Exercises on the Kepler ellipses through a fixed point in space, after Otto Laporte

TL;DR

This paper explores geometric exercises related to Kepler's laws inspired by Otto Laporte's work, highlighting historical mathematical insights and their connection to quantum integrability of the Kovalevsky top.

Contribution

It presents geometric exercises on Kepler ellipses through a fixed point, emphasizing historical context and linking to quantum integrability results by Laporte.

Findings

Historical exercises on Kepler ellipses analyzed

Connection between Kepler laws and quantum integrability highlighted

Laporte's 1933 results on integrability recognized

Abstract

This article has a twofold purpose. On the one hand I would like to draw attention to some nice exercises on the Kepler laws, due to Otto Laporte from 1970. Our discussion here has a more geometric flavour than the original analytic approach of Laporte. On the other hand it serves as an addendum to a paper of mine from 1998 on the quantum integrability of the Kovalevsky top. Later I learned that this integrability result had been obtained already long before by Laporte in 1933.