Harmonic force excitation analysis of a small-body asteroid/satellite system

Abstract

A harmonic force excitation analysis is used to determine orbit stability of a small satellite around an asteroid with a complex gravitational field. Harmonic excitation phenomena occurs with both natural and man-made satellites. Jupiter influences asteroid distribution in the main asteroid belt through mean motion resonance where some regions are devoid of asteroids while other regions have an abundance. Simulations of a man-made satellite in orbit around the asteroid Itokawa, which was visited by the Hayabusa Space Mission, have also displayed harmonic excitation phenomena, including regions of high dynamic interactions. Specifically, the influence of the rate of spin of the asteroid and the stability of the orbit was investigated. The radial acceleration of the satellite is used to determine the frequency of gravitational perturbation from the asteroid on the satellite. It has been shown when the satellite is placed in an orbit away from its resonant frequency, the orbit remains stable. An early model was created to study this phenomenon and showed promise to predict regions of stability. From this initial study, further work using a more complex model and an updated harmonic force excitation analysis of the system was shown to be a more accurate predictor of orbital stability.