The role of true anomaly in ballistic capture

Abstract

A massless particle may perform a ballistic capture about a primary when two or more gravitational attractions are considered. The dynamics governing the ballistic capture depend on the mutual position of the primaries, if these are let to revolve in eccentric orbits. This paper studies the effect of the primaries true anomaly on the ballistic capture about the smaller primary in the planar elliptic restricted three-body problem. The dynamics of the Hill curves are studied, and the conditions for a favorable capture are derived. It is shown that these lead to regular, quasi-stable post-capture orbits. This is confirmed by numerical simulations implementing the concept of capture set: a set of initial conditions that generates ballistic capture orbits with a prescribed stability number.