The inverse problem of estimating the gravitational time dilation


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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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