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Two systems of Earth-centered inertial Newtonian orbital equations for a spherical Earth and three systems of post-Newtonian nonlinear equations, derived from the second post-Newtonian approximation to the Earth Schwarzschild field, 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 corrections to the Newtonian trajectories of middle-size space objects with respect to space-based acquisition, pointing, and tracking laser systems, and it turns out to be highly efficient. In fact, we can show that running the standard adaptive ode45 MATLAB routine with the absolute and relative tolerance, TOLa=10(-16) and TOLr=10(-13), respectively, provides corrections that are final within the eclipses caused by the Earth and close to final during the noneclipse 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.