Optimal Satellite Transfers Using Relative Motion Dynamics

Abstract

A first-order approximation of optimal two-burn transfers between satellite orbits within a formation is presented and discussed. The orbital transfer problem is based on the well-known fact that, to first order, such orbits are elliptic, with centers at the target or offset in the in-track direction. The methodology allows for a target in a (generally) elliptic orbit in its motion about the center of force. The solution obtained makes use of a transformation of the problem to the reference frame of an auxiliary target in circular orbit in the inertial frame. The total required |Δ v| is expressed in terms of the identifying parameters for the initial and final orbits in the formation, corresponding to their respective sizes as measured by their minor axes, location of their centers, and their orientation. This expression allows for numerical parametric studies in the case where the initial and final orbits are in the same or parallel planes. It is shown that the optimal total |Δ v| depends on the relative sizes of the orbits and the distance between their centers. When the initial and final orbits are concentric, four optimal two-burn transfers, all of the same total |Δ v|, are identified. It is further shown that the optimal |Δ v| changes with the distance between the centers of the orbits and attains a minimum when this distance is about 2.2 times the difference between the minor axes of the orbits.