Answer:
[tex] r^\frac{1}{2}[/tex]
Explanation:
Angular momentum, L = m v r
areal velocity = [tex]\frac{dA}{dt}[/tex]
according to kepler's 2nd law
[tex]\frac{dA}{dt}=\frac{L}{2m}[/tex]
since, we know that
[tex]v=\sqrt{\frac{Gm}{r} }[/tex]
areal velocity= [tex]\frac{mvr}{2m} = \frac{vr}{2}[/tex]
now substituting value of v in areal velocity we get
[tex]\frac{1}{2}\sqrt{GMr}[/tex]
hence from above equation of rate of change of area swept i.e. areal velocity is proportional to [tex] r^\frac{1}{2}[/tex]
