Circular-orbit energy ratio in a power-law potential
= Circular-orbit energy ratio in a power-law potential
{title2=$2K=sU\quad(U=Ar^s)$}
A <circular orbit> in a <central potential> $U(r)=Ar^s$ requires inward <force> $U'(r)=mv^2/r>0$. Thus $2K=rU'(r)=sU$, giving $K/U=s/2$ for the specified zero of potential. The ratio depends on that choice of zero; adding a constant to $U$ leaves the orbit unchanged but changes $K/U$. This is the circular special case of the <virial theorem>.