Carter-like Constant of Motion in Newtonian Gravity is the Vinti Integral

TL;DR

This paper demonstrates that the Vinti integral in celestial mechanics and a Carter-like conserved quantity in Newtonian gravity are identical, providing insights into the Newtonian limit of Kerr geometry.

Contribution

It establishes the equivalence between the Vinti integral and a Carter-like integral, clarifying their relationship in Newtonian gravity.

Findings

The integrals are mathematically identical.

This equivalence sheds light on the Newtonian limit of Kerr geometry.

Provides a unified understanding of conserved quantities in celestial mechanics and general relativity.

Abstract

We compare the Vinti integral of the classic celestial mechanics with a conserved Carter-like integral of motion for an axially-symmetric body in the Newtonian theory that has been recently found by Clifford Will. We demonstrate that the integrals are identical. It sheds new light on the Newtonian limit of the Kerr geometry.