Question

if suddenly gravity of earth becomes zero then in which direction moon start to move if no other celestial object effects on it

Answer 1

Moon will be moving in tangent of its orbit.

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Answer 2

If suddenly the gravity of Earth became zero, then the direction of moon’s movement will be like the sudden release of a rope tied stone which is spinning over your head.

In that case, the direction that the planet will follow will be the tangential direction.

As a result, the moon will be flying away far from the Earth along a straight line.