Frozen Orbits Under Radiation Pressure and Zonal Gravity Perturbations

Abstract

The orbital motion of spacecraft around asteroids is strongly disturbed primarily because of solar radiation pressure (SRP) and higher-order gravitational forces. To achieve stable orbits in such an environment, the implementation of frozen orbits is a promising approach. This research derives semi-analytical solutions of frozen orbits subject to SRP and zonal gravity up to the fourth order based on singly averaged Lagrange planetary equations. Moreover, the stability of frozen orbits is characterized analytically by introducing linearized variational equations, revealing the complex eigenstructures of the proposed frozen orbits. These analytical theories identify several different types of stable frozen orbits, which are further validated via high-fidelity numerical simulations. Consequently, this paper demonstrates the feasibility and intriguing dynamic characteristics of frozen orbits around asteroids.