Work

Note on the Attraction of an Ellipsoid in a Spherical Universe

Year: 2024

Type: article

Abstract: A classical theorem states that two confocal ellipsoids, each of them endowed with a surface distribution of mass which is called homeoidal, exert the same Newtonian force on an exterior point if they have the same total mass. We extend this theorem to the spherical geometry by adapting a forgotten proof by Chasles of the classical theorem. Compared to the existing results, this is a slightly stronger statement with a much shorter proof.

Source: Proceedings of the Steklov Institute of Mathematics

DOI: 10.1134/s0081543824060026

Author: Alain Albouy

Institution: Institut de Mécanique Céleste et de Calcul des Éphémérides

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4403707803

FWCI: 0.191

Cites: 13

Cited by: 1

Related to: 10