Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[Max White]

I'm suggesting that by 'space' he is hanging by he's space suit not far above the ground of some planet, not in outer space, far from a planet,  with no measurable gravity space.
The aliens thought it would be funny to screw him to something 100 meters away from the station. Because he is attached to something solid, he isn't moving relative to the Mir, and he can get himself down with the screw driver.
Mir might be a space station, but it is the type on the surface of a planet.

Although this is just a guess.

[Il Palazzo]

Nah, come on Max, it's not a trick question like that. In the world that Zdravko inhabits, Mir is still floating in space. Maybe it all happens in the past or something.

Well, one assumes he is wearing an oxygen pack, lest he be dead. He could presumably adjust it to allow some air to escape, thereby providing propulsion.

Now, you have to realise that this question is something I'd made up on the spot, so it's all my own judgement and understanding of physics that I'm going by, but this is actually, in my opinion, the best way of doing it. I'm not conversant enough with the design of soviet-era spacesuits to know if they were given an emergency relief valve, but I find it unlikely(so many safety problems, so little gains). That's why I'd suggest using the screwdriver to puncture the many layers of the spacesuit and allow the air to escape and provide propulsion(that'd be some hard work but doable, I suppose).
It would be interesting to actually try and calculate how much air would he have to release to give his ~150-200kg self some meaningful velocity(~0.1m/s?) without compromising his life support system, but we'd need some better design data on the spacesuit first.

There's still one thing, though. Would Zdravko waste his precious breathing gases to turn around in space, or would he rather use some other technique?

[TheBronzePickle]

The aliens are only pranksters, right? He could do something to compromise his wellbeing and force them to either save him or, at the very least, feel guilty about inadvertently killing him if not getting space law on their asses for putting a member of a sentient species in a dangerous situation.

Hell, he could just actually throw the screwdriver. If he gets it right, he floats back to the Mir. If he screws up, they'd have to save him.

Yes, I know, there's a chance they won't save him because they just don't care, but since they seem sentient, they've probably got some idea of morality.

[Il Palazzo]

Well, despite all the zany alien fluff included in the problem, this is still purely a physics question.

Zdravko still needs to know how to turn around in space without wasting his precious bodily fluids air.

[TheBronzePickle]

Every action has an equal and opposite reaction. If he, say, tucked his legs in to his chest with enough force, he might get a small spin that would straighten out once he let them back out to their original position. Same idea if he twisted his torso or some other movement. That would allow him to turn in space with some iota of precision. Considering he's only at a distance of 100 meters to a space station, which should have a fairly large cross section, accuracy is important, but it doesn't have to be perfect.

[Il Palazzo]

You're close, but it's not exactly how it works.
You can't really make yourself spinning like that, since e.g. tucking your legs in is an action that starts with changing momentum of your lower body, and by reaction your upper body(as you described), but ends with having to stop the movement of your legs once they're fully tucked in, thus stopping the movement of your upper body. To keep on spinning, you'd have to find a way to tuck your legs in and let them float away somehow(I guess a newt could do that with it's tail, providing an appropriate spacesuit design. That would still be a one time action though, as it'd have to stop its spin by chucking away some other body part - rather wasteful form of direction control).

Note that the "force" with which you move your legs, that is how fast the action is performed is irrelevant here. It would be relevant in an environment with dense surroundings instead of vacuum, as quicker movement of any body part produces more drag than a slow one, letting you apply some net force by alternating the speed - there's a lot of swimming movements that make use of this fact.
In vacuum, however, it's irrelevant.

[Urist Imiknorris]

He doesn't. He stabs himself in the back with the screwdriver, completely blind, leaving his fate up to luck (and maybe a well-thrown screwdriver).

[irmo]

Every action has an equal and opposite reaction. If he, say, tucked his legs in to his chest with enough force, he might get a small spin that would straighten out once he let them back out to their original position.

Conservation of angular momentum ruins your day here. With nothing to push against, he goes nowhere.

How about this: Toss the screwdriver straight down and then catch it between his feet. Tossing it causes him to rotate backward slightly, catching it stops him. He then bends down, grabs the screwdriver, straightens up, and then tosses it again. Repeat until he's facing away from Mir, then throw. It doesn't have to be exact--he's a hundred meters away and Mir is about thirty meters wide, and as long as he's close enough to get a hand on Mir he can climb to the airlock. If he misses, he can take off one of his boots and throw that.

Though considering how long that would take, and that he'd have to throw the screwdriver without being able to see Mir, he might have better luck just throwing it backward over his shoulder.

(Edit: Assuming a 200 g screwdriver, held at arm's length (1 meter radius), thrown at your feet at 5 m/s (meaning you get around half a second of flight time), you gain ~1 kg*m^2/s angular momentum while the screwdriver is in motion. An Air Force study by Santchi et al. (1963) gives a moment of inertia for the human body of 11.64 kg*m^2 in this posture, so you're rotating at 0.086 rad/s = 4.9 degrees/s. So every throw gives you about 2.5 degrees of rotation.)

[Il Palazzo]

How about this: Toss the screwdriver straight down and then catch it between his feet. Tossing it causes him to rotate backward slightly, catching it stops him. He then bends down, grabs the screwdriver, straightens up, and then tosses it again. Repeat until he's facing away from Mir, then throw. It doesn't have to be exact--he's a hundred meters away and Mir is about thirty meters wide, and as long as he's close enough to get a hand on Mir he can climb to the airlock. If he misses, he can take off one of his boots and throw that.

