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 J2� 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 u Ω, the longitudes of perihelia u and mean anomalies u M 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 -10 −4 for the PPN parameters and, more interestingly, of 10 −9 for J2� . 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.

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

Here we explore the possibility of extending to the Solar System scenario the combined residual approach employed for the deterination of the Lense-Thirring effect in the Earth-LAGEOS satellites system. After calculating the secular gravitoelectric advance of the mean anomaly, we propose several linear combinations of the residuals of the nodes, the perihelia and the mean anomalies of some inner planets in order to measure the gravitoelectric advance, the Lense-Thirring effect and the solar quadrupole mass moment. The obtainable accuracies are comparable to those of new complex and expensive missions involving the launch of one or more spacecrafts. They are 10^-4 for the PPN parameter beta, 10^-5 for gamma, 10^-9 for the solar J2, 20-30% for the Lense-Thirring effect. In the case of the solar gravitomagnetic field, it would be the first attempt to measure its effect on the planetary motions. However, the improvements in the ephemerides of Mercury thanks to the Messenger and BepiColombo missions will map into an increasing accuracy of the proposed tests.

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

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 gamma and beta independently. We propose to analyze the time series of three linear combinations of the experimental residuals of the rates of the nodes, the longitudes of perihelia and mean anomalies of Mercury, Venus and Mars 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 ephemerides accuracy, the obtainable precision would be of the order of 10^-4-10^-5 for the PPN parameters and, more interestingly, of 10^-9 for J_2. The future BepiColombo mission should improve the Mercury's orbit by one order of magnitude.

/pdf/on-the-possibility-of-measuring-the-solar-oblateness-and-3yjruv4go6.pdf

If the gravitational metric tensor field of Einstein’s General Relativity is supplemented by other long range, very weakly coupled interaction fields, then General Relativity’s Equivalence Principle foundations are violated, or its post-Newtonian (1/c 2order) structure is altered, or both. Space experiments test for and measure such possibilities; presently universality of free fall is confirmed to about a part in 1012, and no deviations of post-Newtonian metric gravity from general relativity are seen down to the few parts in 104 level. Future experiments in space can significantly increase the precision to which fundamental physical law is probed. In particular, transponded interplanetary laser ranging can measure presence of metrically coupled scalar fields in gravity with two or three orders of magnitude higher precision than past experiments, and can begin to measure the second post-Newtonian (1/c 4) structure of gravity. A space-based experiment of the universality of free-fall (STEP) can detect additional interactions of a non-metric nature with five or six orders of magnitude higher precision than today’s experiments.

Kenneth Nordtvedt

Papers

An Overview of Solar System Gravitational Physics: The Theory—Experiment Interface