Numerical Investigations of Non-equal Mass and Non-equal Spacing Packing of Planetary Bodies

Zhixing Liu
2022 Zenodo  
The optimal packing of non-equally massed and non-equally spaced multi-planet systems through numerical N-body simulations are studied and the recent results will be presented. Previous studies have generally assumed that a system of equal mass planets will be optimally packed if they are also equally spaced, i.e., if the semi-major axis ratios between planet pairs is a constant. We explicitly test this assumption by obtaining the stability timescales of 5-planet systems around a Sun-like star
more » ... with masses varying from 3 Earth masses to 3 Jupiter masses) with increasing degrees of non-uniform-spacing represented by the parameter 0 < k < 1. For planets with equal masses, a value of k = 1 corresponds to equal spacing, whereas a value of k < 1 leads to the inner planets being more widely spaced than outer planets. We study the optimal value of k for optimal planet packing (i.e., longest stability time) under both equal mass and non-equal mass scenarios and find evidence that k = 1 may not be optimal under all scenarios and. We also find system stability will decrease with the increase of mass variation. The role that distance to mean-motion resonances (MMRs) and Fourier analysis of complex eccentricity play in determining the configurations of optimal planet packing will also be demonstrated. The distinction of different exponents and different mass variation in system stability is potentially explained by their MMR distributions and complex eccentricity frequency. The graph illustrations for both cases will also be presented.
doi:10.5281/zenodo.6965438 fatcat:jbpp7w6o4rd5xdhcq2hvcvcnii