Gravitational Multipole Expansion -- from Eric Weisstein's World of Physics

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Gravitational Multipole Expansion

Since the gravitational potential satisfies Laplace's equation in the region outside the mass, it must be expressible in a Laplace series Eric Weisstein's World of Math

where
with and constants and an associated Legendre polynomial, Eric Weisstein's World of Math and and real spherical harmonics Eric Weisstein's World of Math.

Multipole Expansion