# Tag Info

The Kepler laws, or simple insertion of $z(t)=re^{iωt}$, tell that for a circular orbit of radius $r$ in the central field $\ddot z=-\mu\frac{z}{|z|^3}$ the angular speed $\omega$ is given by $$r^3ω^2=μ.$$ That is how you get the initial velocity $(0,\sqrt{\mu/r})$ at the point $(r,0)$. The period of the orbit is $$T=\frac{2\pi}{ω}=2π\sqrt{r^3/μ}.$$ ...