Discrete fields and the Pioneer anomalous acceleration

TL;DR

This paper proposes that the Pioneer anomaly may be explained by sub-dominant effects of a discrete gravitational interaction, which produce a small, constant acceleration observable in nearly radial trajectories but not in circular orbits.

Contribution

It introduces a model where discrete gravitational interactions lead to observable effects like the Pioneer anomaly, highlighting the role of sub-dominant contributions.

Findings

Discrete interactions produce a standard potential as an effective continuous field.

Sub-dominant effects are linear in the number of interaction events.

The model explains the Pioneer anomaly as a consequence of these effects.

Abstract

The dominant contributions from a discrete gravitational interaction produce the standard potential as an effective continuous field. The sub-dominant contributions are, in a first approximation, linear on n, the accumulated number of (discrete) interaction events along the test-body trajectory. For a nearly radial trajectory n is proportional to the traversed distance and its effects may have been observed as the Pioneer anomalous constant radial acceleration, which cannot be observed on the nearly circular planetary orbits.