Analytical Solutions for Impulsive Elliptic Out-of-Plane Rendezvous Problem via Primer Vector Theory

This paper focuses on the fixed-time minimum-fuel out-of-plane (OOP) rendezvous between close elliptic orbits of an active spacecraft, with a passive target spacecraft, assuming a linear impulsive setting. It is shown that the OOP elliptic relative dynamics are simple enough to allow for an analytical solution of the problem reviewed. Indeed, the approach relies on the primer vector theory by writing down and directly solving the optimality necessary conditions. After analyzing the characteristics of the dynamics of the optimal primer vector candidates, the complete analytical optimal solution is obtained for arbitrary durations of the rendezvous and arbitrary boundary conditions.