Can the Pioneer anomaly be induced by velocity-dependent forces? Tests in the outer regions of solar system with planetary dynamics

TL;DR

This study tests velocity-dependent forces proposed to explain the Pioneer anomaly by analyzing their effects on outer planetary orbits, finding most predicted variations are inconsistent with observations except for perihelion precessions.

Contribution

The paper evaluates the impact of proposed velocity-dependent forces on planetary orbits and compares predictions with observational data, discarding models with detectable orbital variations.

Findings

Predicted semimajor axis variations are too large for most planets, inconsistent with observations.

Predicted perihelion precessions are generally too small to be detected, except for Jupiter.

Models predicting undetectable perihelion precessions remain compatible with current data.

Abstract

In this paper we analyze the impact on the orbital motions of the outer planets of the solar system from Jupiter to Pluto of some velocity-dependent forces recently proposed to phenomenologically explain the Pioneer anomaly, and compare their predictions (secular variations of the longitude of perihelion \varpi or of the semimajor axis a and the eccentricity e) with the latest observational determinations by E.V. Pitjeva with the EPM2006 ephemerides. It turns out that while the predicted centennial shifts of a are so huge that they would have been easily detected for all planets with the exception of Neptune, the predicted anomalous precessions of \varpi are too small, with the exception of Jupiter, so that they are still compatible with the estimated corrections to the standard Newton-Einstein perihelion precessions. As a consequence, we incline to discard those extra-forces predicting secular variations of a and e, also for some other reasons, and to give a chance, at least observationally, to those models predicting still undetectable perihelion precessions. Of course, adequate theoretical foundations for them should be found.