Grayocean,
Thanks for your comments. Some of your facts are correct, that rotational momentum is conserved, that the moment of inertia of an ice skater decreases with arms pulled in so rotational rate increases and vice versa.
The c.g. of the bowling ball-golf ball system will be very close to the center of the bowling ball. The contribution to the moment of inertia of any mass is proportional to the square of its distance from the center of gravity. Thus, the ant's mass, moving from the surface of the bowling ball to the golf ball increases its distance from the c.g. of the system and thus increases the moment of inertia of the system which would slow the rotational rate of the system very slightly.
Looking at this thought experiment using a free body analysis of the ant, his tangential velocity increases significantly - it starts at W(RBB), where RBB is the radius of the bowling ball, and W is the rotational rate of the system, and ends up at W(LGG), where LGG is the length of the tether holding the golf ball (W doesn't change much). The force accelerating the ant is supplied by the tether in the bowstring mode, which I described in an earlier missive, so the tension force in the tether is large, depending on how rapidly the ant climbs, and is transfered to the golf ball whose distance from the c.g. of the system decreases and position relative to the original radial vector from the bowling ball also changes. The ant chooses his rate of climb which determines whether a large force is applied to the golf ball (space station) for a short time or a small force for a long time; in either case, the angular momentum of the golf ball (space station) decreases the same amount - roughly equal to the change in angular momentum of the ant.
Also, gravity is not zero, it decreases as 1/R^2, where R is the distance to the mass center of the system, so it decrease from 1 g to (4/26)^2g as a mass moves from the surface of the Earth to Geo altitude. (Gravity is not zero in orbit, it just appears to be so because all bodies are in free fall).
The ant (or the space elevator climber) would be climbing subjected both to gravity and to the force that is required to increase its tangential velocity (accelerate it).
Any way, whether the system is bowling and golf balls with an ant or the Earth, a geosynchronous space station and a climber, Isaac Newton and God agree, you don't get something for nothing.
An asteroid in orbit???? The effort and energy expenditure to modify an asteroid's Sun central orbit to one around the Earth would buy an awful lot of Titan IVs (whoops, sorry, no more Titan IVs. They would be Delta 4s or Atlas 5s)
Now at last, I think I can see some of the issues. I think Mr.Hughes arguement rests on an energy balance question, first law of thermodynamics and all that nice stuff. The crux of the issue making it an impossible feat is the fact that the energy required by the system (both to overcome gravity and to modify the angular momentum of the system) is so high that the added energy to carryt the propellant with the elevator (hence the comment about the weight of propellant) make the thing impossible. Other issues are clearly technological, the use of unobtanium for instance.
Is this a reasonably clear statement of your concerns Mr, Hughes? My impression that is the getting something for nothing comment in the last post.
This space elevator concept is a thought experiment, as such let your mind wander and wonder.
As for the amount of energy required to lift a payload using the ‘elevator’ it would be many orders of magnitude less that today’s methods. Yes the orbit of the elevator will be modified by the lifting of payloads, but the reverse is true of any payload dropped to earth also through the elevator. I imagine the operator of such a system would keep a detailed tally of loads in both directions.
Orbital corrections in the elevator could and would use the more efficient methods of thrust that would be available when unobtanium is invented or discovered such as ion drive (current today) or a proton beam, (accelerating protons to near the speed of light as reaction mass.) It would not require the very very high energy consumption of a chemical rocket engine needed just to lift its own mass with its resulting expended reaction mass to lift off the ground. I am not saying it its free but the energy will be from where we can make it cheaply.
The power for either payload lift or orbital corrections could be from photovoltaic solar power stations in orbit or power plants on earth again based upon technology available at that time, or who knows what source of energy then.
Leonardo Da Vinci did a drawing of a helicopter when steam power had very limited uses, but that did not stop him from dreaming an impossible then but now everyday reality. A lot has and can happen in four centuries.
As I was pondering this an interesting point came up. How about a system with 2 elevators, one going up[ and one going down. Very hard to implement perhaps, but there went the angular momentum problem out the proverbial window. I believe the people currently working on this are looking at a microwave beam type power source so no propellant is actually part of the lifted weight.
Thx all for the participation btw, this has been very enlightening so far.
You've convinced me!!! Please tell NASA to send me 1% of the "Hundreds of millions of dollars" in research money.
I downloaded the NASA report "Space Elevators An Advanced Earth-Space Infrastructure for the New Millennium", "based on the findings from the Advanced Space Infrastructure Workshop on Geostationary Orbiting Tether Space Elevator Concepts ...".
