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Old 02-29-2008, 10:00 PM   #41
GVsdJZ2H

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The tube isn't in orbit though - it's attached to the Earth (well, unless we want to take this notion even further into la-la-land and have it somehow freely orbiting the planet, at a fixed distance above the surface). The "centrifugal" force will not negate gravity either; if it did, then the rotation of the atmosphere normally would cause it to lift away. A simple calculation shows this:

F = -m(w)^2r calculates the "centrifugal" force (actually, the centripetal but no matter) shows that the force per unit mass, taking a point on the equator at the surface of the Earth, would be 0.03 N/kg. Compare that to the gravitational force per unit mass of 9.8 N/kg. One can calculate the distance from the centre of mass where the "centripetal" force per unit mass is equivalent to the gravitational force per unit mass though:

(w)^2r = GM/r^2

r^3 = GM/w^2

r = 42,226 km which means the only region that the air experiences zero-g is 35,800 km above the surface of the Earth (the rest of the tube below this point, if attached to the Earth and perfectly rigid, is "geosynchronous" but not zero-g. For example, a point on the tube 1000 km above the surface of the Earth will be moving at 540 m/s but the speed required for zero-g at that point is 7400 m/s).

Anyway, if one assumes that this is the exit point of the tube then a reasonable of molecules released here will have insufficient escape velocity: 3 km/s (provided that the particles have the same speed as the tube) vs. the 4.2 km/s required. Of course, one could go with an even longer tube, where the exit is further out resulting in a lower escape velocity requirement, greater exit speed and a lower gravitational field strength.

By far the most important thing here (trying hard to keep this sensible!) though is the amount of work that needs to be done. Per unit mass of air, a minimum of 60 MJ of work needs to be done to the air at the surface of the Earth, for it to fully escape. The true value will be much higher than this due to inefficiencies in the pumping mechanism, the work done in compressing the air, the energy lost as a heat and so on.

Edit: too slow in replying! Oops!
I'm not saying the centrifugal forces will negate any power required to push the air up the tube, all I'm saying is, assuming the tube is in a geosynchronous orbit, as stated in the original proposal (it would be almost impossible to support the tube otherwise), that means its centre of mass will be at 35780 Km. Therefore any air exiting the top of the tube will have supassed escape velocity anyway due to the rotational speed of the top of the tube, so all that we need to do is somehow push the air out of the top of the tube. As long as we do that, the air will vent.

The reason why the upper atmosphere does not vent due to the rotation of the Earth is that it is not all in geosynchronous orbit. The very outer layers of the atmosphere do not rotate at the same speed as the Earth.
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Old 02-29-2008, 10:17 PM   #42
dremucha

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I'm not saying the centrifugal forces will negate any power required to push the air up the tube, all I'm saying is, assuming the tube is in a geosynchronous orbit, as stated in the original proposal (it would be almost impossible to support the tube otherwise), that means its centre of mass will be at 35780 Km. Therefore any air exiting the top of the tube will have supassed escape velocity anyway due to the rotational speed of the top of the tube, so all that we need to do is somehow push the air out of the top of the tube. As long as we do that, the air will vent.
not really, the "rotation speed" you said or orbital speed is the speed required to just maintain at a given height. if you were to throw something outward from there, the object will just have a higher apoapsis. with an orbit that look like a scretched rubber band. because the escape velocity is still alot faster than the geosync's orbital speed.

go and read about orbit and you will see. a rocket doesn't reach the moon by firing it's rocket directly at it. it is actually trickier than that!

ok, sorry i guess i should explain:

when you throw something, you apply speed to the object just once. the thing is, gravity is not speed but acceleration, so for each second, it is pulling you down at the given speed(eg 9.8m/s on earth). you will need to impart enough thrust during the vent to overcome the duration it will take you to travel out of the effective earth gravitation reach.

The reason why the upper atmosphere does not vent due to the rotation of the Earth is that it is not all in geosynchronous orbit. The very outer layers of the atmosphere do not rotate at the same speed as the Earth. i dunno what you mean, but the upper atmosphere does not vent simply cause there is not enough energy to counter the gravity pulling it downward. the reason why it is staying up there, is because as it fall, it hit other atoms and is bounce back up, that is how air pressure work. smaller atom travel further with the same energy since it has less mass to move, which allows them to stay higher.
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Old 02-29-2008, 10:31 PM   #43
GVsdJZ2H

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not really, the "rotation speed" you said or orbital speed is the speed required to just maintain at a given height. if you were to throw something outward from there, the object will just have a higher apoapsis. with an orbit that look like a scretched rubber band. because the escape velocity is still alot faster than the geosync's orbital speed.

go and read about orbit and you will see. a rocket doesn't reach the moon by firing it's rocket directly at it. it is actually trickier than that!

ok, sorry i guess i should explain:

when you throw something, you apply speed to the object just once. the thing is, gravity is not speed but acceleration, so for each second, it is pulling you down at the given speed(eg 9.8m/s on earth). you will need to impart enough thrust during the vent to overcome the duration it will take you to travel out of the effective earth gravitation reach.

i dunno what you mean, but the upper atmosphere does not vent simply cause there is not enough energy to counter the gravity pulling it downward. the reason why it is staying up there, is because as it fall, it hit other atoms and is bounce back up, that is how air pressure work. smaller atom travel further with the same energy since it has less mass to move, which allows them to stay higher.
Well explained. Looks like I need to brush up on my orbital physics!
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