A satellite goes along an elliptical path around earth. The rate of change of arc length ‘a’ swept by the satellite is proportional to:

r r2 r1/2 r-1

r-1

$\frac{dA}{dt}=\frac{1}{2} r^2 \omega$ = constant  k  =  k $\Rightarrow \frac{1}{2} r(r \omega)$ = k     ⇒     vr = 2k ⇒ v ∝ (1/r)