Kinematics in Randers-Finsler geometry and secular increase of the astronomical unit

TL;DR

This paper explores Finsler geometry's kinematics to explain the observed secular increase in the astronomical unit, linking space deformation parameters to lunar orbit anomalies.

Contribution

It introduces a Finsler geometric framework that aligns with observed secular trends in the astronomical unit and lunar orbit eccentricity.

Findings

Finsler kinematics matches the secular increase in the astronomical unit.

The space deformation parameter is very small (~10^{-6}) and constant.

The model explains lunar orbit eccentricity variations.

Abstract

Kinematics in Finsler space is investigated. It is showed that the result based on the kinematics with a special Finsler structure is in good agreement with the reported value of secular trend in the astronomical unit, $d{\rm AU}/dt=15\pm4[{\rm m/century}]$. The space deformation parameter $\lambda$ in this special structure is very small with scale of $10^{-6}$ and should be a constant. This fact is consistent with the reported value of an anomalous secular eccentricity variation of the Moon's orbit.