## Variation of Obital Angular Momentum With Radius

A satellite in orbit about a massive body (or a charged particle orbiting another) decreases in speed as the radius increases - increasing\[r\]

means decreasing \[v\]

Does the orbital angular momentum increase or decrease?

The magnitude of the orbital angular momentum of a satellite is a circular orbit is

\[L=mvr\]

Equating the centripetal and gravitational forces gives

\[\frac{mv^2}{r} = \frac{GMm}{r^2}\]

Rearranging for

\[v\]

: \[v = \sqrt{\frac{GM}{r}}\]

Hence

\[L=m \sqrt{\frac{GM}{r}} r = m \sqrt{GMr} \]

Increasing

\[r\]

means increasing \[L\]

.