The velocity of an orbiting body is given by:
$$v = \sqrt{\frac{Gm}{r}}$$
I was trying to derive this formula earlier but I was struggling with incorporating $G$ into my derivation.
I tried looking at centripetal force in order to derive the equation:
$$F = ma = \frac{mv^2}{r}$$
$$F = \frac{mv^2}{r}$$
So
$$v = \sqrt{\frac{Fr}{m}}$$
But this didn't seem to be the right way to go.