Velocity matching technique revisited

A new approach to the velocity matching problem is presented which provides a way to find all possible transfer orbits when two fixed impulses of constant attitude burns, a parking orbit, and a mission orbit are given. In the proposed approach, the region of validity of all possible solutions is defined by a selected set of independent variables that satisfy the necessary conditions. Uncertainties of the initial guesses of the independent variables are eliminated, iterations for specific solutions or solutions of a given family become straightforward, and converged solutions are guaranteed. The method is illustrated by an example involving a 12-hour elliptical mission orbit. The method is particularly useful for the solid Inertial Upper Stage of the Space Transportation System.