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Physics > Classical Physics

Title: Exact gravitational potential of a homogeneous torus in toroidal coordinates and a surface integral approach to Poisson's equation

Authors: Matt Majic
Abstract: New exact solutions are derived for the gravitational potential inside and outside a homogeneous torus as rapidly converging series of toroidal harmonics. The approach consists of splitting the inter- nal potential into a known solution to Poisson's equation plus some solution to Laplace's equation. The full solutions are then obtained using two equivalent methods, applying differential boundary conditions at the surface, or evaluating a surface integral derived from Green's third identity. This surface integral may not have been published before and is general to all geometries and volume density distributions, reducing the problem for the gravitational potential of any object from a volume to a surface integral.
Comments: 5 pages, 2 figures, 2 Matlab files attached as ancillary
Subjects: Classical Physics (physics.class-ph); Astrophysics of Galaxies (astro-ph.GA); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1803.00003 [physics.class-ph]
  (or arXiv:1803.00003v1 [physics.class-ph] for this version)

Submission history

From: Matt Majic [view email]
[v1] Wed, 28 Feb 2018 01:28:32 GMT (479kb,AD)