If gravity between the sun and Earth suddenly vanished; describe the expected Earth motion.
Give reason for your answer with equation.

When the gravity between the Sun and the Earth suddenly vanishes, then Earth will keep moving in a straight line in a direction where it was moving at the moment when gravity vanished.

Explanation:

The gravitational force between Sun and Earth is given by

Where F is the gravitational force between the Sun and the Earth. M₁ and M₂ are the masses of Sun and Earth and R is the distance between them.

If we assume that the gravity between the sun and Earth suddenly vanishes, then there would not be any force between the Sun and the Earth and the Earth will keep on moving in a straight line. This is endorsed by the Newton's first law that a body in motion remains in motion if no external force is acting on it.

The direction of Earth's motion will be determined by the previous direction of the motion that is the moment when the gravity was vanished.