How Can Hubble Fix Its camera ona single spot in space knowing that it has no moter and is moving?

Answer 1

The Hubble does have motors to change its orientation-- They are the Reaction Control Wheel Assemblies.

Hubble has a system of Fine Guidance Sensors (FGS) which locks onto a target region for observations using star constellations (fixed patterns of stars) as landmarks. Once locked on, the FGS commands the reaction control wheels (gyroscopes) to orient the telescope to the desired direction.

The reaction control wheel assemblies have moving mechanical parts and therefore have a finite lifespan. These do wear out over time and require replacement. The Hubble has 6 of these (several are backups), and so far 3 has completely worn out and it's operating on the minimum required 2, with one shut down as a reserve.

The next servicing mission will be replacing these six reaction control assemblies with new ones to give it another 10 years of life.

Answer 2

Your question contains errors.

The Hubble Space Telescope has solar panels for power,
and contains both manuvering jets, and motors for steering of the telescope in various directions and elevations. Focus is most likely set at infinity because most all of the targets are well out in the deep distances far away from the telescope itself. I would assume that there is a focus motor installed also, however, just in case someone wanted to do an Earth or Moon shot.