Post-Newtonian Equations for Laser Links in Space

The purpose of this article is threefold. We first show that the second-order post-Newtonian (p-N) equations for the Earth exterior Schwarzschild field introduced in this article are the equations that, unlike those of the first p-N order, allow the space-based pointing, acquisition, and tracking laser systems to substantially reduce the size of the p-N corrections to the Newtonian location from the systems of middle size targets in orbit about the Earth. To achieve this goal the trackers must be endowed with very narrow laser beams and atomic clocks. Second, we show that these corrections can be used to speed up the trackers' shooting systems in any scenario where this kind of beam may be involved. In fact, since the first step in any procedure aimed to achieve this goal is to accurately determine the ranging and shooting directions to the targets from the lines of sight, the computation of the second p-N relative orbits of the targets with respect to the trackers must be carried out in real time. Then, the solution of these equations for the target of interest can be uploaded in the closed-loop control system on board the tracker involved, in order to initiate the control process of the respective ranging and shooting direction, as well as to reinitiate it, as soon as the target ceases to be hidden for the tracker due to the Earth. Third, we to show that these equations will be very useful for autonomous trackers to carry out two demanding tasks, namely 1) to steadily maintain intersatellite optical links and 2) to perform laser ablation of middle size LEO debris objects at operative distances.