The Expanding Universe, Planetary Motion and the Pioneer 10/11 Anomaly

TL;DR

This paper investigates whether the universe's expansion influences planetary motion and could explain the Pioneer anomaly, concluding that the effect is negligible and cannot account for the observed anomaly.

Contribution

It provides a first-order analysis of the universe's expansion impact on planetary motion and rules out it as an explanation for the Pioneer anomaly.

Findings

Orbital elements remain unaffected by cosmic expansion.

A small effect on proper time and coordinate time connection is identified.

The effect is too small to explain the Pioneer 10/11 anomaly.

Abstract

The effect of the expanding universe on planetary motion is considered to first order in the Hubble constant H. Orbital elements are shown to be unaffected, but there is a small change in the connection between planetary proper time and coordinate time. This can produce an apparent anomalous acceleration in velocities inferred from echo-ranging, but the effect is too small by many orders of magnitude to account for the Pioneer 10/11 anomaly.