Pioneer's Anomaly and the Solar Quadrupole Moment

TL;DR

This paper investigates whether the Sun's quadrupole moment can explain the Pioneer anomaly, concluding it only accounts for similar accelerations at a few astronomical units, not across the entire observed range.

Contribution

The study provides a relativistic analysis of the Solar quadrupole's effect on spacecraft trajectories to assess its role in the Pioneer anomaly.

Findings

Solar quadrupole induces acceleration comparable to Pioneer anomaly at a few AU.

Quadrupole effect insufficient to explain the anomaly at larger distances.

Relativistic analysis confirms the limited influence of Solar quadrupole on spacecraft trajectories.

Abstract

The trajectories of test particles moving in the gravitational field of a non-spherically symmetric mass distribution become affected by the presence of multipole moments. In the case of hyperbolic trajectories, the quadrupole moment of an oblate mass induces a displacement of the trajectory towards the mass source, an effect that can be interpreted as an additional acceleration directed towards the source. Although this additional acceleration is not constant, we perform a general relativistic analysis in order to evaluate the possibility of explaining Pioneer's anomalous acceleration by means of the observed Solar quadrupole moment, within the range of accuracy of the observed anomalous acceleration. We conclude that the Solar quadrupole moment generates an acceleration which is of the same order of magnitude of Pioneer's constant acceleration only at distances of a few astronomical units.