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J. Gambi, M. Garcia del Pino, J. Mosser, E. Weinmüller:
"Numerical simulation of post-Newtonian ECI equations for orbital motion";
in: "ASC Report 40/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 37.

This paper presents an extension of the work puplished in [1] and [2]. The purpose of this paper is to show that the equations for relative motions derived from two families of post-Newtonian equations presented here, allow to increase the acquisition, poin-ting and tracking (APT) accuracy when compared to the Newtonian equations aiming at describing free-space laser communications between Low Earth Orbit (LEO) satellites, so as between LEO and Medium Earth Orbit (MEO), and Geostationary Earth Orbit (GEO) satellites. The equations discussed in this work are similar, but not equivalent to those proposed for space debris removal, i.e. in the context of space-based systems to throw middle size LEO debris objects into the atmosphere via laser ablation in [3]. In fact, the present equations are computationally much more affordable because the aim is now less demanding, and so they result from subtractions within each post-Newtonian system pro-vided here. Consequently, these equations are used to carry out a performance analysis of a numerical procedure based on the Dormand-Prince method for initial value problems in ordinary differential equations. This procedure provides preliminary post-Newtonian correc-tions to the Newtonian trajectories of middle-size space objects with respect to space-based APT laser systems and it proves to be highly efficient. In fact, we can show that running the standard adaptive ode45 Matlab routine with the absolute and relative tolerance, T OLa = 10−16 and T OLr = 10−13, respectively, provides corrections that are final within the eclipses caused by the Earth and close to final during the non-eclipse phases. These corrections should be taken into account to increase the pointing accuracy in implementing the space-to-space laser links required for ablation of designated objects or communications between space terminals.

http://www.asc.tuwien.ac.at/preprint/2020/asc40x2020.pdf