Radial orbit time transformation
= Radial orbit time transformation
{title2=$d\tau/dt=(q/r)dq/dr$}
For a central-force radial <energy> equation, choose a monotone radius $q=q(r)$ and clock $\tau$ such that $d\tau/dt=(q/r)dq/dr$. Then $q'=(r/q)\dot r$, and multiplying the old <energy> equation by $r^2/q^2$ preserves the centrifugal form $L^2/(2q^2)$. A split of the remaining terms into constant <energy> and a new <Newtonian gravitational potential> produces a transformed radial orbit.