Two satellites revolve around the ‘Sun’ as shown in the figure. First satellite revolves in a circular orbit of radius R with speed `v_(1)` . Second satellite revolves in elliptical orbit, for which minimum and maximum distance from the sun are `(R)/(3)` and `(5R)/(3)` respectively. Velocities at these positions are `v_2` and `v_3` respectively. The correct order of speeds is

Options

A. `v_(2)gtv_(3)gtv_(1)`
B. `v_(3)ltv_(2)ltv_(1)`
C. `v_2gtv_(1)gtv_(3)`
D. `v_(2)gtv_(3)=v_(1)`

Explanation

`V_(1)=sqrt((GM)/(R))` (orbital velocity in circular path)
For elliptical orbit
conservation of angular momentum `mV_(2)(R)/(3)=(5R)/(3)mV_(3)`
conservation energy `-(GMm)/(R//3)+(1)/(2)mV_(2)^(2)=(-GMm)/(5R//3)+(1)/(2)mV_(3)^(2)`
Solving `V_(2)=sqrt((5GM)/(R))` and `V_(3)=sqrt((GM)/(5R))`