Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-12-28
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
27 pages, 9 figures, submitted for publication
Scientific paper
We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions in Minkowski space-time are described in an inertial frame with the origin at the center of an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. In Minkowski space-time, there is a well known relation (see B. Coll, J. J. Ferrando and J. A. Morales-Lladosa, Class. Quantum Grav., 27, 065013, 2010) between the emission and inertial coordinates of any event. Here, this relation is implemented in a numerical code, which is tested and applied. The first application is a detailed numerical four-dimensional analysis of the so-called emission coordinate region and co-region. In a second application, a GPS (Galileo) satellite is considered as the receiver and its emission coordinates are given by four Galileo (GPS) satellites. The bifurcation problem (double localization) in the positioning of the receiver satellite is then pointed out and discussed in detail.
Puchades Neus
Saez Diego
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