New ways in testing post-Newtonian gravity in the Solar System scenario from planetary motion analysis

摘要

Here we explore the possibility of extending to the Solar System scenario thecombined residual approach employed for the deterination of the Lense-Thirringeffect in the Earth-LAGEOS satellites system. After calculating the seculargravitoelectric advance of the mean anomaly, we propose several linearcombinations of the residuals of the nodes, the perihelia and the meananomalies of some inner planets in order to measure the gravitoelectricadvance, the Lense-Thirring effect and the solar quadrupole mass moment. Theobtainable accuracies are comparable to those of new complex and expensivemissions involving the launch of one or more spacecrafts. They are 10^-4 forthe PPN parameter beta, 10^-5 for gamma, 10^-9 for the solar J2, 20-30% for theLense-Thirring effect. In the case of the solar gravitomagnetic field, it wouldbe the first attempt to measure its effect on the planetary motions. However,the improvements in the ephemerides of Mercury thanks to the Messenger andBepiColombo missions will map into an increasing accuracy of the proposedtests.