Capability of satellite-aided ballistic capture

Abstract

In this paper we study a special instance of ballistic capture dynamics: the case in which the capture orbit about a planet experiences a close passage to one or more of its natural satellites. The capability of the satellites in improving ballistic capture is assessed. The dynamical framework considers at least the gravitational attractions of the Sun, the planet, and its satellites, all acting on a massless particle. The effect of the satellites is introduced explicitly by modifying a previously developed method, which relies on three-dimensional stable sets and n-body dynamics with precise ephemeris. Once a stability criterium is defined, initial conditions defined over a computational grid are integrated forward and backward. This allows us to classify orbits into different sets. Ballistic capture orbits with prescribed features are generated by manipulating these sets. Two indices, namely the hyperbolic velocity and the stability index, are used to assess the performance of pre- and post-capture portions, respectively. A Pareto frontier is used to extract orbits of practical interest. Case studies are performed in the context of Earth and Jupiter environments. Comparing to the situation with no moons, the satellite-aided ballistic capture can evidently increase the pre-capture energy and post-capture stability, so making it possible to have permanent capture of a particle at zero-cost. This is a desirable feature in mission design.