Constraining the Nordtvedt parameter with the BepiColombo Radioscience experiment

TL;DR

This paper assesses how uncertainties in solar system parameters affect the BepiColombo mission's ability to measure the Nordtvedt parameter, showing it can improve current constraints despite these uncertainties.

Contribution

It introduces a semi-analytic model to quantify the impact of solar system parameter uncertainties on relativistic measurements by BepiColombo.

Findings

Estimated measurement uncertainty of η is about 4.5×10⁻⁵.

Uncertainties increase the error by roughly an order of magnitude.

The experiment can improve current constraints on η by about ten times.

Abstract

BepiColombo is a joint ESA/JAXA mission to Mercury with challenging objectives regarding geophysics, geodesy and fundamental physics. The Mercury Orbiter Radioscience Experiment (MORE) is one of the on-board experiments, including three different but linked experiments: gravimetry, rotation and relativity. The aim of the relativity experiment is the measurement of the post-Newtonian parameters. Thanks to accurate tracking between Earth and spacecraft, the results are expected to be very precise. However, the outcomes of the experiment strictly depends on our "knowledge" about solar system: ephemerides, number of bodies (planets, satellites and asteroids) and their masses. In this paper we describe a semi-analytic model used to perform a covariance analysis to quantify the effects, on the relativity experiment, due to the uncertainties of solar system bodies parameters. In particular, our attention is focused on the Nordtvedt parameter $\eta$ used to parametrize the strong equivalence principle violation. After our analysis we estimated $\sigma[\eta]\lessapprox 4.5\times 10^{-5}$ which is about 1~order of magnitude larger than the "ideal" case where masses of planets and asteroids have no errors. The current value, obtained from ground based experiments and lunar laser ranging measurements, is $\sigma[\eta]\approx 4.4\times 10^{-4}$. Therefore, we conclude that, even in presence of uncertainties on solar system parameters, the measurement of $\eta$ by MORE can improve the current precision of about 1~order of magnitude.