In this paper, we introduce a computational procedure that enables autonomous LEO laser trackers endowed with INSs to increase the current accuracy when shooting at middle distant medium-size LEO debris targets. The code is designed for the trackers to throw the targets into the atmosphere by means of ablations. In case that the targets are eclipsed to the trackers by the Earth, the motions of the trackers and targets are modeled by equations that contain post-Newtonian terms accounting for the curvature of space. Otherwise, when the approaching targets become visible for the trackers, we additionally use more accurate equations, which allow to account for the local bending of the laser beams aimed at the targets. We observe that under certain circumstances the correct shooting configurations that allow to safely and efficiently shoot down the targets, differ from the current estimations by distances that may be larger than the size of many targets. In short, this procedure enables to estimate the optimal shooting instants for any middle distant medium-size LEO debris target.
In this paper, we introduce a computational procedure that enables autonomous LEO laser trackers endowed with INSs to increase the current accuracy when shooting at middle distant medium-size LEO debris targets. The code is designed for the trackers to throw the targets into the Atmosphere by means of ablations. In case that the targets are eclipsed to the trackers by the Earth, the motions of the trackers and targets are modeled by equations that contain post-Newtonian terms accounting for the curvature of space. Otherwise, when the approaching targets become visible for the trackers, we additionally use more accurate equations, which allow to account for the local bending of the laser beams aimed at the targets. We observe that under certain circumstances the correct shooting configurations that allow to safely and efficiently shoot down the targets, differ from the current estimations by distances that may be larger than the size of many targets. In short, this procedure enables to estimate the optimal shooting instants for any middle distant medium-size LEO debris target.
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.
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