Question

The Moon is moving away from the Earth

Answer 1

moon never move, just the earth rotates. when earth rotates, the shape of moon get change which we can see from earth.. and we thought that the moon is moving.. but its still on the same place..
earth complete its rotate in 365 days. and it never stop rotating. we cant feel that earth is rotating because its speed is low. we cant compare the speed of earth with anything..
thats why, moon never moves and earth never stop rotating.

Answer 2

This happens because moon revolves around the earth in an elliptical orbit. All the planets revolve around the sun in an elliptical orbit, not a perfectly circular orbit. These orbits are such that the moon and planets become closer to earth and sun at a particular point. The point at which a planet is nearest to its star is called apogee [not sure]. Even if moon goes away from the earth, it is only for sometime.