Forced periodic motion by solar radiation pressure in the polyhedral gravity model

The exploration of small bodies in our solar system is of great interest for the planetary science community due to their high scientific value. However, their generally weak and irregular gravity fields increase the difficulty associated with close proximity operations. Moreover, solar radiation pressure (SRP) can significantly perturb the motion of objects in their vicinity, particularly for bodies with high area-to-mass ratios. In this work, we adopt the polyhedral gravity model and identify natural dynamical structures that can be used for mission operations. Further, we study forced periodic motion in the body fixed frame while accounting for the effect of SRP with eclipses. Overall, our work seeks to identify suitable orbits and locations in the vicinity of small bodies that can be exploited for the design of science orbits. To obtain periodic orbits in the model accounting for SRP perturbations, we use a Melnikov function to find orbits that satisfy resonances with the asteroid spin and show no net change in energy over the orbit. We then use a differential correction scheme to find numerical solutions in the time-periodic model. Our test cases are potentially hazardous asteroid 101955 Bennu and main belt asteroid 16 Psyche.