…is there any way of predicting where it would land? Not in a planned re-entry, mind you, but if circumstances caused it to fall to earth in an uncontrolled manner.
I know that much of Salyut 7 landed in Argentina, but I don’t know if that was chance or if they knew where it would eventually come to ground.
The simple answer, yes and no.
First, there are only limited reasons for ANY satellite to fall from orbit, such as a deorbit burn or from orbital decay.
The ISS currently DOES experience drag from the tenuous atmosphere still present, hence requires occasional thruster burns to stay in orbit.
So, what could cause a sudden, unplanned reentry? Well, if an object hit the station and was large enough to cause it to come apart, it won’t reenter immediately, it would scatter in pieces, as a destroyed satellite did a few years back after a certain government shot down a satellite or even when a dead Russian satellite struck a satellite phone satellite, both of which required the ISS to move out of the path of the debris.
The ISS could run out of fuel or the thrusters break down and not be replaced, but the decay would be measurable and predictable, mostly.
A super massive coronal mass ejection could kill the station and the astronauts, ionizing and heating the upper atmosphere, causing the drag to increase and increase the orbital decay. BUT, it wouldn’t be anywhere NEAR immediate reentry, it would still be months of watching it.
A manual, suicidal reentry burn, conducted by an insane astronaut could certainly do it.
BUT, like Skylab and Mir, very, very little survives to reach the ground. Only the most dense objects would survive reentry. Even THEN, the reentry can be quickly modeled and predicted impact zones could be rapidly provided.
Just like how they found shuttle parts and astronaut remains when the shuttle broke up, from radar data, they predicted the dispersion of parts of the shuttle.
Said another way, as it begins to get closer to re-entry time (for whatever reason) the predictions of the impact point will get better & better.
Today all we can say is it’ll impact sometime in the next (WAG) century and (for sure) someplace between ~52 deg N & ~52 deg S. The orbital inclination gives solid bounds on the latitude of the impact. But the complete uncertainty of the time of final engagement with the atmosphere means the longitude of impact could be anything.
A day before expected reentry they could probably tie it down to a hemisphere or so of longitude. And coupled with knowledge of the ground track of the next dozen orbits, they could reduce it to several diagonal swaths under risk and adjacent swaths of zero risk.
Once it gets almost into the atmosphere with just 1 orbit left, they’d probably be able to localize it to maybe +/- 50 miles cross-range & +/- 1000 miles downrange. But by then you’ve got just a couple hours to impact. Even if you’re inside that 100 x 2000 mile ellipse your odds are still pretty good since the total amount of wreckage arriving at ground level might be a jetliner or two’s worth. IOW, enough to wreck maybe a couple of city blocks. Which is a minuscule percentage of ~200K square miles.
If the thing is tumbling or damaged, the chaos factor in the solutions would go way up. Naturally a lot of folks would be putting a lot of effort into modeling the reentry based on continuous radar tracking data. But their solutions would still have much larger error bars than if we were doing a controlled intact re-entry / disposal.
I mostly agree with LSLGuy and Wizard One, with the caveat that the ISS is made of many modules. It’s not going to hit somewhere, it’s going to hit in many places. Where those impacts are could depend on where and when the pieces break apart, and that might not be predictable.
The parts which make it to the ground will be big chunks of contiguous structure. Flimsy things like antennas and solar panels will break off, break up, & mostly burn up before they get to the ground.
If we assume it’s still in one piece as it gets into those last couple orbits, then all the big chunks will land in the target ellipse. Yes, it’ll be a shotgun, not a rifle shot. But it’s not like big parts will be breaking off over a period of many minutes and each starting a separate steeper trajectory from the point of separation. The trajectory of the whole and the trajectory of any given good-sized broken-off segment will be pretty similar.
Parts may still impact over a multistate- or multicountry-sized area. Hence the error ellipse.
Thanks, Folks 
Follow up question: so the unexpected happens (fill in with hit by an object, attacked by aliens, that insane astronaut mentioned in post #2, whatever) and it’s so badly damaged that it’s going to fall, do we have eyes on the space station to know what’s gone wrong so people could calculate the debris path? Are we watching it with the Hubble or satellite(s), and could record an image of the damage for the news? Or are we simply relying on the space station staff checking in to know the status? I assume the former.
Hubble would be utterly useless for observing anything in low Earth orbit. But everything in orbit (or at least, everything bigger than about a golf ball) is tracked via radar by NORAD, which is much better for determining these things anyway. Plus, there are GPS devices and the like on board the station itself, so as long as anything’s running, it can measure and transmit its own position.
To get a feel for the decay rate and its variability, check out the height vs. time plot of the ISS at “Heavens Above.”
http://www.heavens-above.com/IssHeight.aspx
There is a longer term plot here:
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Does NORAD actually track orbiting objects by radar? At one time, I know they used optics, but that was a couple decades ago. I haven’t kept track of their capabilities.
Well, I thought they used radar, but I could certainly be mistaken about that. In any event, they certainly track (somehow) objects far smaller than the ISS.
What does “track” mean in this context? “Oh, there it is, that little dot there” or “holy God, there’s a gaping hole in the side of the space station, those poor people!”?
Looks like the ISS covers a lot of ground - as far north as the southern Irish coast, and as far south as the bottom tip of South America. The ISS and Space Shuttle Challenger icons appear just west of Central America here: http://www.challenger.org/programs/iss/images/LargeTrackingMap.JPG
Remember SkyLab?
They know the orbit of every one of the objects they track, so at any given moment, they know where each of them should be. Whenever one of them is above one of their ground stations, they do more observations of it, to refine the orbital parameters to account for experimental error in previous observations or hard-to-model orbital decay or other perturbations. They would know well in advance if something of significant size were going to strike the station, and would warn them to adjust their orbit slightly before it hit. If you’re asking if they could see a hole in the station itself, I don’t know (probably; you can see the general shape of the station even in an amateur telescope, if you aim it right), but they could probably detect a change in the orbit from any event that could cause a big gaping hole.
Given I was two, no.
