Mapping the Spacetime Metric with a Global Navigation Satellite System

A constellation of satellites moving in spacetime probe its geometry. If communication between the satellites is provided then one could extract a set of data in order to do relativistic gravimetry.

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The natural evolution of GNSS is to become more and more accurate and autonomous, with the help of very stable clocks and cross links capabilities. If relativistic coordinates are used to account for General Relativity effects, the spacetime geometry acting on the satellite constellation can be inferred solving an inverse problem [1].

The ACT started an Ariadna Project in collaboration with the University of Ljubljana to study the feasability of doing relativistic gravimetry. The aim of this study is to simulate the data generated by a GNSS in an ideal framework, the Schwarzschild geometry, and to assess the influence of non gravitational perturbations (clock noise, ...) on the relativistic coordinates. To know more about the project read the study description.

In order to simulate the set of data delivered by a GNSS one has to solve the time transfer problem between the satellite. In a preliminary study, the ACT studied three methods in order to solve the time transfer problem [2].

References

1. Tarantola, A., Klimes L., Pozo, J.M., and Coll, B., "Gravimetry, Relativity, and the Global Navigation Satellite Systems", Int. School on Relativistic Coordinates, Reference and Positioning Systems held at Salamanca (Spain), 2005, arXiv:gr-qc/09053798
2. Delva, P. and Olympio, J., "Mapping the Spacetime Metric with GNSS: a preliminary study", 2nd International Colloquium, Scientific and Fundamental Aspects of the Galileo Programme, COSPAR colloquium, Padua, Italy, 2009.