A Parametric Shape Model Applied to Tracing the Migration of the Objects Near an Asteroid

In the past decades, space missions to small bodies (Galileo, OSIRIS-REx, Hayabusa, Hayabusa2, Chang'e 2, Rosetta, etc.) have enriched us greatly with voluminous new knowledge on our solar system. In situ observations by these missions have revealed the extreme complexity and remarkable diversity of the spatial environment around their target asteroids. A study on the motion of objects in such complex environments is of great importance for understanding the evolution history of surface/subsurface materials on the asteroids. Establishing a reasonable dynamic model is obviously a crucial step. This paper proposes a method for tracking the motion of an object near the surface of an arbitrary asteroid. This method combines the irregular shape, an unlimited rotational state and asymmetric gravitational field, which are three key factors that dominate the complex movement of an object on and off the asteroid's surface. The gravitational attraction and potential are computed using the polyhedral method with corrections for the possible singularities. The asteroid's surface is then approximated using a continuous and differentiable surface, and the parametric representation forms of the body are derived based on polynomial series. An event-driven scheme is designed, so that the orbital motion and surface motion are processed separately by checking the triggering events. The algorithm was implemented using C++. Benchmarking tests are organized on a local cluster, showing a satisfactory performance in both accuracy and efficiency. This method was further applied to improve the control accuracy of the landing spot of an asteroid surface lander.