A light satellite is initially rotating around a planet in a circular orbit of radius r. Its speed in this circular orbit was `u_(0)`. It is put in an elliptical orbit by increasing its speed form `u_(0) " to " v_(Q)` ( instantaneously). In the elliptical orbit, the satellite reaches the farthest point P, which is at a distance R from the planet. Satellite's speed at farthest point is `v_(P)`. At point Q, the speed required by satellite to escape the planet's gravitational pull is `v_("esc")`

Options

A. a.`v_("esc")=2u_(0)`
B. b.`v_(Q)=u_(0)r sqrt((2)/(R(r+R)))`
C. c.`v_(Q)=u_(0) sqrt((2R)/((r+R)))`
D. d.`v_(P)=u_(0)r sqrt((2)/(R(r+R)))`

Answer

C, D