Question

The orbital speed of a satellite revolving around a planet in a circular orbit is $v_o$. If its speed is increased by $10\%$, then

• A. It will escape from its orbit.
• B. It will start rotating in an elliptical orbit.
• C. It will continue to move in the same orbit.
• D. It will move in a circular orbit of radius $20\%$ more than radius of initial orbit

Answer 1

The correct option is B It will start rotating in an elliptical orbit.

The orbital speed of a satellite, revolving around a planet is given by, $$v_o=\sqrt{gR}$$ The escape velocit of a satellite, revolving around a planet is given by,
$$v_e=1.41\sqrt{gR}$$When the orbital speed of a satellite revolving around a planet is increased from $v_o$ to $v$ by $10\%$, it becomes $1.1\sqrt{gR}$,

So, it corresponds to the $v_o<v<v_e$.

Hence, the velocity will be higher than the orbital velocity of the circular orbit but the satellite will not escape either. So, it will move in an elliptical orbit.

Hence, option (b) is the correct answer.