Closed form expressions for gravitational multipole moments of elementary solids

Julian Stirling, Stephan Schlamminger

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Abstract

Perhaps the most powerful method for deriving the Newtonian gravitational interaction between two masses is the multipole expansion. Once inner multipoles are calculated for a particular shape, this shape can be rotated, translated, and even converted to an outer multipole with well-established methods. The most difficult stage of the multipole expansion is generating the initial inner multipole moments without resorting to three-dimensional numerical integration of complex functions. Previous work has produced expressions for the low-degree inner multipoles for certain elementary solids. This work goes further by presenting closed-form expressions for all degrees and orders. A combination of these solids, combined with the aforementioned multipole transformations, can be used to model the complex structures often used in precision gravitation experiments.
Original languageEnglish
Article number124053
JournalPhysical Review D
Volume100
Issue number12
DOIs
Publication statusPublished - 24 Dec 2019

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