Elementary derivation of the Lense-Thirring precession

TL;DR

This paper provides an elementary derivation of the Lense-Thirring precession using the Hamilton vector, linking it to the precession of orbital elements in a gravitomagnetic field.

Contribution

It introduces a simple pedagogical derivation of the Lense-Thirring effect based on the Hamilton vector, a lesser-known conserved quantity in Kepler problems.

Findings

Hamilton vector precesses in gravitomagnetic fields

Precession rates match Lense-Thirring predictions

Simplifies understanding of gravitomagnetic effects

Abstract

An elementary pedagogical derivation of the Lense-Thirring precession is given based on the use of Hamilton vector. The Hamilton vector is an extra constant of motion of the Kepler/Coulomb problem related simply to the more popular Runge-Lenz vector. When a velocity-dependent Lorentz-like gravitomagnetic force is present, the Hamilton vector, as well as the canonical orbital momentum are no longer conserved and begin to precess. It is easy to calculate their precession rates, which are related to the Lense-Thirring precession of the orbit.