Measuring the relativistic perigee advance with satellite laser ranging

The pericentric advance of a test body by a central mass is one of the classical tests of general relativity. Today, this effect is measured with radar ranging by the perihelion shift of Mercury and other planets in the gravitational field of the Sun, with a relative accuracy of the order of 10⁻²–10⁻³. In this paper, we explore the possibility of a measurement of the pericentric advance in the gravitational field of Earth by analysing the laser-ranged data of some orbiting, or proposed, laser-ranged geodetic satellites. Such a measurement of the perigee advance would place limits on hypothetical, very weak, Yukawa-type components of the gravitational interaction with a finite range of the order of 10⁴ km. Thus, we show that, at the present level of knowledge of the orbital perturbations, the relative accuracy, achievable with suitably combined orbital elements of LAGEOS and LAGEOS II, is of the order of 10⁻³. With the corresponding measured value of (2 + 2γ − β)/3, by using η = 4β − γ − 3 from lunar laser ranging, we could get an estimate of the PPN parameters γ and β with an accuracy of the order of 10⁻²–10⁻³. Nevertheless, these accuracies would be substantially improved in the near future with the new Earth gravity field models by the CHAMP and GRACE missions. The use of the perigee of LARES (LAser RElativity Satellite), with a suitable combination of orbital residuals including also the node and the perigee of LAGEOS II, would also further improve the accuracy of the proposed measurement.