Mass multipole moment (source code)

= Mass multipole moment
{title2=$I_{i_1\cdots i_\ell}=\int\rho x_{i_1}\cdots x_{i_\ell}\,d^3x$}

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.