A planet of mass m is revolving round the sun (of mass M_s) in an elliptical orbit. If $\vec{v}$ is the velocity of the planet when its position vector from the sun is r , then areal velocity of the planet is.

$\frac{1}{2}(\vec{r} \times \vec{v})$

Areal velocity = $\frac{\Delta \vec{A}}{\Delta t}=\frac{\vec{L}}{2 m}$

⇒ Areal velocity = $\frac{1}{2 m}[m(\vec{r} \times \vec{v})]=\frac{1}{2}(\vec{r} \times \vec{v})$