On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging
Abstract
In this paper we first calculate the postNewtonian gravitoelectric 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 J_{2☉} and the 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 dotΩ, the longitudes of perihelia dotπ and mean anomalies dot{M} of Mercury, Venus and Mars suitably built up in order to absorb the secular precessions induced by the solar oblateness and the postNewtonian gravitoelectric forces. The values of the three investigated parameters can be obtained by fitting the expected linear trends with straight lines, determining their slopes in arcseconds per century and suitably normalizing them. According to the presentday EPM2000 and DE405 ephemerides accuracy, the obtainable precision would be of the order of 10^{3}10^{4} for the PPN parameters and, more interestingly, of 10^{9} for J_{2☉}. It must be pointed out that the future BepiColombo mission should improve the knowledge of the Mercury's orbit perhaps by one order of magnitude.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 2005
 DOI:
 10.1051/00046361:20047155
 arXiv:
 arXiv:grqc/0406041
 Bibcode:
 2005A&A...433..385I
 Keywords:

 relativity;
 gravitation;
 celestial mechanics;
 Sun: fundamental parameters;
 planets and satellites: general;
 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 LaTex2e, 11 pages, no figures, 3 tables. Extensively rewritten version. The role of the classical Nbody secular precessions has been discussed. New observable found for J2. Improved accuracy in it: 10^9. The role of BepiColombo discussed