Precessions in Relativity

The angular momentum of a star is an important astrophysical quantity related to its internal structure, formation and evolution. On average, helioseismology yields S = 1.92 10^41 kg m^2 s^-1 for the angular momentum of the Sun. We show how it should be possible to measure or, at least, constrain it in a near future by using the gravitomagnetic Lense-Thirring effect predicted by general relativity for the orbit of a test particle moving around a central rotating body. We also...

A brief outline of the history of the discrepancies within Newtonian mechanics at the end of the nineteenth century is given. The framework of general relativity is described briefly and the famous 'tests' of general relativity are considered and alternative solutions discussed, with particular attention concentrating on the advance of the perihelion of the planet Mercury. The implications for the claims of relativity are discussed, all with reference to both pre and post 191...

The predicted Lense-Thirring perihelion precession of Mercury induced by the Sun's angular momentum through its general relativistic gravitomagnetic field amounts to 2 milliarcseconds per century. It turned out to be compatible with the latest experimental determinations of the supplementary perihelion precession of Mercury with the INPOP15a ephemerides, whose accuracy level has nowadays reached the magnitude of the predicted relativistic effect itself thanks to the analysis ...

Due to its relatively large eccentricity and proximity to the Sun, Mercury's orbital motion provides one of the best solar-system tests of relativistic gravity. We emphasize the number of feasible relativistic gravity tests that can be performed within the context of the parameterized weak field and slow motion approximation - a usefulframework for testing modern gravitational theories in the solar system. We discuss a new approximation method, which includes two Eddington pa...

Let $r(\varphi)$ denote the orbit of Mercury. We compare the formulae obtained via general relativity for $r(\varphi)$ and for the corresponding perihelion precession angle $\Delta \varphi$, with the formulae obtained via the relativistic gravitational law, $F=GMm\gamma^6/r^2$. The latter law can be derived from Newton's gravitational law by employing the gravitational rather than the rest masses of the Sun and Mercury. Remarkably, it is found that the two expressions for the...

The perihelion advance of the orbit of Mercury has long been one of the observational cornerstones for testing General Relativity (G.R.). The main goal of this paper is to discuss how, presently, observational and theoretical constraints may challenge Einstein's theory of gravitation characterized by beta=gamma=1. To achieve this purpose, we will first recall the experimental constraints upon the Eddington-Robertson parameters gamma, beta and the observational bounds for th...

Extrasolar circumbinary planets are so called because they orbit two stars instead of just one; to date, an increasing number of such planets have been discovered with a variety of techniques. If the orbital frequency of the hosting stellar pair is much higher than the planetary one, the tight stellar binary can be considered as a matter ring current generating its own post-Newtonian stationary gravitomagnetic field through its orbital angular momentum. It affects the orbital...

Recently, Will calculated an additional contribution to the Mercury's precession of the longitude of perihelion $\varpi$ of the order of $\dot\varpi_\textrm{W}\simeq 0.22$ $\textrm{milliarcseconds per century}$ ($\textrm{mas cty}^{-1}$). It is partly a direct consequence of certain 1pN third-body accelerations entering the planetary equations of motion, and partly an indirect, mixed effect due to the simultaneous interplay of the standard 1pN pointlike acceleration of the pri...

The effect of general relativistic prediction of the dependence of mass on gravitational potential on the dynamics of a planet moving around the sun is shown to have a negative contribution of 14.326 arcsec/century towards the overall non-Newtonian perihelion advance of Mercury.

We study a general relativistic gravitomagnetic 3-body effect induced by the spin angular momentum ${\boldsymbol S}_\textrm{X}$ of a rotating mass $M_\textrm{X}$ orbited at distance $r_\textrm{X}$ by a local gravitationally bound restricted two-body system $\mathcal{S}$ of size $r\ll r_\textrm{X}$ consisting of a test particle revolving around a massive body $M$. At the lowest post-Newtonian order, we analytically work out the doubly averaged rates of change of the Keplerian ...