If the Hubble Telescope orbits the earth every 97 minutes how the heck can it stay focused on one thing long enough to get a good picture?

It only has to remain stable around the 3 axes through its center of mass. That's 'relatively'
easy to accomplish with gyros and heavy flywheels. Once 3-axis stability is achieved, it doesn't
matter where the whole thing goes ... it still stays pointed toward the same field of view for
long exposures. (Just remember to rig a timer to close the shutter when the earth is in that
direction from it, to avoid sunlight or artificial light from the surface being added to the exposure.)

Actually ... you know what ? That may actually be easier in space than it is on the surface
of the revolving earth. Never thought about that before!
It only has to remain stable around the 3 axes through its center of mass. That's 'relatively'
easy to accomplish with gyros and heavy flywheels. Once 3-axis stability is achieved, it doesn't
matter where the whole thing goes ... it still stays pointed toward the same field of view for
long exposures. (Just remember to rig a timer to close the shutter when the earth is in that
direction from it, to avoid sunlight or artificial light from the surface being added to the exposure.)

Actually ... you know what ? That may actually be easier in space than it is on the surface
of the revolving earth. Never thought about that before!