Algebraic Approach to the Minimum-Cost Multi-Impulse Orbit-Transfer Problem

Abstract

A purely algebraic formulation (i.e., polynomial equations only) of the minimum-cost multi-impulse orbit-transfer problem without time constraints is presented, while keeping all the variables with a precise physical meaning. General algebraic techniques are applied to solve these equations (resultants, Gröbner bases, etc.) in several situations of practical interest of different degrees of generality. For instance, a proof of the optimality of the Hohmann transfer for the minimum-fuel two-impulse circular-to-circular orbit-transfer problem is provided. Finally, a general formula is also provided for the optimal two-impulse in-plane transfer between two rotated elliptical orbits under a mild symmetry assumption on the two points where the impulses are applied (which, it is conjectured, can be removed).