Pseudo Periodic Orbit Around an Asteroid in a Circular Orbit

Abstract

This study discusses a pseudo periodic orbit that is a nearly periodic orbit around a small asteroid such as the Martian moon Deimos. By taking differences of orbital elements between the spacecraft and the asteroid as state variables, basic equations of the relative motion are derived based on Gauss' variational equations. From the basic equations, the initial state of the spacecraft to fly on the pseudo periodic orbit and its period are approximately derived. Furthermore, the stability of the pseudo periodic orbit is analytically examined from the state transition matrix of the linearized equation around the nominal orbit. Numerical studies are executed to verify the analytical results of the conditions and stability of the pseudo periodic orbit.