Orbit averaging
= Orbit averaging
{title2=$\langle x\rangle=P^{-1}\int_0^P x\,dt$}
= Orbital averaging
{synonym}
For a quantity on a periodic <Kepler orbit>, its orbit average is $\langle x\rangle=P^{-1}\int_0^P x(t)\,dt$. Equal increments of <true anomaly> are not equal increments of time. <Eccentric anomaly> gives the weight $dt=(1-e\cos E)dE/n$, which yields $\langle\cos f\rangle=-e$. Slow orbital perturbations can be averaged using elements held fixed over a single <orbital period>.