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Space Elevator Could Cost Less Than You Thought
WolfWithoutAClause writes: "We've had Space Elevator stories before on Slashdot, mainly saying how impractical they are for the foreseeable future. Now however, there's an 8M pdf paper on NASA Institute of Advanced Concepts [NIAC] website that says it may now be possible with existing materials and can be done for about $40 billion. That's less than the entire launch market for a single year. If he's right, the first elevator may be complete in 10 years time, with the second and third following 2-3 years afterwards."
This version of the Space Elevator doesn't go all the way to the ground. That's why it can be built with existing materials. You still need a (hydrogen fueled) rocket to get to the dock at the lower end of the tether, which is about 250 km up. However the dock is moving significantly slower than orbital velocity, which increases payload and allows cheaper (more reliable & maintainable) rockets.
That 8M download only gives you the slides - pretty pictures but no text. The actual phase I paper is here. It's a 15M download - and you can year the server creaking under the strain.
You are probably not thinking about angular momentum, but energy in circular motion.
Energy contained in circular motion is equal to:
(This is the energy associatied with angular momentum)
E = 1/2 I * (w^2)
Where I is the moment of inertia and w is the angular frequency (in this case about 7.27 x 10^-5 1/s because the period of rotation will be 24 hours). The moment of inertia will increase as the load gets further away from the Earth.
I = m * (r ^ 2)
m is mass
and r is radius from the center of the earth.
So, the energy in circular motion at each height would be:
E = 1/2 * m * (r^2) * (w^3)
To get the formula for the total energy at each height, add the potential energy from Earth's gravitational pull.
To answer your question, the increase in angular momentum of the payload is a result of the force exerted by the elevator doing work on the payload, resulting in a change in energy of circular motion.
If you are worried about what is called conservation of angular momentum, the increase in angular momentum comes from a decrease in the angular momentum of the Earth. Conservation laws are usually written like so:
initial = final
So,
L (angular momentum) initial = L final
I forgot, angular momentum = I * w
Where L is the sum of the angular momentums in the system.
So,
L(earth) + L(payload) + L(elevator) initial = L(earth) + L(payload) + L(elevator) final
Because the radius from center of mass of the elevator and the Earth don't (negligibly) change during the lifting of the payload (this would affect I) and that for the payload does, the final angular frequency of something must be slower. Since they are all tethered together going at the same angular frequency, their angular frequencies must remain the same, and the anular frequency of the Earth will decreas very slightly (negligibly actually) and days will become slightly shorter while the payload is in space. You wouln't notice it though, because this happens every time any payload is sent into space -- every satellite space ship, etc.
When you drink too much physics, alchohol just doesn't make any sense anymore.
One reason why the cable might NOT burn up in the atmosphere would be that, as a heat conductor, the heat generated by re-entry would be distributed throughout the cable, lowering the overall temperature of the cable and reducing the likelihood that any part of it would burn up.