Non-linear Post-Newtonian Equations for the Motion of Designated Targets with Respect to Space Based APT Laser Systems

The equations introduced in this paper are aimed to gain accuracy in the determination of the motion of middle size space objects with respect to space based APT laser systems; therefore, they can be used for these systems to engage cataloged space debris objects whose size ranges between 1 and 10 cm. The equations are derived under the assumption that the framework of the Earth surrounding space is post-Newtonian and, unlike the standard p-N equations, they are valid for distant targets. Further, their time validity is also substantially larger than that of the standard equations. The reason is that they include non-linear terms that model the Earth tidal potential along the lines joining the systems and the targets. The equations are derived in local Cartesian orbital coordinates; therefore, they are primarily adapted for use with inertial-guided systems.