What would happen to the moon if there was not any gravity What about the planets?

Without gravity, there would be no largescale structure to the universe. If it simply stopped existing, the moon would fly off from earth orbit; the earth and planets would fly away from the sun into deep space, and not only would the solar system dismantle itself but so would the galaxy. Also, the atmosphere would drift off into space, as would (the shortly thereafter dead) human race, and everything else not fixed to the surface of the planet.

However, gravity is very much built into the universe - the structure of the universe is based on it being there (and having the relationship with other fundamental forces that it does). It's a very hypothetical question - the thought that you could "lose" gravity but keep everything else in the universe somehow well-behaved.