Whatever he gains by throwing the screwdriver down, is being lost by raising it back up. It's actually still almost the same as with BronzePickle's leg-tucking. Conservation of momentum still ruins your day here.

Here's a hint: Zdravko can use his screwdriver to do this, but he should also be able to do without.(and without throwing it away. It's a good screwdriver.)

(Edit: Assuming a 200 g screwdriver, held at arm's length (1 meter radius), thrown at your feet at 5 m/s (meaning you get around half a second of flight time), you gain ~1 kg*m^2/s angular momentum while the screwdriver is in motion. An Air Force study by Santchi et al. (1963) gives a moment of inertia for the human body of 11.64 kg*m^2 in this posture, so you're rotating at 0.086 rad/s = 4.9 degrees/s. So every throw gives you about 2.5 degrees of rotation.)

Ah, actually, that's one way of doing it, yes. You just need to make sure to throw the screwdriwer down with your arm outstretched, and bring it back up as close to your body as possible. You will get net angular displacement this way.
It's kinda tricky, though. One clumsy throw and you might not catch it.

[TheBronzePickle]

One question: what's the altitude of Mir? If they're in roughly the same height range as the ISS currently is, then there's a very minute amount of atmosphere. He could just swim to the station. Taking hundreds of hours to do so.

[Il Palazzo]

Wikipedia tells me the perigee is at 354 km. Zdravko considers this proposition for a moment, but he doesn't really fancy spending that much time floating in space. Besides, he can't swim.

[irmo]

Whatever he gains by throwing the screwdriver down, is being lost by raising it back up. It's actually still almost the same as with BronzePickle's leg-tucking. Conservation of momentum still ruins your day here.

The difference between this and some kind of leg-tucking maneuver that won't work is that his legs remain attached to his body. The gain with this method comes from the time of flight between throwing and catching the screwdriver. During that time, the screwdriver has angular momentum about Zdravko's center of mass, and so Zdravko has equal and opposite angular momentum. After the catch, they're connected again and he can raise it back to his hands without rotating himself at all.

And yes, it does depend on him being able to catch every single throw. On the other hand, the angular displacement notably does not depend on how fast the throw is, so he can throw it as slowly as he wants and still get his 2.5 degrees per throw.

[TheBronzePickle]

As was said: lifting the screwdriver would cause the equal and opposite reaction that would reset his physical position. Unless the screwdriver was imparting its energy somewhere other than Zdravko, it wouldn't work.

That being said, although he may not be in enough atmosphere to effectively 'swim,' there should be enough to make it so that he could paddle himself around slowly. It would still take some time, but not nearly as much time as trying to make it to the station.

[irmo]

As was said: lifting the screwdriver would cause the equal and opposite reaction that would reset his physical position. Unless the screwdriver was imparting its energy somewhere other than Zdravko, it wouldn't work.

Incorrect. While he's lifting the screwdriver it's attached to him, so he doesn't rotate at all. He can have non-zero angular momentum only while the screwdriver is not attached to him (ignoring other possibilities like removing his shoes, opening his oxygen line, etc.).

(Here's a better solution: Zdravko raises both arms above his head, holds the ends of the screwdriver, and flicks them with both hands so that it spins in place. When he's rotated as far as he wants to go, he catches the screwdriver and he stops rotating. This works on the same principle but with much less risk of losing the screwdriver.)

[Il Palazzo]

As was said: lifting the screwdriver would cause the equal and opposite reaction that would reset his physical position. Unless the screwdriver was imparting its energy somewhere other than Zdravko, it wouldn't work.

As I'd put it two posts above(albeit in the edited section, so it might've been missed), lifting the screwdriver will produce less angular displacement than throwing it down, as long as the lifting part is done by keeping the screwdriver as closer to the centre of Zdravko's mass than when it was thrown down.
@Irmo - the fact that it has been thrown, i.e. actually in-flight, and not connected to Zdravko himself doesn't factor here at all.
In fact, there is no need to throw the screw driver at all. You just need to hold it in your arm extended as you bring it down towards your feet, and then keep the arm close to your body as you lift it. You are in this way moving the screwdriver in closed circles, and according to the conservation of momentum, causing the rest of your body to rotate in the opposite direction. What's more, there's no need to use screwdriver at all(but it makes it somewhat faster) - Zdravko can simply move his arms(or legs) in circles to cause the same effect. It's a nice method, because the rest of his body stops spinning as soon as he stops moving his hands. He should take care to keep the movements symmetrical, so as not to start turing alongside some weird axis.

There is another way of doing it - it's slower, but less tiring(oh, Zdravko you lazy bum you) and involves conservation of angular momentum as well.
Take the screwdriver, and make it spin somewhere close to Zdravko's centre of mass(close to the stomach, I presume) - you're transfering some angular momentum to the screwdriver, and so for the rest of the cosmonaut-screwdriver system to still have 0 net spin, Zdravko's body must spin in the direction opposite to screwdriver's spin.
To stop rotating, Zdravko simply needs to catch the screwdriver.(this has been suggested above by Irmo the ninja)