Measuring the relativistic perigee advance with Satellite Laser Ranging

TL;DR

This paper investigates measuring the relativistic perigee advance around Earth using Satellite Laser Ranging data from existing and future geodetic satellites, aiming to test General Relativity with improved precision.

Contribution

It proposes a method to measure the gravitoelectric perigee advance using satellite laser ranging data, including upcoming satellite missions, to enhance tests of General Relativity.

Findings

Current measurement precision is about 10^-3 with LAGEOS satellites.

Future data from CHAMP and GRACE will improve accuracy.

Using LARES satellite could further refine the measurement.

Abstract

One of the most famous classical tests of General Relativity is the gravitoelectric secular advance of the pericenter of a test body in the gravitational field of a central mass. In this paper we explore the possibility of performing a measurement of the gravitoelectric pericenter advance in the gravitational field of the Earth by analyzing the laser-ranged data to some existing, or proposed, laser-ranged geodetic satellites. At the present level of knowledge of various error sources, the relative precision obtainable with the data from LAGEOS and LAGEOS II, suitably combined, is of the order of $10^{\rm -3}$. Nevertheless, these accuracies could sensibly be improved in the near future when the new data on the terrestrial gravitational field from the CHAMP and GRACE missions will be available. The use of the perigee of LARES (LAser RElativity Satellite), in the context of a suitable combination of orbital residuals including also LAGEOS II, should further raise the precision of the measurement. As a secondary outcome of the proposed experiment, with the so obtained value of $\ppn$ and with $\et=4\beta-\gamma-3$ from Lunar Laser Ranging it could be possible to obtain an estimate of the PPN parameters $\gamma$ and $\beta$ at the $10^{-2}-10^{-3}$ level.