Relativity and Cosmology


Using a Syntonized Free Fall Grid of Atomic Clocks in Ehlers-Pirani-Schild Weyl Space to Derive Second Order Relativistic GNSS Redshift Terms

Authors: E.P.J. de Haas

In GNSS, the improvement of atomic clocks will lead to Phi/c^2 in relativistic gravitational redshift three to four decades from today. Research towards a relativistic positioning system capable of handling this expected accuracy is all based upon the Schwarzschild metric as a replacement of todays GNSS Euclidian-Newtonian metric. The method employed in this paper to determining frequency shifts between atomic clocks is an intermediate Minkowski-EEP approach. This approach is based on relating two atomic clocks to one another through a background ensemble of frequency gauged clocks, a grid. The crucial grid of this paper, the Free Fall Grid or FFG, can be related to the Ehlers-Pirani-Schild P-CP Weyl space formalism, when applied to a central mass. The FFG second order in Phi/c^2 redshifts are derived for static to static, static to satellite and satellite to satellite atomic oscillators and then compared to GR-Schwarzschild and PPN (Parametrized Post Newtonian) results.

Comments: 35 Pages.

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Submission history

[v1] 2017-10-17 16:05:16
[v2] 2017-10-21 03:57:54

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