6533b870fe1ef96bd12d06ba

RESEARCH PRODUCT

Relativistic positioning: four-dimensional numerical approach in Minkowski space-time

Diego SáezNeus Puchades

subject

PhysicsInertial frame of referencebusiness.industryFOS: Physical sciencesAstronomy and AstrophysicsGeneral Relativity and Quantum Cosmology (gr-qc)GeodesyGeneral Relativity and Quantum Cosmologysymbols.namesakeSpace and Planetary ScienceAssisted GPSMinkowski spacePhysics::Space PhysicsGlobal Positioning SystemGalileo (satellite navigation)symbolsSatellitebusinessEvent (particle physics)Schwarzschild radius

description

We simulate the satellite constellations of two Global Navigation Satellite Systems: Galileo (EU) and GPS (USA). Satellite motions are described in the Schwarzschild space-time produced by an idealized spherically symmetric non rotating Earth. The trajectories are then circumferences centered at the same point as Earth. Photon motions are described in Minkowski space-time, where there is a well known relation, Coll, Ferrando & Morales-Lladosa (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.

yearjournalcountryeditionlanguage
2011-12-27
https://dx.doi.org/10.48550/arxiv.1112.6054