Suppose a space station orbits a planet in a circular orbit. The station has a mass m, and the planet has a mass $M_P$ (with a capital letter P). The radius of the planet's surface is $R_P$ (again capital letter P) and the space station orbits at an altitude r above that surface.
What is the speed v at which the space station is orbiting? Answer in terms of the given quantities and Newton's constant G.
$v = \sqrt{\frac{GM_P}{R_P + r}}$
How much time T does it take for the space station to make one full orbit of the planet?
$T = \frac{2\pi}{\sqrt{\frac{g}{R_P}}} \sqrt{(R_P + r)^3}$