Post-Newtonian corrections to the Newtonian predictions for the motion of designated targets with respect to space based APT laser systems

Abstract

Numerical experiments are carried out to validate the short/long term differences between the solutions of the Newtonian equations for the relative motion of middle size targets in space with respect to space based APT systems and the respective solutions of a system of non-linear post-Newtonian equations. This system has been introduced in the ECMI 2016 contribution Non-linear post-Newtonian equations for the motion of designated targets with respect to space based APT laser systems . Two auxiliary systems of post-Newtonian equations are used to carry out the validation. The simulations are made under the following assumptions: (i) the structures of the Earth surrounding space are respectively the Euclidean and that of the post-Newtonian approximation to the exterior Schwarzschild field; (ii) the tar- gets are on equatorial circular orbits, and (iii) the APT systems are ECI oriented inertial-guided systems placed onboard HEO, MEO and LEO satellites in equatorial orbits about the Earth. The APT systems have initially been placed at short and successively increasing distances from targets.