How long would it take to travel up an orbital elevator?

[Venusian Broon]

If we drop something a few hundred metres across we might just have to look embarrassed when people mention those countries that no longer exist, but if its a dinosaur killing kilometres sort of thing we might be heading into post apocalypse territory.

Hey Sapheron, your thoughts got me into looking into the numbers, but first I just read an illuminating comment in a magazine from Timothy Spahr, director of the asteriod-hunting Minor Planet Center at Harvard University. I quote, 'Orbital Mechanics are well understood, he says, making asteriod trajectory calculations simple. "Hitting the Earth is a damn hard thing to do" '

There does seem to be a thinking, perhaps because we have all watched far too many disaster movies, that such asteriod/satellite/big thing in space disasters would be easy to pull off or could happen because 'the Earth's gravity will suck everything onto it' and everything is teetering on a knives edge of stability

I think the science actually tells us it's quite difficult (or at least you'd have to be actively trying to achieve it)

If the Moon's gravity began to move the anchor, even slightly, I could see this causing huge problems. A little bit of compression, and the whole life buckles; a little extension and it will come apart. Neither is a good result.

I'm sure Chrispenycate has the real answer, but looking up the masses involved, I estimated* that a dinosaur killing asteroid could weigh, of the order of, 1 to 2 x10^15 kg, which compared to the mass of the Moon is nothing - The mass of moon is ~4 million times heavier.

BUT

You have to remember that in the Earth-asteriod-moon system, even the moon itself is extremely light-weight compared to the Earth, it is only ~1.2% the mass of the Earth.

Hence my physicist instinct is telling me that the moons influence will be quite small in the 'big, cosmic' scale of things on the this system. (Of course this 'small' perturbation causes our tides which is pretty nice and lovely!) The biggest influence by far is the Earth.

However as you state, I'm sure there will be some influence and it will be interesting to know if there will be a noticable effect. My first guess would be yes, as I see that current geosynchronous satellites have to take this factor into account to remain at the correct point. However if we've managed to 'drive' this asteriod, from presumably a very long distance away and to my mind is a pretty difficult thing to do, surely the minute adjustments to keep the counterweight in the sweet spot would be a dawdle if we kept whatever locomotion was used to move the asteroid into position?

* Scribbles on a scrap of paper involving the known masses and approximate volumes of some really big asteroids in our solar system

 

[Sapheron]

It's amazing how much of my first year at university came back with some of the figures you gave!

I agree that hitting Earth is unlikely for an asteroid (though we are overdue for a major impact, based on the average gap between them), but in this case we're thinking of deliberately getting one and sending it straight towards Earth, only to stop it (in space scale) a hair's breadth away. If there's a way to get one to hit us, I think this is it!

As for the Moon, yes, it's much smaller and all, but if it can move some water by a few metres, perhaps it could do the same to an orbiting station. After all, the station is considerably further from the Earth and closer to the Moon than most other things about these parts, and a few metres could easily cause a lot of problems.

 

[RJM Corbet]

I suppose the mineral composition of asteroids varies quite a lot. Ideally one would be looking for one with a high weight/volume ratio. Pure uranium would be good, weightwise. Or would weight matter, in freefall around the earth's gravity?

 

[Venusian Broon]

I agree that hitting Earth is unlikely for an asteroid (though we are overdue for a major impact, based on the average gap between them),

Well on the bright side. If we have advanced to the point where we can shift a 10km diameter asteriod from deep in planetary space to park it in orbit around us, then we should never get a rogue asteroid hit us 'naturally' ever again. Would be easy enough to deflect it off (or mine it and convert it into cash )

After all, the station is considerably further from the Earth and closer to the Moon than most other things about these parts, and a few metres could easily cause a lot of problems.

My engineering thinking/understanding is poor, but I would think that it would be possible to design the whole structure to flex and withstand such movements. (Thinking about all those sky scrapers built on soft ground in Earthquake regions...) The moon is regular feature in our local, so you know exactly what you need your whole structure has to do and the stresses and strains that would result.

