# Orbital speed

A satellite is kept in its orbit by the gravitational force $$F_{\text{g}}$$ which acts as a centripetal force. For a circular orbit, $$F_{\text{g}}$$ must be exactly equal to the centripetal force $$F_{\text{c}}$$ for the specific orbit. This is the basis for deriving the equation for the orbital speed.

**Orbiting speed requirement**: $$F_{\text{g}}=F_{\text{c}}$$

**Centripetal force** (keeping satellite in orbit): $$F_{\text{c}}= ma=mv^2/r$$

**Gravitational force** (of primary on satellite): $$F_{\text{g}}=GMm/r_{\text{o}}^2$$

From Newton's second law,$$$\begin{align*}m\frac{v^2}{r}= G\frac{Mm}{r^2} \iff & v^2= G\frac{M}{r}\\\iff & v=\sqrt{ \frac{ G M}{r}}\end{align*}$$$

The formula applies to circular orbits and assumes that the primary is stationary.