Multipole moment

A multipole moment is a coefficient in the far-field angular expansion of a localized source. Successive moments describe progressively finer departures from spherical symmetry.

Spatial moments of a mass density distribution organize its far gravitational field. Symmetric trace-free parts isolate angular multipoles; the second moment gives the mass quadrupole moment. In slow-motion linearized gravity, changes of the quadrupole produce the leading gravitational radiation; the conserved monopole and centre-of-mass dipole do not radiate independently.