From emission to inertial coordinates: a numerical approach

Neus Puchades and Diego Sáez

We simulate satellite constellations similar to those of GPS and Galileo global positioning systems. At any time, all the satellite positions are calculated with respect to an inertial frame centered in Earth; thus we can easily know if a given satellite is visible from the Earth surface. We numerically implement the relation (in Minkowski space-time) found by B. Coll, J.J. Ferrando and J.A. Morales (Class. Quantum Grav. 27, 2010, 065013) between the inertial coordinates of the receiver and the emission coordinates. The orientation criterion described by the same authors (talk by J.A. Morales in this meeting) has been also implemented. The code has been appropiately tested and then it has been applied to study: the structure of the so-called emission co-region, the relative errors in the inertial coordinates due to uncertanties in satellite positions, and other subjects which are hard to be studied without numerical calculations.