A Parametric Shape Model Applied to Tracing the Migration of the Objects
Near an Asteroid
Abstract
In the past decades, space missions to small bodies (Galileo,
OSIRIS-REx, Hayabusa, Hayabusa2, Chang’ e 2, Rosetta, etc.) have
enriched us greatly with a lot of new knowledge on our solar system. In
situ observations of 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/sub-surface materials on the asteroids. Establishing a
reasonable dynamic model is obviously the most important 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 smooth 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 satisfying performance in both
accuracy and efficiency. And this method was also applied to motion
control of surface detectors.