On the possibility of measuring the solar oblateness and some relativistic effects from planetary ranging

Abstract

Abstract. In this paper we first calculate the post-Newtonian 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 nodesΩ, the longitudes of periheliaπ and mean anomaliesṀ of Mercury, Venus and Mars suitably built up in order to absorb the secular precessions induced by the solar oblateness and the post-Newtonian 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 present-day EPM2000 and DE405 ephemerides accuracy, the obtainable precision would be of the order of 10 −3 -10for 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.

How to take into account the relativistic effects in dynamical studies of comets

“…(2.1) is the well known relativistic effect on the argument of the perihelion and, for small eccentricities, Eq. (2.2) coincides, for example, with the approximate expressions for the secular drift in M given by Iorio (2005b) and with the secular drift in M generated by the relativistic model for low eccentricities used by Vitagliano (1997). The exact formula, valid for all eccentricities, is Eq.…”

The relativistic factor in the orbital dynamics of point masses

“…The effect on ω due to the relativistic effects of the Sun is given by ∆ω = 0.0384/(a 5/2 (1 − e 2 )) arcseconds per year where a is in AUs (Will, 1981;Sitarski, 1983;Shahid-Saless & Yeomans, 1994). For low eccentricity orbits the variation in M as measured by a far observer at rest is given approximately by ∆M ∼ −0.115/(a 5/2 √ 1 − e 2 ) arcseconds per year and it is possible to show that the short period effects are negligible (Iorio, 2005). Both secular effects should be considered, for example, in the case of comets when obtaining their non gravitational forces from the observed temporal evolution of the orbital elements (Yeomans et al, 2005).…”

Perihelion precession for modified Newtonian gravity

“…Further, it should be mentioned, that for very distorted orbits, [28] and [29] give exact results for the perihelion precession for a perturbed Newtonian potential. For c = 4, eq.…”