Revolutionizing Gravitational Potential Analysis: From Clairaut to Lie Groups

TL;DR

This paper presents a new Lie group-based theoretical framework for accurately analyzing non-linear gravitational perturbations and deformations in fluid celestial bodies under external forces, enabling precise computation of multipole moments and Love numbers.

Contribution

It introduces a novel Lie group approach to derive exact differential equations for non-linear gravitational perturbations and shape deformations in fluid stars and planets.

Findings

Derivation of exact differential equations for large gravitational perturbations

Foundation for precise analytic and numerical computation of multipole moments

Enhanced understanding of shape deformations under external forces

Abstract

This letter introduces an advanced novel theory for calculating non-linear Newtonian hydrostatic perturbations in the density, shape, and gravitational field of fluid stars and planets subjected to external tidal and rotational forces. The theory employs a Lie group approach using exponential mappings to derive exact differential equations for large gravitational field perturbations and the shape function, which describes the finite deformation of the body's figure. This approach lays the foundation for the precise analytic determination and numerical computation of the induced body's multipole moments and Love numbers with any desired degree of accuracy.