## >> Saturday, November 9, 2013

I haven't actually died. Just been sick and overworked which isn't a combination I recommend. But I haven't forgotten I had more to say on this subject. So I touched on the EVA things that drove me nuts on the the first post , but that wasn't all that made me a little bit crazy with Gravity. And, in the second post, I touched on why orbital debris IS a big problem, but not exactly a problem in the way portrayed. But, yes, there's more.  And I'll be describing them, so they'll be spoilers, so STOP HERE if you don't want details on what happened in Gravity.

Seriously, spoilers below, I'm not kidding.

First, foremost, most importantly, zipping around from Hubble Space Telescope (HST) to the International Space Station (ISS) to Tiangong (Chinese Space Station) using the dregs in an MMU and then some retrorockets in a Soyuz by eyeballing the target is utter nonsense. Not slightly nonsensical but completely noncredible. I'm going to start with a picture here (from Wikipedia) so you can quickly see why it's not possible.

So, at the start of the movie, the ISS is visible from the HST quite clearly. So, using the diagram above, we could assume they were at the same spot off the coast of Africa at the same instant, but still 130 km apart since HST is in a higher altitude. Note this is BEFORE the orbital debris entered into the picture. If we, quite optimistically, assume that it took 15 minutes  from the time Bullock was ordered to abort, was attacked by flying space junk, separated from the Shuttle, hyperventilated enough to use up most of the remaining oxygen (since she wasn't cleaning up, she should have had at least an hour left because they need to clean up for the last half hour), was fetched miraculously by an astronaut using obsolete hardware to the time they returned to the now dead Shuttle/HST with it's floating corpses, the ISS would be, say over Greece and HST would be over Saudi Arabia. Maybe within sight, but at best  as a speck in the distance, physically 1500-2000 km apart at a WAG (wild ass guess).

If, instead, we assumed all that took 46.45 minutes rather than 15 (which would make more sense), in theory, they are close to crossing orbits at near the same time again (that magic witching hour when the debris comes winging by again, but I digress) since that's when ISS would likely cross HST's orbit again, but close in space doesn't mean within arm's distance. HST, though it's going faster (8.16 km/second) has a larger orbit so it takes longer to go around. So, when ISS is "there" HST is some 1.55 minutes "behind" which doesn't sound like much but let me remind you of the speed: 8.16 km/s which translates to about 759  km in addition to the 130 km altitude difference.

So, assuming that changing inclination and altitude wasn't even part of the concern, but just straight translation, you'd be going more crossing more than 800 km outside your established orbit (so you get to supply all the force) to hit a moving target that's also going pretty damn fast (7.6 km/s) but not in the exactly same direction you're going in. And "not exactly" is as helpful as "close" in space.

But let's say, I'm sitting on a viable propulsion source that can propel me the 800 km at 5 gees (5X the force of gravitational pull on the earth which probably way more than the body can withstand without support - the Shuttle, during launch pulled less than three). At a constant acceleration (of 50 m/s^2) and "zero" initial velocity  the formula for distance is x=1/2at^2 which means t=SQRT(2x/a)=~179s, which is pretty fast (just under three minutes). Only problem is that the ISS is now 1360.4 km from where you last saw it. If you went at a more reasonable acceleration, it would be even further away. Plus you are now going an even faster clip and, even if you hit it, you'd be hitting it at a speed of 8950 m/s, yes many times faster than a speeding bullet. In fact, you'd probably want to spend half of that time slowing down the same rate you'd been accelerating, but that will cost you more time and the ISS will get that much further. But I digress.

Perhaps you can see why eyeballing this operation is, um, not effective. Could it be done? Not really, because, in order to do so, you'd have to know where it would be some 3 minutes later and the relative motion in zero g is very hard to gauge give the lack of landmarks, even for seasoned pilots, which Bullock was not. And this is at the best possible conjunction after you first saw it 46 minutes before. By the time you get to where you were in perfect conjunction some 90 odd minutes earlier, that distance has at least doubled and it just gets worse from there. Over the next hours, the distance lagging gets larger and larger so you get one shot really and one only to tag it. But wait, there's more.

Now the thrust to perform this nigh impossible task in theoretical conditions that have nothing to do with reality would require F=mass*acceleration with the mass of two EMUs (at a svelte 124.7 kg apiece per here) + the mass of two astronauts, let's say 81 kg for Clooney (180 lbs for you non-science American types) and 54 kg for Bullock (119 lbs), the total mass is 384 kg. With our acceleration at 50 m/s^s, we have a total force required of 19.2 kN (for 179s, I might add), which  is somewhat less than, say, an Orbital Maneuvering System engine (used by the Shuttle to deorbit at the end of mission) which has a thrust of 26.7 kN, but is nothing to sneeze at. That should, in fact, give you an idea of the kind of thrust you're going to need: more than 1/4 of the thrust (two OMS/vehicle) needed to deorbit the Space Shuttle Orbiter vehicle (which clocks in at 68,600 kg EMPTY) though the burn is much much longer. Do I have to point out that the MMU doesn't have anywhere near that propulsive power?

[Hey, if you're a real rocket scientist or a physicist yourself and note a dozen things wrong with my calculations, I hear you, you're right. I've got so many simplifying assumptions to make these doable that it's nonsense. It's all buffalo chips. I'm trying to make a point here.]

