Tuesday 23 August 2005

G8

PT0078
A new consistent relativistic orbitography software: SCRMI
Barriot, Jean-Pierre¹, Pireaux, Sophie¹, Rosenblatt, Pascal²
1 OMP/GRGS and OCArance, France
2 ORB, Belgium
Author email: jean-pierre.barriot@cnes.fr
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 can be furthermore error prone. In the more appropriate framework of General Relativity, we study a method to numerically integrate the native relativistic equations of motion for a weak gravitational field, taking into account not only gravitational forces, but also non-gravitational ones (atmospheric drag, solar radiation pressure, albedo pressure, thermal emission). When considering gravitational forces alone, the unperturbed satellite motion follows the geodesics of the local space-time. For the appropriate metric at the required order, the latter equations contain all the gravitational effects at the corresponding order. Indeed, computing the geodesic equations for the Geocentric Coordinate Reference System metric (IAU conventions 2000) will take into account gravitational multipole moment contributions from the central planetary gravitational potential, perturbations due to solar system bodies, the Schwarzschild, geodesic and Lense-Thirring precessions. When non-gravitational forces are present, the relativistic equation of motion generalizes to include non-gravitational forces encoded in a quadrivector. Non-gravitational forces can be treated as perturbations, in the sense that they do not modify the local structure of space-time (the metric). A sketch for a prototype software (SCRMI: Semi-Classical Relativistic Motion Integrator) is derived, with a dedicated symplectic numerical integrator.

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