Granted the hypothetical is silly but you seemed to be suggesting that because figuring out orbital mechanics is hard it would be a reason for NASA to not try and put the shuttle in a different orbit. My point was that, fuel allowing, NASA would easily figure how to get the shuttle in a new orbit. Even if the math would make my brain melt this sort of thing is easily within NASA’s grasp to do. I merely suggested unlimited fuel to illustrate that point.
Two off-the-wall ideas:
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Deorbit at a shallow angle so they enter the atmosphere and bounce out once or twice. They’ll come back in again, of course, but perhaps they can bleed off some speed, and reduce the maximum temperature and pressure on the final re-entry. Okay, slim to no chance of working I know.
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Okay, this idea is REALLY stupid, but I’ll say it anyway. In the future, put some spacecraft into orbits that are designed to rendezvous with stranded, manned spacecraft. These rescue vehicles can be operated via remote control and, and… well I don’t know what – have an open door, a retro rocket, food, water, air, liquor, and a good ol’ return capsule with ablative heat shields. (yeah, I know, not yet designed, no money for it, and a million other things wrong with the idea.)
You launch these things with a few Congressmen and others who have sliced NASA to ribbons, and baddabing. Problem solved. Someday you’ll rescue the Chinese astronauts and promote world peace. Heck, I’ll be on Larry King to explain how I thought of it and get laid too. What more d’ya want?
Just like to point out that the X-38 is anything but “pure fantasy”. It does exist, and was 90% complete and about to enter flight testing when its funding got cut by a bunch of bureaucrats looking to save money by (as usual) shaving it off of someplace that the average voter would never notice or care about, aka NASA. Now they’re spending as much money as it would have taken to just finish the darn thing to instead catalogue and store the remnants of the project should they ever wish to revive it in the near future.
Not to deny the validity of your post though. The way things are going, it might as well be pure fantasy. 
I think most of us are just convincing ourselves that a rescue would be possble as a way of dealing with the shock. It’s a perfectly healthy and normal response.
I think a rescue would have been possible. I think a rescue of most of teh Titanic passengers was possible. Meanwhile, I do NOT think a Challenger rescue would have been possible. Just because it’s a shocking disaster of any kind doesn’t automatically mean that there was no hope. That’s going the other way to deal with the problem, IMO–shrugging off feelings of guilt and blame by saying “there was nothing that anybody could have done.”
Of course, in this situation, they never really even KNEW there was a problem–so the crew was as good as dead right from the start. But if such a problem were to occur in a future launch, under similar circumstances, and the problem was known to crew and Mission Control early on, I bet an attempt would be made to save them.
If they had enough fuel to change orbital planes (which is actually much harder than changing altitude: Generally, the way to change inclination is to first boost to a higher altitude where it’s easier, then change inclination, then change back down), then the orbit to reach the ISS would have been a cinch to calculate. It’s only rocket science, which frankly, is just about the most straightforward branch of science you’re ever likely to find. NASA has more than enough computing power to work it out: A single engineer with a slide rule could figure it exactly in a couple of hours. And the pilot is most assuredly qualified to put it into practice. Heck, my mom’s dog would be qualified to put it into practice: It’s all done by the onboard computers anyway.
But they didn’t have enough fuel, so that’s a moot point anyway. So what would they do? Just sit tight and wait for rescue, while the ground crews expedited the next launch as much as possible. You don’t need to worry about orbital decay: There’s some fuel on board to be used to de-orbit the craft, and if the craft is a loss anyway, you might as well use it to boost the orbit. Boosting the orbit, by the way, is a procedure so simple that you don’t even need to calculate it. Just point the ship so the engines are aft, and let 'er rip.
So would they have been able to survive long enough for rescue? Even if the next launch can’t be rushed at all, we’re only talking a factor of three longer than planned. Food and water supplies can definitely be stretched by that amount, although the crew would probably need medical attention afterwards. I don’t know how much oxygen can be stretched, though, or how much they had on board.
So suppose that they’ve waited, and the rescue ship is now there. What now? The rescue ship matches velocity at whatever is considered a safe distance, which would probably be easily within a hundred feet, and sends over a tether. Possibly one of the rescue astronauts needs to go over in an MMU to attach the tether, so we’ll assume that they thought to bring one along. Likewise, the rescue ship would have to have an airlock. All of the stranded crew then put on their pressure suits, vent the whole cabin and open the hatch (assuming the stranded crew has no airlock), and goes over on the tether. They enter the rescue ship via airlock, of course. There would be a risk of micrometeorites due to using just pressure suits rather than full spacesuits, and they might all end up with sunburns, and they’d lose some heat while transfering, but none of those things is likely to kill them in the time that they’re moving across.
So the only unknown is whether they’d have enough oxygen to last them. Other than that, a rescue is perfectly feasible.
Or, NASA looks at the whole scope of flying Shuttles and accepts that crossing fingers and praying is the final answer, because in the end, a failed rescue and two Shuttle tragedies closes the agency, whereas one disaster is merely a setback.
Science can save them, but reality of business and politics says they disintegrate.
End of Story. No rocket science required. They were expendable.
…If they don`t have to answer to the public. This morbid stance would never be made public for fear of backlash.
Fear of something happening on the rescue mission really isn’t a factor. I mean, even if whatever caused the failure on Columbia is inherent to the Shuttle design, they were still able to launch over a hundred missions before it happened. So you’d want to try to figure it out in the immediate future, but the risk for a single rescue mission is not all that great. Think about it: No rescue, 100% chance of losing one crew. Rescue attempt, 98% chance of losing no crew, 2% chance of losing two crews (one of which is much smaller, anyway, being only 1 or 2 people). If you’re willing to accept seven people being expendable, then surely you’re willing to accept a 2% chance of losing nine people.
The reality that no one has really touched on–except when I did so in my own hijacked Columbia thread–is that having the crew program the Columbia orbiter for ditching into the Pacific and then climbing aboard a rescue shuttle all based on the conjecture that Columbia would be lost in deorbit would have been politically very, very difficult.
Imagine the howl of controversy if a “few” missing tiles forces the scuttling of a $2.1 billion shuttle–the flagship of the US space program.
NASA’s computations in deciding to risk reentry, I believe, were greatly colored by their desire to return the craft and the political fallout if they did not.
One of the principal investigators of the Challenger disaster said this evening that he could not understand why NASA did not bother to at least try imaging the shuttle, using the latest and greatest in terrestrial optics. Columbia could have awaited an accelerated rescue from the next shuttle, but doing so may have proven political ruinous.