= Synchronous circular orbit
{title2=$r=(GMT^2/4\pi^2)^{1/3}$}
A satellite remaining above a fixed point of a uniformly rotating spherical planet must have a prograde equatorial <circular Kepler orbit> with angular speed $2\pi/T$. Balancing gravitational acceleration and centripetal acceleration gives the displayed radius and speed $v=2\pi r/T$. The satellite's own mass cancels. A physically realizable external orbit additionally requires this radius to exceed the planet's radius.
Back to article page
