Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006iaujd..16e..64p&link_type=abstract
Nomenclature, Precession and New Models in Fundamental Astronomy, 26th meeting of the IAU, Joint Discussion 16, 22-23 August 200
Astronomy and Astrophysics
Astronomy
Scientific paper
Even nowadays the following mathematical result is almost unknown in spite of its fundamental importance in the construction of positioning systems. In the 4-dim Newtonian spacetime there exists 4, and only 4, causal classes of reference frames, whereas in the relativistic 4-dim Lorentzian spacetime, due to the freedom introduced by the finite propagation of light, there exists 199, and only 199, causal classes of reference frames. A causal class is defined by a frame a dual coframe and the 2-dim surfaces generated by the vectors of the frame. Only a causal class, among the 199 Lorentzian ones, is privileged to construct a generic (valid for a wide class of spacetimes), gravity free (the previous knowledge of the gravitational field is not necessary) and immediate (non retarded) positioning system, this is the causal class of the emission coordinate system. Emission coordinates are a class of space-time coordinates defined and generated by four emitters (satellites) broadcasting their proper time by means of radio signals. They are the constitutive ingredient of the simplest conceivable relativistic positioning systems. The emission coordinates are covariant (frame independent) and completely independent of any observer. Measuring the arrival time, the redshift and the angles subtended by four emitters (satellites), any observer can measure the values of the emission coordinates which give his position, the components of his 4-velocity and can obtain the metric of the spacetime (the gravitational field). The study of emission coordinates is aimed to develop an exact theory of positioning systems, based on the framework and concepts of General Relativity, as opposed to introducing `relativistic effects' in a classical Newtonian framework, which is the customary approach yet now used in the GPS and the GLONASS.
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