Constraints to a Yukawa gravitational potential from laser data to LAGEOS satellites

TL;DR

This study explores how laser-ranging data from LAGEOS satellites can set stringent limits on a hypothetical fifth force modeled by a Yukawa potential, potentially improving existing constraints significantly.

Contribution

The paper proposes a novel method combining orbital residuals of LAGEOS satellites to tighten constraints on Yukawa coupling at Earth's scale, with potential improvements from future satellite data.

Findings

Current constraints on Yukawa coupling are around |α| < 10^{-5} to 10^{-8}.

The proposed method could constrain α to 4×10^{-12} or less.

Future data from CHAMP, GRACE, and LARES could further improve these limits.

Abstract

In this paper we investigate the possibility of constraining the hypothesis of a fifth force at the length scale of two Earth's radii by investigating the effects of a Yukawa gravitational potential on the orbits of the laser--ranged LAGEOS satellites. The existing constraints on the Yukawa coupling $\alpha$, obtained by fitting the LAGEOS orbit, are of the order of | \alpha | < 10^{-5}-10^{-8} for distances of the order of 10^9 cm. Here we show that with a suitable combination of the orbital residuals of the perigee \omega of LAGEOS II and the nodes \Omega of LAGEOS II and LAGEOS it should be possible to constrain \alpha at a level of 4 X 10^{-12} or less. Various sources of systematic errors are accounted for, as well. Their total impact amounts to 1 X 10^{-11} during an observational time span of 5 years. In the near future, when the new data on the terrestrial gravitational field will be available from the CHAMP and GRACE missions, these limits will be further improved. The use of the proposed LARES laser--ranged satellite would yield an experimental accuracy in constraining \alpha of the order of 1 X 10^{-12}.