How the orbital period of a test particle is modified by the Dvali-Gabadadze-Porrati gravity?

TL;DR

This paper investigates how Dvali-Gabadadze-Porrati gravity modifies the orbital period and mean motion of a test particle, providing theoretical corrections and comparing them with current observational accuracy.

Contribution

It derives the specific modifications to orbital period and mean motion caused by Dvali-Gabadadze-Porrati gravity, highlighting their dependence on system parameters and observational prospects.

Findings

Correction to mean motion is about 2×10^-3 arcseconds per century.

Current observational accuracy is 10^-2 to 5×10^-3 arcseconds per century.

Future spacecraft data may improve detection of these modifications.

Abstract

In addition to the pericentre \omega, the mean anomaly M and, thus, the mean longitude \lambda, also the orbital period Pb and the mean motion $n$ of a test particle are modified by the Dvali-Gabadadze-Porrati gravity. While the correction to Pb depends on the mass of the central body and on the geometrical features of the orbital motion around it, the correction to $n$ is independent of them, up to terms of second order in the eccentricity $e$. The latter one amounts to about 2\times 10^-3 arcseconds per century. The present-day accuracy in determining the mean motions of the inner planets of the Solar System from radar ranging and differential Very Long Baseline Interferometry is 10^-2-5\times 10^-3 arcseconds per century, but it should be improved in the near future when the data from the spacecraft to Mercury and Venus will be available.