Dynamical orbital effects of General Relativity on the satellite-to-satellite range and range-rate in the GRACE mission: a sensitivity analysis

TL;DR

This study numerically assesses the impact of General Relativity on satellite range and range-rate measurements in the GRACE mission, highlighting the magnitude of relativistic effects and their potential to influence Earth's gravity models.

Contribution

It provides a detailed numerical sensitivity analysis of GTR effects on satellite measurements, including their magnitude and potential impact on gravity field estimations.

Findings

GTR effects cause range shifts of 80 to 6000 micrometers.

Range-rate effects are up to 0.012 micrometers per second.

Relativistic effects could bias Earth's gravity models if unaccounted for.

Abstract

We numerically investigate the impact of GTR on the orbital part of the satellite-to-satellite range \rho and range-rate \dot\rho of the twin GRACE A/B spacecrafts through their dynamical equations of motion integrated in an Earth-centered frame over a time span \Delta t=1 d. Instead, the GTR effects connected with the propagation of the electromagnetic waves linking the spacecrafts are neglected. The present-day accuracies in measuring the GRACE biased range and range-rate are \sigma_\rho\sim 1-10 \mum, \sigma_\dot\rho\sim 0.1-1 \mum s^-1; studies for a follow-on of such a mission points toward a range-rate accuracy of the order of \sigma_\dot\rho\sim 1 nm s^-1 or better. The GTR range and range-rate effects turn out to be \Delta\rho=80 \mum and \Delta\dot\rho=0.012 \mum s^-1 (Lense-Thirring), and \Delta\rho=6000 \mum and \Delta\dot\rho=10 \mum s^-1 (Schwarzschild). We also compute the dynamical range and range-rate perturbations caused by the first six zonal harmonic coefficients J_L, L=2,3,4,5,6,7 of the classical multipolar expansion of the terrestrial gravitational potential in order to evaluate their aliasing impact on the relativistic effects. Conversely, we also quantitatively, and preliminarily, assess the possible a-priori \virg{imprinting} of GTR itself, not solved-for in all the GRACE-based Earth's gravity models produced so far, on the estimated values of the low degree zonals of the geopotential. The present sensitivity analysis can also be extended, in principle, to different orbital configurations in order to design a suitable dedicated mission able to accurately measure the relativistic effects considered.