Perspectives in measuring the PPN parameters beta and gamma in the Earth's gravitational fields with the CHAMP/GRACE models

摘要

The current bounds on the PPN parameters gamma and beta are of the order of10^-4-10^-5. Various missions aimed at improving such limits by several ordersof magnitude have more or less recently been proposed like LATOR, ASTROD,BepiColombo and GAIA. They involve the use of various spacecraft, to belaunched along interplanetary trajectories, for measuring the effects of thesolar gravity on the propagation of electromagnetic waves. In this paper weinvestigate what is needed to measure the combination nu=(2+2gamma-beta)/3 ofthe post-Newtonian gravitoelectric Einstein perigee precession of a testparticle to an accuracy of about 10^-5 with a pair of drag-free spacecraft inthe Earth's gravitational field. It turns out that the latest gravity modelsfrom the dedicated CHAMP and GRACE missions would allow to reduce thesystematic error of gravitational origin just to this demanding level ofaccuracy. In regard to the non-gravitational errors, the spectral noise densityof the drag-free sensors required to reach such level of accuracy would amountsto 10^-8-10^-9 cm s^-2 Hz^-1/2 over very low frequencies. Although not yetobtainable with the present technologies, such level of compensation is muchless demanding than those required for, e.g., LISA. As a by-product, anindependent measurement of the post-Newtonian gravitomagnetic Lense-Thirringeffect with a 0.9% accuracy would be possible as well. The forthcoming Earthgravity models from CHAMP and GRACE will further reduce the systematicgravitational errors in both of such tests.