of the problem for the case of the J2 perturbation, showing the performance of the methodology for different kinds of orbits.
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a linear system for the unperturbed problem and, in addition, a completely polynomial system when considering the perturbation produced by the zonal harmonics from the gravitational force of an oblate celestial body. These orbital elements present no singularities and are able to represent any kind of orbit, including elliptic, parabolic, and hyperbolic orbits. Moreover, an application to this formulation of the Poincaré–Lindstedt perturbation method is included to obtain an approximate first-order solution of the problem for the case of the J2 perturbation, showing the performance of the methodology for different kinds of orbits.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/MNRAS/STAA4040
