Lambert's theorem and projective dynamics

TL;DR

This paper extends Lambert's theorem and related properties from classical Kepler and Hooke problems to spaces of constant curvature, broadening their applicability in celestial mechanics.

Contribution

It generalizes Lambert's theorem and analogous properties of the Hooke problem to curved spaces, providing new insights into orbital dynamics in non-Euclidean geometries.

Findings

Lambert's theorem extends to Kepler problem in curved spaces.

Hooke problem exhibits a similar property in constant curvature spaces.

Results unify classical and curved space orbital mechanics.

Abstract

We prove that the classical Lambert theorem about the elapsed time on an arc of Keplerian orbit extends without change to the Kepler problem on a space of constant curvature. We prove that the Hooke problem has a property similar to Lambert's theorem, which also extends to the spaces of constant curvature.