# "Kepler Harmonies" and conformal symmetries

## TL;DR

This paper reveals a new conserved quantity related to Kepler's rescaling symmetry in a higher-dimensional spacetime, with implications for celestial mechanics and cosmology.

## Contribution

It introduces a novel conserved Noether charge from Kepler's rescaling symmetry in Bargmann spacetime, extending understanding of symmetries in celestial mechanics.

## Key findings

- Identifies a conserved quantity associated with Kepler rescaling in Bargmann spacetime.
- Connects the symmetry to the Virial Theorem and Kepler's Third Law.
- Extends the framework to Newtonian Cosmology.

## Abstract

Kepler's rescaling becomes, when "Eisenhart-Duval lifted" to $5$-dimensional "Bargmann" gravitational wave spacetime, an ordinary spacetime symmetry for motion along null geodesics, which are the lifts of Keplerian trajectories. The lifted rescaling generates a well-behaved conserved Noether charge upstairs, which takes an unconventional form when expressed in conventional terms. This conserved quantity seems to have escaped attention so far. Applications include the Virial Theorem and also Kepler's Third Law. The lifted Kepler rescaling is a Chrono-Projective transformation. The results extend to celestial mechanics and Newtonian Cosmology.