Question

suppose gravity of the earth suddenly becomes zero then towards which direction will the moon begins to move is no other celestial body affect it ?????

Answer 1

In the absence of gravity of earth, the moon flies off along a straight line. This straight line will be a tangent to the circular path. 

Answer 2

if.. gravity becomes zero than I think the force of attraction and repulsive should be zero and.. the law of gravity disappear.
so the moon should travel in a straight path..

hope it helps you.!