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. `sqrt2 `
C. `sqrt2 + 1 `
D. `(1)/(sqrt2 - 1)`

Answer

B

Explanation

The initial velocity of the satellite is `v = sqrt((GM)/( R))`
The satellite will remain in the elliptical orbit as long as `v lt v_e` where `v_e` is the escape velocity.
Also `v_e = sqrt((2GM)/(R ))`
`therefore nv lt= v_e " or " n sqrt((GM)/( R)) lt= sqrt((2GM)/( R))`
`n lt= sqrt2 " or " n_(max) = sqrt2 `