Unfortunately, that very simplistic, but effectively impossible, example is many times more impossible than that because, in order to interact with said ISS (cause you don't really want to punch into it at 9km/s, which, when combined with your existing orbital velocity, would likely have sent you out of orbit and off into outer space, but I digress), you need to match orbits at least to some extent: that means changing altitude and changing inclination. Impossible? No. Easy? Not exactly (haha).

Well, to change altitude (lower) in space is relative easy. You just slow down, inject delta V in the opposite direction you're going (which changes your orbit from "circular" to elliptical), than speed back up a little when you reach the right altitude to go back to a circular orbit.  Not something I'd want to do by eyeball or feel myself, but relatively simple, actually much simpler than the hypothetical translation I was talking about earlier and uses relatively little fuel, just enough delta V to go from 8.16 km/s to 7.6 km/s (or 0.56 km/s). Space craft do that kind of maneuvering quite a bit. Usually just a couple times a flight, though because it uses fuel (going down and going up).

Inclination changing, however, is a different beastie. To calculate delta V to change inclinations, assuming you have two circular orbits of the same altitude, you can use this equation:
$\Delta{v_i}= {2v\, \sin \left(\frac{\Delta{i}}{2} \right)}$ where v is the orbital velocity, delta i is the change in inclination and delta v sub i is the delta v required.
In this case, v=7.6 km/s (assuming we've already gone to ISS altitude) and i=-23.15 so delta v required is -3.05 km/s, nearly 6 times more than required to change altitude. And, of course, to match orbits, you'd have to do it just when the orbits conjoin (which is not exactly something you can eyeball) or, instead you'll just travel in parallel (from behind of course, since you were already behind and have had to slow down bunches to lower orbit and increase inclination. Space vehicles do NOT ordinarily change inclination during flight since launching at the right inclination is far more efficient than changing it after the fact (moving up in inclination from the ground is easier than moving down, which is why the ISS is at an inclination friendly to the more Northerly Russians). It's a big hairy deal.

Everyone still with me? Anyone go into a math coma?

No matter how you slice it, this maneuver that looks so cool in the movie,  (a) takes resources our free floating astronauts didn't have, notably a handy rocket engine, many times their mass in fuel, and time and (b) requires really tricky calculations done by big computers that know where everything is and will be in the near future. Eyeballing it ain't gonna fly. Even then, not sure it's possible because you have to simultaneously slow down (to change inclination and altitude) and catch up (because it's ahead of you). You might be able to if and only if you had those resources and a good lead.

I'm guessing I don't have to explain that the same holds true for bouncing over to Tiangong (which is at yet another (far smaller) inclination and even lower altitude.

So what? Why do you care? Why do I care? (And, yes, I do).  I'll tell you why. I've mentioned this was a beautiful movie, lots of very realistic space scenes going on. I don't think it would upset me so much if that weren't so. There is already a large faction of people who are of the opinion they could run the space program better, that this isn't so hard, that, for Columbia, if someone had noticed the damage, we could have done something.

No. We couldn't. Even if we had seen the damage (assuming it was readily visible), there was no way to repair it with anything we had at hand (no duct tape would not have sufficed), no way to get to the ISS (which was on a different inclination, just like HST).

If we had miraculously made it there, there was no way to hang out there long enough for someone to come rescue Columbia's crew because, unlike the movie, there are generally just enough Soyuz rescue crafts to take the number of people on the ISS down, no more no less (largely because that's how most of the crew gets there) and limited amounts of consumables.

We don't have extras return vehicles waiting around. I don't know about Tiangong, but I'm guessing it wouldn't have a rescue craft sitting there with the crew gone either. It's too expensive getting stuff into space to just leave it up there without a good reason.

It's a great movie to give you some hint of the challenges and dangers of being in space, how cool it is, but it hardly scratches the surface on how tough it is, how unforgiving the physics is, why for every crewmember on orbit, there are dozens of people round the clock to help out in case of danger. Exactly how much planning and know-how and technology goes into what they nominally do in space. And it could easily give the layman a skewed view of what options the crew really has in an emergency. Fortunately, as I mentioned last time, the danger scenario we're using isn't particularly realistic, but what happens afterwards is pure fantasy.

I could go on about how stupid I think it is she tried to take off in Soyuz when she knew it was tangled up in the ISS and a dozen or so rather minor issues like the likelihood of the Tiangong's escape capsule being usable by an non-pilot who doesn't speak Chinese, but the physics trumps everything and it's absolutely no go in that way.

So, no more party pooping. I'm done. Please, enjoy the show. ;)

• Lauralee

math coma doesn't even BEGIN to describe it.

• Roy

Heh, heh! I'm with Flit on that one! But the complexity you describe makes your point - the way they did it in the movie is impossible in oh so many ways.

• Stephanie Barr

Heck, this is basic first level physics and orbital mechanics and I probably made a few errors I didn't catch (almost missed the km vs. m transition at one point). Still my errors are going to stem from oversimplifying, not from making it more complicated.

(Note to self: no quantum physics for even hardcore readers of my blog. Math they no likey.)

Perhaps the scariest thing about me is that I was in a really self-pitying miserable mood and doing this math cheered me up. However to I keep the men at bay?