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

摘要

We numerically investigate the impact of GTR on the orbital part of thesatellite-to-satellite range \rho and range-rate \dot\rho of the twin GRACE A/Bspacecrafts through their dynamical equations of motion integrated in anEarth-centered frame over a time span \Delta t=1 d. Instead, the GTR effectsconnected with the propagation of the electromagnetic waves linking thespacecrafts are neglected. The present-day accuracies in measuring the GRACEbiased range and range-rate are \sigma_\rho\sim 1-10 \mum, \sigma_\dot\rho\sim0.1-1 \mum s^-1; studies for a follow-on of such a mission points toward arange-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 dynamicalrange and range-rate perturbations caused by the first six zonal harmoniccoefficients J_L, L=2,3,4,5,6,7 of the classical multipolar expansion of theterrestrial gravitational potential in order to evaluate their aliasing impacton the relativistic effects. Conversely, we also quantitatively, andpreliminarily, 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. Thepresent sensitivity analysis can also be extended, in principle, to differentorbital configurations in order to design a suitable dedicated mission able toaccurately measure the relativistic effects considered.