Multipole calculation of gravitational forces

Multipole calculation of gravitational forces In this paper we introduce a method to directly calculate the Newtonian gravitational forces using multipole moments. Gravitational torques for precision tests of Newtonian gravitation are regularly calculated with multipole expansions due to the elegance and efficiency of the calculations. Tests of Newtonian gravity which probe forces rather than torques often resort to less efficient numerical calculation of sextuple integrals. Unlike multipole expansions these cannot easily be adapted for numerous permutations of the system, and instead the calculation has to be repeated, often in full. The method derived in this paper calculates the forces from any 1/r potential given the outer multipoles of the system and the inner multipoles calculated at any arbitrary point. The result derived can be written as a simple recursion relation for efficient calculation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Multipole calculation of gravitational forces

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Multipole calculation of gravitational forces

Abstract

In this paper we introduce a method to directly calculate the Newtonian gravitational forces using multipole moments. Gravitational torques for precision tests of Newtonian gravitation are regularly calculated with multipole expansions due to the elegance and efficiency of the calculations. Tests of Newtonian gravity which probe forces rather than torques often resort to less efficient numerical calculation of sextuple integrals. Unlike multipole expansions these cannot easily be adapted for numerous permutations of the system, and instead the calculation has to be repeated, often in full. The method derived in this paper calculates the forces from any 1/r potential given the outer multipoles of the system and the inner multipoles calculated at any arbitrary point. The result derived can be written as a simple recursion relation for efficient calculation.
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Publisher
The American Physical Society
Copyright
Copyright © © 2017 American Physical Society
ISSN
1550-7998
eISSN
1550-2368
D.O.I.
10.1103/PhysRevD.95.124059
Publisher site
See Article on Publisher Site

Abstract

In this paper we introduce a method to directly calculate the Newtonian gravitational forces using multipole moments. Gravitational torques for precision tests of Newtonian gravitation are regularly calculated with multipole expansions due to the elegance and efficiency of the calculations. Tests of Newtonian gravity which probe forces rather than torques often resort to less efficient numerical calculation of sextuple integrals. Unlike multipole expansions these cannot easily be adapted for numerous permutations of the system, and instead the calculation has to be repeated, often in full. The method derived in this paper calculates the forces from any 1/r potential given the outer multipoles of the system and the inner multipoles calculated at any arbitrary point. The result derived can be written as a simple recursion relation for efficient calculation.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Jun 15, 2017

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