[annie123 (OP)]

What would happen if an astronaut on a space walk got disconnected from the  base? WOuld he/she float away? die from suffocation/freezing once the suit supplies weren't working? Where would the bodily remains end up? Would he fall down/up/float around, be reachable for reacapture?

[Phractality]

Consider the infamous tool bag. It burned up in the atmosphere about nine months after being released from the ISS. That's because a smaller object has a higher drag to mass ratio, and its orbit decays more rapidly. With each orbit, it moved farther ahead of the ISS. (Orbital mechanics are such that, if you slow down, you speed up.)

With quick action, it might have been possible to retrieve the bag. I don't know if NASA has thought of it yet, but (with good aim) a spring-loaded fishing reel with grappling hooks on the end could retrieve objects up to a few hundred meters away.

An astronaut with jet pack could travel several kilometers from the ship. For safety, fishing line would serve as a tether. The tether is only a redundant safety feature, so it needn't be very strong; as long as there is no sudden jerk, 10-pound test line would be adequate.

NASA space suits carry enough oxygen to last 6 to 8½ hours (when combined with a CO₂scrubber). If the oxygen runs out, the astronaut will suffocate. If the suit leaks, he soon will be freeze dried.

[CliffordK]

Certainly if the astronaut is deemed to be alive, then the responsible space agency would make all effort to swing by and pick the person up.  The space shuttle has quite a bit of maneuvering capabilities, and I believe even the International Space Station would have some maneuvering capabilities too.

Oddly, I don't think they've designed the ISS to have a ship docked there at all times for short hops such as satellite adjustments and repairs, or emergency descents to Earth.

The tool bag is a good point...
If I was the astronaut lost in space, I'd be thinking of all possible methods to get back, including chucking any tools I had in my possession into space in the direction opposite to where I wanted to travel. 

If there was a way to use the oxygen (or CO₂ exhaust) as a jet, it might be worth it to sacrifice some of it.  I.E.  take an extra oxygen cylinder and knock the top off and it would be like watching a deflating balloon flying around the room.  Although, if you had access to a spare oxygen cylinder, you would likely choose to do a more controlled release of the oxygen.

[annie123 (OP)]

Thanks for these, but I was also interested in what would actually happen to whatever material remains were there - assuming no rescue. Where would they go? End up? If the whole disintegrated where would the bits
 go?

[Geezer]

Thanks for these, but I was also interested in what would actually happen to whatever material remains were there - assuming no rescue. Where would they go? End up? If the whole disintegrated where would the bits
 go?

They would gradually slow down, fall into ever lower orbit and eventually burn up in the Earth's atmosphere.

[annie123 (OP)]

why would they slow down? I thought once things were set in motion in space there was nothing to resist, and why would they fall into earth's atmosphere? Why wouldn't they just keep on going round?

[Phractality]

why would they slow down? I thought once things were set in motion in space there was nothing to resist, and why would they fall into earth's atmosphere? Why wouldn't they just keep on going round?

The atmosphere is extremely thin up there, but not a perfect vacuum. The ISS orbits at about 350 km above sea level. When the tool bag was released, the air drag slowed it very slowly, at first. But slowing an object in orbit makes it fall to a lower orbit, so it ends up going faster. The lower the orbit the greater the air drag, so the orbit decays faster and faster until it burns up like a meteor at about 60 km altitude.

[Geezer]

But slowing an object in orbit makes it fall to a lower orbit, so it ends up going faster.

Are you really sure about that?

[Phractality]

Are you really sure about that?

Absolutely! It' orbital mechanics 101. The lower the orbit, the faster the average speed. If you want to go from a higher circular orbit to a lower one, you must first do a retro burn. This makes your speed too slow to remain in the higher orbit, so you coast downhill to the lower orbit, but when you get there, you will be going too fast to stay in the lower orbit. To remain in the lower orbit, you must do a second retro burn to match the speed of the lower orbit. If you don't do a second retro burn, you will coast uphill until you reach the original orbit; you will remain in an elliptical orbit which crosses the two circular orbits.

