Question

A satellite is moving in a circular orbit round the earth with a diameter of orbit $2R$. At a certain point a rocket fixed to the satellite is fired such that it increases the velocity of the satellite tangentially and satellite is still bound to earth. The resulting orbit of the satellite would be

• A. same as before.
• B. circular orbit with diameter greater than $2R$.
• C. elliptical orbit with minimum distance from the earth equal to $R$.
• D. elliptical orbit with maximum distance from the earth equla to $R$.

Answer 1

The correct option is C elliptical orbit with minimum distance from the earth equal to $R$.

The orbital velocity of a satellite orbiting the earth is given by,$$v=\sqrt{\frac{GM}{R}}$$Where,
$M\to$Mass of earth,
$R\to$Radius of orbit,

When rocket is fired it increases the velocity of the satellite tangentially. Let the increased tangential velocity is $v_t$, so
$v_t>\sqrt{\frac{GM}{R}}$

As, we know that if the tangential velocity of satellite increases from the its original velocity, it will move in elliptical orbit.

So, the resulting orbit of the satellite will become elliptical orbit with minimum distance from the earth equal to $R$.

Hence, option (c) is correct answer.