Authors: S. Pireaux (Observatoire Royal de Belgique, Department 1, Brussels, Belgium), B. Chauvineau (Observatoire de la Cote d'Azur, Department ARTEMIS, Grasse, France)
Date: 23 Jan 2008
Abstract: The Relativistic Motion Integrator (RMI) consists in integrating numerically the EXACT relativistic equations of motion, with respect to the appropriate gravitational metric, instead of Newtonian equations plus relativistic corrections. The aim of the present paper is to validate the method, and to illustrate how RMI can be used for space missions to produce relativistic ephemerides of satellites. Indeed, nowadays, relativistic effects have to be taken into account, and comparing a RMI ephemeris with a classical keplerian one helps to quantify such effects.
LISA is a relevant example to use RMI. This mission is an interferometer formed by three spacecraft which aims at the detection of gravitational waves. Precise ephemerides of LISA spacecraft are needed not only for the sake of the orbitography but also to compute the photon flight time in laser links between spacecraft, required in LISA data pre-processing in order to reach the gravitational wave detection level.
Relativistic effects in LISA orbitography needed to be considered and quantified. Using RMI, we show that the numerical classical model for LISA orbits in the gravitational field of a non-rotating spherical Sun without planets can be wrong, with respect to the numerical relativisitic version of the same model, by as much as about 9 km in radial distance during a year and up to 59 km in along track distance after a year… with consequences on estimated photon flight times.
We validated RMI numerical results with an analytical developpement. Finally, the RMI relativistic numerical approach is soon more efficient than the analytical development. Moreover, RMI can be applied to other space missions.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis