Spacecraft Dynamics near a Binary Asteroid

We study a simple model for an asteroid pair, namely a planar system consisting of a rigid body and a sphere. This model is interesting because it is one of the simplest that captures the coupling between rotational and translational dynamics. By assuming that the binary is in a relative equilibria of the system, we construct a model for the motion of a spacecraft about this asteroid pair without affecting its motion (that is, we consider a restricted problem). This model can be studied as a perturbation of the standard Restricted Three Body Problem (RTBP). We use the stable zones near the triangular relative equilibrium points of the binary and a normal form of the Hamiltonian to compute stable periodic and quasi-periodic orbits for the spacecraft, which enable it to observe the binary while the binary orbits around the Sun.