Fuel-Equivalent Relative Orbit Element Space

This paper presents a new tool to analytically perform the guidance for reconfiguration of formation flying spacecraft. The technique consists in mapping the relative orbit elements into a fuel-equivalent space where similar displacements correspond to an equivalent fuel consumption. The minimal-fuel maneuver problem is consequently translated into a simple geometric problem in the fuel-equivalent space. The theory is applied to two well-known formations: the J2J2-invariant formation and the projected circular formation. The use of the fuel-equivalent space leads to very simple solutions for the most fuel-efficient way to attain both formations. [PUBLISHER ABSTRACT]