A Class of Optimal Two-Impulse Rendezvous Using Multiple-Revolution Lambert Solutions

In minimum-fuel impulsive spacecraft trajectories, long-duration coast arcs between thrust impulses can occur. If the coast time is long enough to allow one or more complete revolutions of the central body, the solution becomes complicated. Lambert’s problem, the determination of the orbit that connects two specified terminal points in a specified time interval, affords multiple solutions. For a transfer time long enough to allow N revolutions of the central body there exist 2N + 1 trajectories that satisfy the boundary value problem. An algorithm based on the classical Lagrange formulation for an elliptic orbit is developed that determines all the trajectories. The procedure is applied to the problem of rendezvous with a target in the same circular orbit as the spacecraft. The minimum-fuel optimality of the two-impulse trajectory is determined using primer vector theory.