Anomalous precession of planets on a Weyl conformastatic solution

TL;DR

This paper examines anomalous planetary precession within a Weyl conformastatic gravitational model, comparing theoretical predictions with observational data, and finds the anomalies are statistically insignificant according to recent ephemerides.

Contribution

It introduces a non-standard perihelion advance expression based on Weyl conformastatic solutions and assesses its relevance with current observational data.

Findings

Anomaly in planetary precession is statistically insignificant with INPOP10a data.

The model aligns with observational data when analyzed with the Levenberg-Marquardt algorithm.

Application to giant planets confirms the negligible anomaly in relativistic precession.

Abstract

In this paper, we investigate the anomalous planets precession in the nearly-newtonian gravitational regime. This limit is obtained from the application of the slow motion condition to the geodesic equations without altering the geodesic deviation equations. Using a non-standard expression for the perihelion advance from the Weyl conformastatic vacuum solution as a model, we can describe the anomaly in planets precession compared with different observational data from Ephemerides of the Planets and the Moon (EPM2008 and EPM2011) and Planetary and Lunar Ephemeris (INPOP10a). As a result, using the Levenberg-Marquardt algorithm and calculating the related Chi-squared statistic, we find that the anomaly is statistical irrelevant in accordance with INPOP10a observations. As a complement to this work, we also do an application to the relativistic precession of giant planets using observational data calibrated with the EPM2011.