Orbital distances and options for small body satellites in Non-Keplerian orbits dominated by solar radiation pressure

Abstract

We offer a comprehensive description for the dynamics of a spacecraft affected by solar radiation pressure (SRP) orbiting a small body. Constrains are given for regions, in which stable motion is possible. For short and long time scales two different analytical frameworks are summarized and applied. (1) For time scales well below one heliocentric revolution we examine the “static” case, involving SRP fixed in both magnitude and direction. We demonstrate a closed-form solution for quasi terminator orbits using parabolic coordinates. (2) Next, we study the “dynamic” case where the asteroid is in an eccentric orbit about the Sun, involving changing solar aspect angle and distance. To solve this Augmented Hill Three-Body Problem (AH3BP), SRP effects are averaged over the anomaly of the orbiter. From this approximation we derive constrains for Sun-synchronous orbits in size and eccentricity. The findings of the analysis (1) and (2) are then applied to small- and medium-sized spacecraft orbiting specific asteroids, comets, dwarf planets and (for comparison) planets. We consider ranges of orbiter mass and surface area exposed to the Sun, as well as small body parameters, including mass and orbit. We show the resulting constrains on orbit size as well as parameters of Sun-synchronous orbits and frozen orbits in tables. While terminator orbits may only vary in size, quasi terminator orbits can cover wide regions best described in the parabolic coordinates of case (1). This region has four parameters for our orbit options. As alternative application for orbit stability we calculate constraints on orbit and particle sizes for dust particles. Numerical integration is used to validate the resilience of these solutions to further perturbation by third bodies or the small body's non-spherical shape. • We estimated orbital distances for spacecrafts in Sun-synchronous orbits around 9 small bodies. • Orbital shapes deviate greatly from Keplerian conic sections due to solar radiation pressure. • Quasi-terminator orbit dynamics are confined and described by up to four parabolas. • For orbiting dust a frozen state is assumed, limits to orbital sizes are given. • Numeric simulations add perturbing effects and validate predictions about orbit stability.