The Restricted Hill Full 4-Body Problem: application to spacecraft motion about binary asteroids

The Restricted Hill Full 4-Body Problem (RHF4BP) models the motion of a spacecraft or particle about two mutually orbiting distributed bodies in the tidal gravity field of a larger body. The practical application of this problem is to the motion of a spacecraft or particle about a binary asteroid system. Current estimates are that up to 16% of near-Earth asteroids (NEAs) may be binary asteroids, thus this is an extremely relevant topic for future missions to NEAs. It is also an interesting topic from an academic point of view, as this problem integrates four classical problems of astrodynamics: the Hill problem, the restricted 3-body problem, the non-spherical orbiter problem, and the full 2-body problem. In this paper, we define the RHF4BP in terms of these classical models and present results that the RHF4BP inherits from these classical problems. Some initial steps towards the analysis of this problem are also given, relating to the stability of motion about the Lagrange points in the Restricted Full 3-Body Problem and the Restricted Hill 4-Body Problem, both one-stage simplifications of the RHF4BP.