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

Mechanics

Gravity

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 $Eric Weisstein's World of Math$


			(1)

where

			(2)
			(3)

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