Is it possible to test directly General Relativity in the gravitational field of the Moon?

TL;DR

This paper evaluates the feasibility of detecting general relativistic effects, like gravitomagnetic and gravitoelectric phenomena, in the Moon's gravitational field using lunar orbiters, highlighting current limitations and future prospects.

Contribution

It provides the first detailed analysis of relativistic effects in lunar orbit, assessing their detectability with current and future lunar missions, especially SELENE.

Findings

Gravitoelectric effect is 1-2 orders of magnitude below current measurement sensitivity.

Systematic errors from lunar gravitational harmonics exceed relativistic signals by three orders of magnitude.

Future lunar missions could potentially measure relativistic effects with improved accuracy.

Abstract

In this paper the possibility of measuring some general relativistic effects in the gravitational field of the Moon via selenodetic missions, with particular emphasis to the future Japanese SELENE mission, is investigated. For a typical selenodetic orbital configuration the post-Newtonian Lense-Thirring gravitomagnetic and the Einstein's gravitoelectric effects on the satellites orbits are calculated and compared to the present-day orbit accuracy of lunar missions. It turns out that for SELENE's Main Orbiter, at present, the gravitoelectric periselenium shift, which is the largest general relativistic effect, is 1 or 2 orders of magnitude smaller than the experimental sensitivity. The systematic error induced by the mismodelled classical periselenium precession due to the first even zonal harmonic J2 of the Moon's non-spherical gravitational potential is 3 orders of magnitude larger than the general relativistic gravitoelectric precession. The estimates of this work could be used for future lunar missions having as their goals relativistic measurements as well.