Space is not true zero gravity. When an astronaut experiences what is called zero gravity, he really is still being held by gravity in the same orbit as his moving spacecraft.

An orbiting body moves on a course determined by the equilibrium between it's straight line trajectory, the torque created by it's own spin, and the gravity generated by other large objects in space. If the orbiting object is significantly lopsided in the distribution of it's mass, it will eventually stop spinning and settle with one side facing the object which it is orbiting. That is why we on earth only see one side of the moon.

The deeper mystery is the source of gravity itself, which no physicist has ever conclusively explained.

Orbit and rotation itself is perpetuated by an incredible amount of inertia. Only a major collision with another large object would interrupt the inertia of orbit and rotation.