Relativistic Reductions in Precision Measurements of the Earth’s Gravitational Field Using Low-Orbit Spacecraft

The advancement of space technology opens new perspectives in developing high-resolution models of the Earth’s gravitational field. The use of a precision laser interferometric system requires taking relativistic effects in the inter-satellite ranging within the satellite constellation into account. The main quantity measured by the laser system is the phase incursion of the laser beam when passing a double one-way range between the satellites. A solution for the relativistic phase is obtained that considers not only the usual Shapiro term but also the contribution of the quadrupole term to distributions of the Earth’s mass, the Earth’s spin, and tidal gravitational fields caused by the gravitational potentials of the outer bodies of the Solar System. Relativistic reduction terms are estimated at the accuracy level of ∼1 nm, which fully satisfies the accuracy of precision measurements in the two-spacecraft formation. It will be necessary to take the relativistic effects of the next order of smallness into account in the next-generation gravitational twin missions.