Area velocity of earth around the sun is – \(\frac{dA}{dt}\)= \(\frac{L}{2m}\)
[L = angular momentum, m = mass of earth]
But angular momentum, L = \(\vec{r}\times\vec{p}\)
= \(\vec{r}\times m{\vec{v}}\)
Areal velocity, \(\big(\frac{dA}{dt}\big)=\frac{1}{2m}\)\((\vec{r}\times m\vec{v})\)
= \(\frac{1}{2}(\vec{r}\times \vec{v})\)
Therefore, the direction of \((\vec{r}\times \vec{v})\) areal velocity is in direction of i.e. perpendicular to the plane of \(\vec{r}\) and \(\vec{v}\) (as by Maxwell’s right hand grip rule).
