Relativistic Reductions in Distance Measurements between Spacecraft with Picometer Accuracy

A near-Earth gravity experiment is considered in which a pair of satellites exchange laser signals. As a concrete example, numerical estimates were made using the satellite configuration in the GRACE-FO mission. An expression for the signal phase is obtained, which provides an accuracy of 1 picometer (pm) when calculating the distance between satellites. The influence of all significant gravitational effects on the signal propagation, such as the gravimagnetic field of the Earth and the tidal fields of the Sun and Moon, is considered. Special attention is paid to the study of the contributions of the Earth’s potential harmonics. Phase perturbations of the first and second orders are considered, and it is shown that the effect of the second-order corrections lies beyond the accuracy of 1 pm. This makes it possible to express the signal phase in a fairly compact form.