Simple solution to optimal cotangential transfer between coplanar elliptic orbits

The aim of this paper is to propose a semi-analytical method for the analysis of a two-impulse transfer between two coplanar elliptic orbits, assuming each maneuver to change the magnitude of the spacecraft velocity only, without affecting its direction. Using a recent mathematical model that describes the spacecraft dynamics in a compact analytical form within a two-dimensional multiple-impulse scenario, this work proposes an algorithm to calculate the global minimum velocity variation required to complete the transfer. The characteristics of the optimal transfer trajectory, which is tangent to both the parking and the target orbit, are obtained as a function of a single variable, which defines the angular position of the first maneuver. This feature allows the designer to analyze the cotangential transfer in a parametric form, thus obtaining a trade-off solution between the total velocity variation and the desired characteristics of the transfer orbit.