What would happen to Earth, if the Sun suddenly vanishes? (Neglect the gravitational force due to other planets)
The Earth will move straight along the direction of velocity at that time
Because of the gravitational force between the Sun and the Earth, the earth orbit around the Sun. If suddenly the Sun vanishes, the gravitational force between the Sun and the Earth will disappear. So, the Earth will no more be able to orbit around the sun. Thus, it will start moving in the direction of velocity in a straight line. It will be same as whirling of stone using a thread. If suddenly the thread breaks, the stone will break its path and move in a straight line along the direction of velocity.