Flyby Anomaly in the Variation Principle of General Relativity

TL;DR

This paper investigates the flyby anomaly within General Relativity by analyzing the Lense Thirring metric and deriving equations of motion, revealing an energy anomaly consistent with empirical observations.

Contribution

It introduces a relativistic derivation of the flyby anomaly using the Lense Thirring metric and Hamilton principle, providing a theoretical basis for the observed velocity deviations.

Findings

Energy anomaly matches Anderson's empirical formula

Derivation from relativistic theory explains flyby velocity deviations

Provides a new theoretical framework for flyby anomaly

Abstract

The anomalous velocity deviation in the osculating planetary flyby attracts enough attention as a problem of General Relativity. In connection of rotating weak field massive source the Lense Thirring metric is diagonalized to find the equation of motion from action invariance Hamilton principle in pure relativistic theory. The computation for near Earth flyby shows energy anomaly over the asymptotic in and out velocity obeying Anderson's empirical formula.