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

Abstract. In this chapter we first calculate the post–Newtonian gravito-electric secular rate of the mean anomaly of a test particle freely orbiting a spherically symmetric central mass. Then, we propose a novel approach to suitably combine the presently available planetary ranging data to Mercury, Venus and Mars in order to determine, simultaneously and independently of each other, the Sun’s quadrupole mass moment J2⊙ and the post-Newtonian gravito-electric secular advances of the perihelion and the mean anomaly. This would also allow to obtain the PPN parameters γ and β independently. We propose to analyze the time series of three linear combinations of the observational residuals of the rates of the nodes Ω̇, the longitudes of perihelia π̇ and mean anomalies Ṁ of Mercury, Venus and Mars built up in order to account for the secular precessions induced by the solar oblateness and the post-Newtonian gravito-electric forces. According to the present-day EPM2000 and DE405 ephemerides accuracy, the obtainable precision would be of the order of 10–10 for the PPN parameters and, more interestingly, of 10 for J2⊙. Second, we investigate the possibility of measuring the post-Newtonian Lense-Thirring secular effect induced by the gravito-magnetic field of the Sun on the planetary orbital motion by analyzing two linear combinations of the residuals of the nodes Ω of Mercury, Venus and Mars. The proposed combinations are, by construction, unaffected by the quadrupole mass moment J2 of the Sun’s gravitational potential. Moreover, they are insensitive also to the post-Newtonian gravito-electric field of the Sun because it affects only the perihelia ω and the mean anomalies M. The obtainable observational accuracy in the proposed measurement would be of the order of 19% and 36%. However, it must be pointed out that a major source of systematic error could be represented by the residual mismodelled classical N−body secular precessions. The second proposed combination is insensitive just to such aliasing effect.