Extension of the proximity-quotient control law for low-thrust propulsion

In this paper, the proximity quotient control law, first developed by Petropoulos, is extended to account for both third body effects and solar radiation pressure. The perturbing effect of solar radiation pressure becomes relevant when dealing with solar sails, or large optics in space. Equations for the disturbing acceleration and disturbing potential function were derived for the perturbations, then analyzed to determine the minimum and maximum rate of changes of the Keplerian elements given the thrust vector and true anomaly of the spacecraft. These were then analytically incorporated into the Q-law feedback function. The complete mathematical derivations are presented. The extended Q-law is compared to the fully optimal control law, stemming from optimal control theory, for the same dynamical model. Two missions are used as test cases.