I suppose the mineral composition of asteroids varies quite a lot. Ideally one would be looking for one with a high weight/volume ratio. Pure uranium would be good, weightwise. Or would weight matter, in freefall around the earth's gravity?

I believe the weighter the asteriod the more stable the whole structure, so yes a big core of Uranium on paper might suit. (Although the peoples of the world might get worked up about the 'bomb' in the sky and not allow it) Possibly also Uranium is far too valuable to have it just as a nice counterweight.

EDIT - oh and if you your going to have people and electronics on the counterweight, having it highly radioactive may be not particularly wise!!!!

EDIT 2 - sorry, the more I think about it the more problems come up. A massive amount of Uranium is going generate a lot of heat. In space the heat can only be radiated away by infrared, so the I'd imagine that the Uranium counterweight would need some system for actively getting rid of this or using it, further adding to the complexity. Otherwise it might get a bit toasty there.

 

[Venusian Broon]

I was in the mood for calculations and RJM's thoughts has spurred me on.

If we assume a counterweight of 1x10^15 kg, and for the sake of the calculation put half as Uranium to provide a dense solid core. Finally Uranium, I believe, generates 0.1 Watts/tonne of thermal heat.

then by my rough calcs (assumed spherical counterweight and Black body), the counterweight should be at a temperature of 409K or 136 deg Celsius. Not good for water based organisms. Would need pretty serious cooling mechanisms!

 

[RJM Corbet]

Well, perhaps mercury, or lead. I would need to check the periodic table. But it's bringing up the question of weight/volume ratios in freefall?

 

[Ursa major]

I don't want to be critical about the mass of Uranium being proposed, but....

 

[Venusian Broon]

Well, perhaps mercury, or lead. I would need to check the periodic table. But it's bringing up the question of weight/volume ratios in freefall?

The maths/physics nerd in me took over! I guess if you were doing it for real you'd try and find the heaviest, cheapest asteriod and use that. If you found a gold/rare-earth/platiumum -rich asteriod it would probably make much more sense economically to mine it.

So perhaps a big block of Iron-mostly asteroid? Should be loads of that floating about and we're not exactly running out of it down here.

Another factor to perhaps ponder is that if you are going to building structures and other things on the counterweight, it would be good to have an asteriod rich in things that you could just consume and process for manufacturing processes - ice would be good, but not sure we want to make a counterweight out of a proto-comet, as it might significantly evaporate its mass in position and possibly be a bit unstable on the surface, but on the other hand water is darn useful stuff in space.

 

[Ursa major]

If one is able to capture asteroids (and comets?) and place them in very high orbits, I don't see the need to have a asteroid abundant in most of what's required as your counterweight. If you could obtain your materials from other asteroids in Earth orbit, that should be okay. It isn't as if you're going to have to lift this material out of Earth's gravity well.

 

[Venusian Broon]

I don't want to be critical about the mass of Uranium being proposed, but....

As long as it was very predominately U 238 i.e. I think even natural Uranium with only 0.72% U 235 can't go off (and if it was a natural formation then the other crap in the Asteroid could be heavily mixed inbetween the Uranium deposits)...

...Suppose it depends if you are going to process it all into a central core! That's what I'd call a doomsday device squared. Although just crashing it into the earth should be enough to polish off the human race. A big nuclear bomb of that size is just icing on the cake

If nature had found a way to make a fission bomb in space, we probably wouldn't find the asteroid that did it, cause it'd be already triggered!

 

[Venusian Broon]

If one is able to capture asteroids (and comets?) and place them in very high orbits, I don't see the need to have a asteroid abundant in most of what's required as your counterweight. If you could obtain your materials from other asteroids in Earth orbit, that should be okay. It isn't as if you're going to have to lift this material out of Earth's gravity well.

