Dynamical orbital effects of general relativity on the satellite-to-satellite range and range-rate in the GRACE mission: A sensitivity analysis

We numerically investigate the impact of the General Theory of Relativity (GTR) on the orbital part of the satellite-to-satellite range ρρ and range-rate ρ˙ of the twin GRACE A/B spacecrafts through their post-Newtonian (PN) dynamical equations of motion integrated in an Earth-centered frame over a time span ΔP=1d. The present-day accuracies in measuring the GRACE biased range and range-rate are σρ∼1-10μm,σρ˙∼0.1-1μms-1. The GTR range and range-rate effects turn out to be Δρ=80μm and Δρ˙=0.012μms-1 (1PN gravitomagnetic), and Δρ=6000μm and Δρ˙=10μms-1 (1PN gravitoelectric). It turns out that the range shifts ΔρΔρ corresponding to the GTR-induced time delays ΔtΔt on the propagation of the electromagnetic waves linking the GRACE spacecrafts are either negligible (1PN gravitomagnetic) or smaller (1PN gravitoelectric) than the orbital effects by about 1 order of magnitude over ΔP=1d. We also compute the dynamical range and range-rate perturbations caused by the first six zonal harmonic coefficients Jℓ,ℓ=2,3,4,5,6,7 of the classical multipolar expansion of the geopotential to evaluate their aliasing impact on the relativistic effects. Conversely, we quantitatively, and preliminarily, assess the possible a-priori “imprinting” of GTR itself, not solved-for in all the GRACE-based Earth’s gravity models produced so far, on 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 GTR. Moreover, it may be the starting point for more refined numerical investigations concerning the actual measurability of the relativistic effects involving, e.g., a simulation of full GRACE data, including GTR itself, and the consequent parameters’ estimation. Finally, also other non-classical dynamical features of motion, caused by, e.g., modified models of gravity, may be considered in further studies.