= Quadrupole radiation from a harmonically oscillating point mass
{title2=$\langle P\rangle=\frac{16Gm^2L^4\omega^6}{15c^5}$}
For a <point mass> moving as $z=L\cos\omega t$ along one fixed axis, the trace-free <mass quadrupole moment> is $mL^2\cos^2\omega t\,\operatorname{diag}(-1/3,-1/3,2/3)$. Its radiating component has twice the source <angular frequency>. The <quadrupole formula> gives $\langle P\rangle=16Gm^2L^4\omega^6/(15c^5)$ for this contribution in the leading slow-motion <weak-field approximation>. Any physical driver or support has its own quadrupole contribution; this expression is for the prescribed mass alone.
Back to article page
