A Satellite of the earth is revolving in a circular orbit with a uniform speed v. If the gravitational force suddenly disappears, the satellite will

Without gravitational force, the central force of gravity would not affect a satellite so that it will no longer orbit about the Earth. Gravitational force is what provides the inflected force required for a satellite orbiting to trace a curvilinear path. If that force will be removed, a satellite cannot have the tendency to orbit around the earth anymore as there is an inward force to hold and maintain it on a curvilinear trajectory, like a circular or elliptical orbit.

According to Newton’s first law of motion, an object in motion will continue moving in a straight line with constant velocity unless acted upon by an external force. So if the gravitational force were to suddenly disappear, the satellite would stop its curved motion and move tangentially to its original orbit at the same velocity \(v\) it had at the moment gravity vanished.

This tangent motion results because the speed of a satellite at any location on an orbit always points along the tangent of the curve in its trajectory. Without gravitational force, the satellite would just go along this tangent forever. The motion, being rectilinear, could not pull the satellite toward its orbital path or back to Earth, since it would be lacking in a centripetal force. It would drift through space, and Earth’s influence would be felt no longer.