Heliotropic orbits at asteroid 99942 Apophis: Considering solar radiation pressure and zonal gravity perturbations

Heliotropic orbits are ideal for low-altitude science orbits around asteroids since they can maintain long lifetimes by balancing perturbations from the asteroid???s non-spherical gravitational field and the direct solar radiation pressure. In this study, Lagrange Planetary Equations and averaged disturbing potentials are applied to investigate the region around the asteroid Apophis where long-lifetime maintenance-free heliotropic orbits may exist. Based on both singly-averaged and constrained doubly-averaged disturbing potentials, the equations of motion in the orbital elements are derived, considering perturbations from the J2, J3, J4 term and solar radiation pressure including simple shadowing. The possible existence zones of heliotropic orbits at the asteroid Apophis (99942) are obtained with a semi-analytical method, applying the heliotropic and frozen conditions to the motion equations. In addition, consideration of the J4 term is found to diminish the maximum of a, e, i of the possible existence zones. The analysis in this paper helps us to quickly determine the distribution of possibly long-lifetime heliotropic orbits in the a-e-i space at a low computational cost.