Lorentz Covariant Theory of Precise Doppler Measurements
Abstract
The Lorentz covariant theory of precise Doppler measurements (PDM) based on the retarded Li\'enard-Wiechert solution of the Einstein equations is described. An exact solution of equations of light propagation in the field of arbitrary moving bodies, which drastically extends the range of applicability of the new theory of PDM, is obtained. An explicit formula for the gravitational shift of frequency is given in analytic form. The limiting cases of the Doppler observations in gravitational lensing and of the spacecraft's Doppler tracking are described in more detail. We also present the post-Newtonian theory of the PDM developed for searching relativistic effects in close optical binaries and massive planetary systems.
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