I had a few questions that I need to have answered so I can advocate Space Elevators most effectively. For instance, on page 6 they state that the energy required to move payload to geo orbit is 14.8 kWh/kg (I'm paraphrasing). My calculations show that the change in kinetic and potential energy of a 1 kg mass going to geo orbit is about 8512273721.64 kWh. I would like someone to explain where the other 8512273706.84 kWh will come from or where it goes.
Perhaps you have guessed that there is a touch of sarcasm in my above remarks.
The document is rife with similar unsupported statements and calculations, fanciful drawings and paintings, bits and pieces of engineering reality woven into an absurd concoction.
I am appalled at what I found in that report. It makes me ashamed to admit that I am in the same profession as the individuals who wrote the report.
However, if someone will send me the sum that I mentioned in the first paragraph (I'd settle for something a little smaller - chump change by these standards) I might be persuaded to change my point of view.
Well, I get about 16 kWh/kg, 14.7 kWh/kg change in potential energy and 1.3 kWh/kg change in kinetic energy.
Integrating GEMEdR/R2 from RE to RE+22300mi for potential energy
escape velocity at 7mi/s results in 17.6 kWh/kg, geosynchronous orbital speed is only 1.9 mi/s, so kinetic energy is only about 1/14th of escape velocity KE
I hope the viability of the theory has now been solidified. Ok, time for me to switch sides. On science friday they discussed the what if's of an airliner crashing into the ribbon, the 1400 Tons of satellite would hurl off into space. Gone. But my biggest concerns is space junk/meteor showers problem. There is over 40 million square meters of ribbon up there, the probability that it would be hit in the 20 year time scale that it would take to construct the thing would probably make even the ribbon construction impossible. Sooner or later the ribbon would be reduced to Swiss cheese, and then part. Can anyone comment on the probabilities on say a grain of sand sized meteor passing though a specific one square meter at various altitudes?
Thank you for the discussion. I am a high school teacher, not an engineer.
Years ago, one of my Chemistry students informed my class and me of this Space Elevator. We had a great discussion. At the time I confess that I sided with nhughes1.
But now as a teacher of young dreamers, I want to keep it alive. Could there be any chance that returning to fundamental high school principals we might find the obtainium and the possibility that the Space Elevator could work?
Let me review the things that I understand (I think), but from more of the high school linear point of view.
First of all there must be a heavy mass tethered at a distance well beyond 22000 miles, the free fall geosynchronous orbit altitude, with the anchor at the equator. I think I have read the proposed radius is 62000 miles. The heavy mass may be referred to as a geosynchronous satellite.
At the earth surface the linear speed of the elevator is 25000 miles per day = 1042 mph = 0.289 miles per second.
At a radius of 62000 miles the distance for the satellite to make one revolution is C = 2pir = 389557.5 miles = 389557.5 miles per day = 16232 miles per hour, approximately a linear velocity of 4.5 miles per second. That is less than, but close to free fall Low Earth Orbit orbital velocity.
As the elevator moves outward, its linear tangential velocity must increase from about 1042 mph to about 16232 mph to maintain a geosynchronous orbit. I believed it was assumed that the force to provide this acceleration would come from the satellite located at 62000 miles that keeps the tension in the tether. This force would slow the satellite, and it may have been assumed to have a negligible effect.
Did I forget anything?
I have a couple of questions. Can the anchor be offset from the equator? Could the cable go from the N.pole to the S.pole?
First of all, similar to the author of the previous msg., I am a HS teacher myself. I hope it is ok to join the discussion.
Ok, from the HS point of view, how about this argument for trying to keep the project alive?
The satellite (massive captured asteroid or similar) tends to travel in a straight line (inertia). As a planetary satellite, its direction of motion is constantly and uniformly being changed. The force responsible for this directive component of the satellite's acceleration, which would normally come from only from the nanotube (obtainium) cable will be shared by the force that is driving the elevator's acceleration in the tangential direction.
Finally, here are the results of an experiment I performed at home.
I attached a hacky-sack to about one meter of fishing line attached to my ceiling fan. I also attached a heavy, symmetrical mass with a set screw (from my kid's erector set) adjusted to barely slide along the fishing line when under centrifugal force. I turned on the fan. The mass slowly slipped outward. The fan slowed, but the two masses seemed to constantly and continually swing around in a nice, neat uniform motion.
