Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 309 / 3 / b / ii / Solution

The quadrupole formula in units $G=c=1$ isHere $I_{kk}=m{a}^2/3$ is constant, so its trace subtraction has no third derivative. If $B=4m{a}^2{\omega }^3/3$, thenThus ${\stackrel{...}{I}}_{ij}{\stackrel{...}{I}}_{ij}=2B^2$ andRestoring units multiplies this by $G/c^5$.