On the possibility of testing the Weak Equivalence Principle with artificial Earth satellites

TL;DR

This paper explores testing the weak equivalence principle using pairs of artificial Earth satellites with similar orbits, estimating achievable accuracy around 10^-10, limited by orbital injection errors.

Contribution

It analyzes the feasibility and accuracy limits of testing the weak equivalence principle with satellite pairs in identical orbits, considering current and future measurement capabilities.

Findings

Accuracy limited to about 10^-10 due to orbital injection errors.

Current Earth-based tests achieve about 10^-13 accuracy.

Future space missions aim for 10^-15 to 10^-18 precision.

Abstract

In this paper we examine the possibility of testing the equivalence principle, in its weak form, by analyzing the orbital motion of a pair of artificial satellites of different composition moving along orbits of identical shape and size in the gravitational field of Earth. It turns out that the obtainable level of accuracy is, realistically, of the order of 10^-10 or slightly better. It is limited mainly by the fact that, due to the unavoidable orbital injection errors, it would not be possible to insert the satellites in orbits with exactly the same radius and that such difference could be known only with a finite precision. The present-day level of accuracy, obtained with torsion balance Earth-based measurements and the analysis of Earth-Moon motion in the gravitational field of Sun with the Lunar Laser Ranging technique, is of the order of 10^-13. The proposed space-based missions STEP, \muSCOPE, GG and SEE aim to reach a 10^-15-10^-18 precision level.