Continuous drag on a satellite gradually moves it to lower orbits, and the lower the orbit, the faster the satellite. To speed up, you must slow down.

[Geezer]

Are you really sure about that?

Absolutely! It' orbital mechanics 101. The lower the orbit, the faster the average speed. If you want to go from a higher circular orbit to a lower one, you must first do a retro burn. This makes your speed too slow to remain in the higher orbit, so you coast downhill to the lower orbit, but when you get there, you will be going too fast to stay in the lower orbit. To remain in the lower orbit, you must do a second retro burn to match the speed of the lower orbit. If you don't do a second retro burn, you will coast uphill until you reach the original orbit; you will remain in an elliptical orbit which crosses the two circular orbits.

Continuous drag on a satellite gradually moves it to lower orbits, and the lower the orbit, the faster the satellite. To speed up, you must slow down.

That's certainly the case where a vehicle uses thrust to change it's orbit. The angular momentum is conserved, so it's speed has to increase.

In this situation the angular momentum is not conserved. Some of it is being lost to friction.
 

[Phractality]

Are you really sure about that?

Absolutely! It' orbital mechanics 101. The lower the orbit, the faster the average speed. If you want to go from a higher circular orbit to a lower one, you must first do a retro burn. This makes your speed too slow to remain in the higher orbit, so you coast downhill to the lower orbit, but when you get there, you will be going too fast to stay in the lower orbit. To remain in the lower orbit, you must do a second retro burn to match the speed of the lower orbit. If you don't do a second retro burn, you will coast uphill until you reach the original orbit; you will remain in an elliptical orbit which crosses the two circular orbits.

Continuous drag on a satellite gradually moves it to lower orbits, and the lower the orbit, the faster the satellite. To speed up, you must slow down.

That's certainly the case where a vehicle uses thrust to change it's orbit. The angular momentum is conserved, so it's speed has to increase.

In this situation the angular momentum is not conserved. Some of it is being lost to friction.
 

Angular momentum is always conserved. In this case, the tool bag pushes foreward against the air, heating it up. We can't trace the momentum of every molecule, but conscervation of angular momentum dictates that the net change to the angular momentum of the atmosphere must be equal and opposite the change in the bag's angular momentum. As long as the bag's easterly speed is increasing, the atmosphere must be accelerating toward the west. Since the net angular momentum of the atmosphere is eastward, it slow down and/or move closer to the ground. Keep in mind that the atmosphere is not in orbit, so it doesn't obey Kepler's laws; moving closer to the ground does not make it go faster toward the east, but the Coreolis effect does tend to increase its angular velocity.

This attempt at analysing what happens to the atmosphere is hurting my brain. Physicists usually go for the simple answer and avoid unnecessary complications. Why can't you just accept that energy and momentum are always concerved? Anyway, the bag ended up as a meteor, the atmosphere went on about its business as usual, and the angular momentum of the bag was returned to the Earth where it came from in the first place.

P.S.: The fact that the bag's speed is increasing doesn't necessarily mean it's angular momentum is increasing. The angular momentum is the momentum times the distance from the center of Earth, and that distance is decreasing. My brain is already sprained, or I'd attempt the math to find out if the angular momentum is constant.

[Geezer]

Why can't you just accept that energy and momentum are always concerved?

Oh, I agree that all the energy is conserved, but I think you may be overlooking the fact that some of the energy stored in the form of angular momentum is being converted into thermal energy in the gas molecules in the thin atmosphere.

It's not really very different from using a friction brake to slow down a flywheel. The angular momentum is being converted into thermal energy. 

[Phractality]

It's not really very different from using a friction brake to slow down a flywheel. The angular momentum is being converted into thermal energy. 

No. Energy is conserved, and angular momentum is conserved. You can't convert one to the other. When the flywheel is stopped, it's angular momentum is transferred to the Earth. If the Earth weren't so big, you could see that. Imagine a flywheel with a vertical axis attached to a raft floating in a pond. As you start spinning the flywheel clockwise, the raft starts spinning counterclockwise. When you stop the flywheel, the raft also stops. (Assuming there is no friction between the raft and the water.)

