Tests of General relativity with planetary orbits and Monte Carlo simulations

Abstract

Based on the new developped planetary ephemerides INPOP13c, determinations of acceptable intervals of General Relativity violation in considering simultaneously the PPN parameters $\beta$, PPN $\gamma$, the flattening of the sun $J_{2}^\odot$ and time variation of the gravitational mass of the sun $\mu$ are obtained in using Monte Carlo simulation coupled with basic genetic algorithm. Possible time variations of the gravitational constant G are also deduced. Discussions are lead about the better choice of indicators for the goodness-of-fit for each run and limits consistent with general relativity are obtained simultaneously.