Mass ratios in stellar triple systems that admit horseshoe orbits

Abstract

We examine possible configurations of stellar triple systems that give rise to "horseshoe orbits" in the smallest body. Several configurations are tested according to the initial parameters of mass for each of three bodies and position and velocity for the smallest body. The masses are arranged hierarchically, so as to mimic systems like Sun- Jupiter-Trojan. For a mass ratio of 1:10-4:10-8 known to produce horseshoe orbits, a grid search was performed on position and velocity of the small body to determine admissible initial conditions. Then, a strongly suitable initial condition was chosen to run another grid search on masses of the middle and small bodies. Choosing a criterion for stability of horseshoe orbits-given that they all decay-produced a timescale for stability, with (numerical) functional dependences on the middle and smaller masses. Fitting a power law for each resulted in exponents of k1, = -1.006 ± 0.006 and k2 = -1.047 ± 0.005 respectively, which we compare to related results from Murray & Dermott (1981a).