The inverse problem of estimating the gravitational time dilation
- Authors: Gusev A.V.1, Litvinov D.A.1,2,3, Rudenko V.N.1
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Affiliations:
- Sternberg Astronomical Institute
- Astrospace Center, Lebedev Physical Institute
- Bauman Moscow State Technical University
- Issue: Vol 123, No 5 (2016)
- Pages: 814-821
- Section: Nuclei, Particles, Fields, Gravitation, and Astrophysics
- URL: https://journals.rcsi.science/1063-7761/article/view/190974
- DOI: https://doi.org/10.1134/S1063776116110261
- ID: 190974
Cite item
Abstract
Precise testing of the gravitational time dilation effect suggests comparing the clocks at points with different gravitational potentials. Such a configuration arises when radio frequency standards are installed at orbital and ground stations. The ground-based standard is accessible directly, while the spaceborne one is accessible only via the electromagnetic signal exchange. Reconstructing the current frequency of the spaceborne standard is an ill-posed inverse problem whose solution depends significantly on the characteristics of the stochastic electromagnetic background. The solution for Gaussian noise is known, but the nature of the standards themselves is associated with nonstationary fluctuations of a wide class of distributions. A solution is proposed for a background of flicker fluctuations with a spectrum (1/f)γ, where 1 < γ < 3, and stationary increments. The results include formulas for the error in reconstructing the frequency of the spaceborne standard and numerical estimates for the accuracy of measuring the relativistic redshift effect.
About the authors
A. V. Gusev
Sternberg Astronomical Institute
Author for correspondence.
Email: avg@sai.msu.ru
Russian Federation, Universitetskii pr. 13, Moscow, 119991
D. A. Litvinov
Sternberg Astronomical Institute; Astrospace Center, Lebedev Physical Institute; Bauman Moscow State Technical University
Email: avg@sai.msu.ru
Russian Federation, Universitetskii pr. 13, Moscow, 119991; Profsoyuznaya ul. 84/32, Moscow, 117997; 2-ya Baumanskaya ul. 5, Moscow, 105005
V. N. Rudenko
Sternberg Astronomical Institute
Email: avg@sai.msu.ru
Russian Federation, Universitetskii pr. 13, Moscow, 119991
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