Positioning systems in Minkowski space-time: emission and observational data

Details Positioning systems in Minkowski space-time: emission and observational data Positioning systems in Minkowski space-time: emission and observational data

2012-04-10

arxiv.org/abs/1204.2241v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, 7 figures

Scientific paper

The determination of the inertial coordinates of a user is considered in the framework of relativistic positioning systems in Minkowski space-time. For this task, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user need to know {\em independently} the orientation of his emission coordinates. Assuming that the user may observe the relative positions of the four emitters on his celestial sphere, an observational rule to determine this orientation is presented. The indetermination in the location of a pair of different events receiving the same emission coordinates (bifurcation problem) is thus solved by applying this observational rule and, consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system (location problem).

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