A satellite is in a circular orbit very close to the surface of a planet. At some point it is given an impulse along its direction of motion, causing its velocity to increase `n` times . It now goes into an elliptical orbit. The maximum possible value of `n` for this to occur is

Options

A. 2
B. `sqrt(2)`
C. `sqrt(2)+1`
D. `(1)/(sqrt(2)-1)`

Answer

B

Explanation

For the satellite, initial orbital velocity, `v_(o)=sqrt((GM)/(R ))`
and its escape velocity `v_(e )=sqrt((2GM)/(R ))`
Its initial velocity is increased to `nv_(o)` but still it moves in an elliptical orbit. It will continue its elliptical motion as long as `nv_(o)le v_(e )`.
or `n sqrt((GM)/(R ))le sqrt((2GM)/(R ))` or `n le sqrt(2)` or `n_("max")=sqrt(2)`