[Geezer]

No. Energy is conserved, and angular momentum is conserved.

Er, well, I don't believe that's right either.

The only thing that is conserved is energy. Angular momentum is just another form of stored energy, and it can be converted into lots of different forms of energy, quite easily in fact. Flywheels are rather good at doing that.

Bear in mind that we are referring to the angular momentum of the combined orbiting body/Earth system rather than the angular moments of all the particles in the system. 

[Phractality]

The only thing that is conserved is energy. Angular momentum is just another form of stored energy, and it can be converted into lots of different forms of energy, quite easily in fact. Flywheels are rather good at doing that.

Try applying dimensional analysis. Units of angular momentum cannot be converted to units of energy. They are not equivalent.

Hyperphysics: Conservation Laws

Wikipedia: conservation law

[imatfaal]

Geezer - have to go with Fract on the conservation argument - conservation of angular momentum is not merely as special case of energy conservation.  It can be seen in terms of symmetries/lack of change under transformation; Noether's theorem deals with continuous symmetries - and every symmetry has an associated conservation.  Symmetry under transformation in time leads to energy conservation, and symmetry of direction in space leads to angular momentum conservation. 

I always get muddled with orbital speeds, radii, and decay rates - will sharpen pencil and revert

[Geezer]

Geezer - have to go with Fract on the conservation argument - conservation of angular momentum is not merely as special case of energy conservation.  It can be seen in terms of symmetries/lack of change under transformation; Noether's theorem deals with continuous symmetries - and every symmetry has an associated conservation.  Symmetry under transformation in time leads to energy conservation, and symmetry of direction in space leads to angular momentum conservation. 

I always get muddled with orbital speeds, radii, and decay rates - will sharpen pencil and revert

Matt, then how do you explain what happens to the energy stored in a flywheel when you apply a brake to slow it down? It's obviously converted into heat, one way or another. The object falling out of orbit is a variation of the same situation.

Is there a terminology problem here? Maybe we should be referring to rotational energy rather than angular momentum http://en.wikipedia.org/wiki/Rotational_energy

EDIT: I should have said that the object falling out of orbit is a variation of a slowing flywheel if friction is the dominant reason for it falling out of orbit.

[Geezer]

I think I see the problem. Angular momentum has very little to do with this. The angular momentum of the orbiting tool bag or whatever, is really very small. (Its rotational period equals the orbit time.) On the other hand, its kinetic energy is really very large.

It's the kinetic energy being dissipated by friction that causes the orbit to change.

It's interesting that the spinning skater speeding up phenomenon is usually described as an example of conservation of angular momentum. I'm wondering if it should really be described in terms of conservation of rotational energy, or does it come to the same difference?

[imatfaal]

Angular momentum is only conserved in a system with no external torque - your brake on the flywheel will allow an external torque.

It is normally explained that the skater gets faster to conserve angular momentum - and it cannot conserved both the ang-mom and the energy, as one is linear the other is quadratic.  The formulas are as follows:

E_rot=1/2 Iω²

L=Iω

the skater changes I the moment of inertia, ω the angular velocity increases to keep L conserved.  I presume the energy increase that this demands is that provided by the work done in skater pulling his arms and legs to the centre to change the moment of inertia.

[Geezer]

Angular momentum is only conserved in a system with no external torque - your brake on the flywheel will allow an external torque.

It is normally explained that the skater gets faster to conserve angular momentum - and it cannot conserved both the ang-mom and the energy, as one is linear the other is quadratic.  The formulas are as follows:

E_rot=1/2 Iω²

L=Iω

the skater changes I the moment of inertia, ω the angular velocity increases to keep L conserved.  I presume the energy increase that this demands is that provided by the work done in skater pulling his arms and legs to the centre to change the moment of inertia.

Thanks Matt. That explains it very well.