There have been several general critiques of the realism some of the physics depicted in the movie "Gravity" notably regarding the the orbital mechanics of the transition from the Hubble Space Telescope to the International Space Station. I understand that these center around the energetic requirements of getting from the orbits occupied by HST to the ISS, but am foggy on the details. In particular, I'm curious what steps would be involved, and how much energy would be required at each, and whether it would be possible, with any practicable technology, to carry an source that could provide sufficient energy.
My (vague) intuition, from what I can gather, is that one would first need to (1) decelerate from the HST orbit and begin to fall towards the ISS orbital altitude (I'm never clear on whether one also acquires a higher orbital velocity as one falls) (2) accelerate to the orbital velocity for the ISS orbital once one arrives at the ISS orbital altitude, and then maneuver to (3) catch up with the ISS and (4) change direction to match its different orbital inclination.
What are the actual steps involved in getting from the HST to the ISS? How much energy would be required at each step? How big a fuel tank or other energy source would be required to provide this energy? Could a human possibly carry such a source, or survive its use?