P. Rosenblatt
نویسندگان
چکیده
(SC)RMI: A (S)emi-(C)lassical (R)elativistic (M)otion (I)integrator, to model the orbits of space probes around the Earth and other planets Abstract Today, the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called relativistic corrections, computed with the required precision using the Post-(Post-) Newtonian formalism. The current approach, with the increase of tracking precision (Ka-Band Doppler, interplanetary lasers) and clock stabilities (atomic fountains) is reaching its limits in terms of complexity, and is furthermore error prone. In the appropriate framework of General Relativity, we study a method to numerically integrate the native relativistic equations of motion for a weak gravitational field, also taking into account small non-gravitational forces. The latter are treated as perturbations, in the sense that we assume that both the local structure of space-time is not modified by these forces, and that the unperturbed satellite motion follows the geodesics of the local space-time. The use of a symplectic inte-grator to compute the unperturbed geodesic motion insures the constancy of the norm of the proper velocity quadrivector. We further show how this general relativistic framework relates to the classical one. 1 1 The classical approach: GINS In today's planetary orbitography softwares, as in GINS (Géodésie par Intégrations Numériques Simultanées, developed by CNES 1 and GRGS 2), the motion of spacecrafts is still described according to the classical Newtonian equations plus the so-called " relativistic corrections " , computed with the required precision using the Post-(Post-) Newtonian formalism. Hence, it is the 3-dimensional acceleration vector (i = 1, 2, 3), which is numerically integrated with respect to coordinate time T ,
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تاریخ انتشار 2006