Question

A ball is dropped from a spacecraft revolving around the earth at a height of 120 km from earth's surface. What will happen to the ball?

• A. It will continue to move with velocity equal to spacecraft orbital velocity along the original orbit of spacecraft.
• B. It will move with the same speed tangentially to the spacecraft.
• C. It will fall down to the earth immediately.
• D. It will go very far in space.

Answer 1

The correct option is A It will continue to move with velocity equal to spacecraft orbital velocity along the original orbit of spacecraft.

At this height, we know that the spacecraft was orbiting the Earth. i.e the gravitational force of the earth is equal to the centripetal force on the spacecraft (and the ball). Since same gravitational force is still acting on the ball, centripetal force does not change. Hence, the ball continues to rotate in the same orbit.

Orbital velocity can be found as follows:

$\frac{m{v}^2}{r}=\frac{GmM}{r^2}$

$v=\sqrt{\frac{GM}{r}}$

Hence, orbital velocity does not change.