  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.
