Gravitational anomalies in the solar system?

Abstract

Mindful of the anomalous perihelion precession of Mercury discovered by U. Le Verrier in the second half of the nineteenth century and its successful explanation by A. Einstein with his General Theory of Relativity in the early years of the twentieth century, discrepancies among observed effects in our Solar system and their theoretical predictions on the basis of the currently accepted laws of gravitation applied to known matter-energy distributions have the potential of paving the way for remarkable advances in fundamental physics. This is particularly important now more than ever, given that most of the universe seems to be made of unknown substances dubbed Dark Matter and Dark Energy. Should this not be directly the case, Solar system's anomalies could anyhow lead to advancements in either cumulative science, as shown to us by the discovery of Neptune in the first half of the nineteenth century, and technology itself. Moreover, investigations in one of such directions can serendipitously enrich the other one as well. The current status of some alleged gravitational anomalies in the Solar system is critically reviewed. They are: a) Possible anomalous advances of planetary perihelia; b) Unexplained orbital residuals of a recently discovered moon of Uranus (Mab); c) The lingering unexplained secular increase of the eccentricity of the orbit of the Moon; d) The so-called Faint Young Sun Paradox; e) The secular decrease of the mass parameter of the Sun; f) The Flyby Anomaly; g) The Pioneer Anomaly; and h) The anomalous secular increase of the astronomical unit

Solar System constraints on renormalization group extended general relativity: The PPN and Laplace-Runge-Lenz analyses with the external potential effect

“…This section is devoted to estimate the upper bound onν in the Solar System from the Laplace-Runge-Lenz (LRL) vector dynamics using the perihelion precession data from [70], which is more recent and precise than the data set used in [53].…”

Effect of the Cosmological Constant on Light Deflection: Time Transfer Function Approach

“…Thus far, it was found that the cosmological constant Λ contributes to the perihelion shift in principle even though this contribution is presently difficult to detect because of its very small effect (See [6][7][8] and the references therein, and corresponding topic to perihelion advance [9][10][11][12]). …”

Solar system tests for realistic f(T) models with non-minimal torsion–matter coupling

“…The extra perihelion precessions of the planets (from Mercury to Saturn) in the Solar system estimated from the recent ephemerides INPOP10a [62] and EPM2011 [63] (see also [36]) are listed in Table 1.…”

“…On the other hand, any modified gravity theory must confront the Solar system tests which have been passed in GR [33][34][35][36][37]. In fact, Solar system effects in some modified gravities including minimal coupling f (T ) models have been considered [38][39][40][41][42][43][44].…”