If the angular momentum of a planet of mass m, moving around the...

$\overset{\to}{dA} = \dfrac{1}{2}\overset{\to}{r} \times \overset{\to}{v}dt$

$\dfrac{d\overset{\to}{A}}{dt} =$ areal velocity $= \dfrac{1}{2}\overset{\to}{r} \times \overset{\to}{v}$

$= \dfrac{1}{2}\dfrac{\overset{\to}{r} \times m\overset{\to}{v}}{m} = \dfrac{1}{2m}L$

$\dfrac{dA}{dt} = \dfrac{L}{2m}$