From page 2: An oft-asked question is whether or not Columbia could have docked with the ISS, which would have had consumables to spare. There are numerous reasons why this would not have been possible, but the overriding one comes down to simple physics: Columbia would have had to execute what is known in orbital mechanics terminology as a "plane change" maneuver—applying thrust perpendicular to its orbital track in order to shift to match the ISS' inclination. Plane change maneuvers require tremendous amounts of energy—in some cases, even more energy than was required to launch the spacecraft in the first place. Appendix D.13 dismisses the possibility of an ISS rendezvous with just two sentences:
"Columbia's 39 degree orbital inclination could not have been altered to the ISS 51.6 degree inclination without approximately 12,600 ft/sec of translational capability. Columbia had 448 ft/sec of propellant available."
For the record, it wasn't possible in Gravity, either.
Well, physics education definitely spoils Gravity somewhat. They tried to do bunch of stuff in realistic manner and crossed into "uncanny valley" of movie realism. During the movie I was "why medical doctor is servicing Hubble?", "no, you are not going to see it coming", "no, don't remove helmet when there is fire in the cabin!"
And, more importantly, "all three of them on the same orbit sequentially if they can go from one to another?". Basically movie implies that. Of course the question is how they got Hubble on the same orbit, since they where servicing it, by theoretically it could have been repositioned during previous missions.
Kerbal Space Program is a fantastic educational platform for actually trying this at home. Going from an equatorial to polar orbit uses an incredible amount of fuel.
Someone stated elsewhere in negating the possibility of a different type of vehicle providing supplies that said vehicle was incapable of achieving the shuttle's orbit.
Could the shuttle change orbit downward to meet up with a vehicle that itself was otherwise incapable of reaching the shuttle's particular orbit, or is that just as hard of a change? I'll have to fire up KSP, but would it be possible to meet a supply vehicle and use less fuel than an ISS rendezvous?
This is not about changing orbital radius, these are relatively cheap to change. It's about changing orbital plane - for 90 degree change (i.e. polar to equatorial) roughly speaking it would require 1.4 amount of fuel to get to the orbit in the first place (and additional fuel to get this fuel to orbit).
From page 2: An oft-asked question is whether or not Columbia could have docked with the ISS, which would have had consumables to spare. There are numerous reasons why this would not have been possible, but the overriding one comes down to simple physics: Columbia would have had to execute what is known in orbital mechanics terminology as a "plane change" maneuver—applying thrust perpendicular to its orbital track in order to shift to match the ISS' inclination. Plane change maneuvers require tremendous amounts of energy—in some cases, even more energy than was required to launch the spacecraft in the first place. Appendix D.13 dismisses the possibility of an ISS rendezvous with just two sentences:
"Columbia's 39 degree orbital inclination could not have been altered to the ISS 51.6 degree inclination without approximately 12,600 ft/sec of translational capability. Columbia had 448 ft/sec of propellant available."
For the record, it wasn't possible in Gravity, either.