Question

When astronauts go into space..there exist some gravitational force between them..so by Newton's first law of motion why the astronauts don't revolute around the earth like moon

Answer 1

They do experience earth's gravity. It is almost 85% as strong as it is on the surface. If they didn't, they'd fly off into deep space

What they don't experience is gravitational acceleration. This is what they mean by 'zero-g' the capital 'G' is for gravity, and the small 'g' is for gravitational acceleration.

They are in a state of a constant free fall.

Weight is felt due to gravitational acceleration. In Earth when we push the ground below, the ground pushes us back. But in space there is nothing to push against therefore weightlessness is felt.