It would be easier to have most of the things you want in the counterweight and therefore not to expend time and energy fiddling about transferring stuff from other things. Is my guess. But that'll all depend on the economics of shifting large bulky rocks around the solar system, with whatever tech we have at the time to do it (if we ever get to that stage )

 

[RJM Corbet]

Ok VB lets forget about the radioactivity for now. There's depleted uranium, etc. The question I'm asking is whether weight and mass can be considered the same thing, in this case? To provide maximum centrifugal pull on the tether. It seems obvious, but it might not be. Perhaps a lighter counterweight would work better? I don't know. I'm asking ...

 

[Venusian Broon]

Ok VB lets forget about the radioactivity for now. There's depleted uranium, etc. The question I'm asking is whether weight and mass can be considered the same thing, in this case? To provide maximum centrifugal pull on the tether.

oh ok, apologies if I've been a bit all over the place. If I've read chrispenycate's mails properly then the bigger the mass the more stable the system becomes.

For my inner physicist, weight is a force that arises out of interactions between masses (or if I were using general relativity, it is the interaction between the mass and the distorted 'gradient' of spacetime caused by another mass - but for the moment let us keep the Newtonian picture). So weight is a consquence or end result of what happens to an 'input' of a system of masses.

Thus the closer the objects are the heavier the counterweight would become. For the purposes of calculating the physical behaviour and properties of the tether you use the masses. The weight would flucuate according to where the moon was, where the Earth was in orbit around the sun etc...hence presumably cause the counterweight to drift about a tiny bit.

Remember that the Earth's gravititional field extends far out, (theoretically infinite, but...), so even in orbit you have weight, less than if you were standing on the surface of the planet, it's just that all the objects around about you are in freefall.

Does that answer your question RJM?

 

[RJM Corbet]

Yes. So it may take less energy to accelerate a lighter counterweight to generate more torque than a heavier one, without air resistance? Here my mind starts to fuzz, so back to you guys ...

 

[Venusian Broon]

Yes. So it may take less energy to accelerate a lighter counterweight to generate more torque than a heavier one, without air resistance? Here my mind starts to fuzz, so back to you guys ...

Yes. Newton's 2nd Law of motion.

F = m a

so the bigger the mass, the more force (and hence energy) is required to accelerate the object

 

[chrispenycate]

I wasn't too interested in the density of the counterweight (though admittedly the more compact it is the smaller the tidal effects) and had hoped to find a carboniferous chondrite; it seems probable that the material used for tower construction will be largely carbon (yeah, a multimegaton diamond; what's that in carats?), and it would be convenient to have the raw materials on hand. But I'll take nickel/iron, a nice common substance on the cosmic scale, and probably more resistant to my propulsion methods (heavy on nuclear explosions and plasma blasts). Oh sure, a couple of hundred metres diameter should do fine; what I don't want is the people who think a megaton will do to hold a fifty kiloton train. Three orders if magnitude, minimum, and more is better.

Anything solid, even something strong enough to build the tower from, will have a Young's modulus, a certain elasticity. Thirty six thousand kilometres can easily absorb a few hundred metres of extension or compression, and the tension in the – ¿cable? What do you call something that is architectural enough to run a railway up its surface, but is hanging down from its support point? – will tend to pull the mass back to its intended stable point. Mind you, I hate to think at what frequency it would go "boioioioing".

 

[Ursa major]

what's that in carats

A carat and "sticks" in orbit approach, eh?


* Resists the temptation to produce a graph of how the wait for the elevator may depend on the gravity of current and future economic (and other mass-effect phenomena) downturns. *

 

[RJM Corbet]

Any rate, it's not likely to happen soon, the costs and the physics are too hugely daunting?

 

[chrispenycate]

Six years ago I posted a hypothetical "single stage to orbit counterweight launch" at http://www.sffchronicles.co.uk/forum/11518-growing-a-beanstalk-2.html. You could build that (though it is a rather wimpy little counterweight, suitable for lifting lift cages but not container ships) starting now. Fortunately I wouldn't still be alive for the launch itself.

 

[RJM Corbet]

Six years ago I posted a hypothetical "single stage to orbit counterweight launch" at http://www.sffchronicles.co.uk/forum/11518-growing-a-beanstalk-2.html ...

I'd edit and keep that short story if I was you. It's impressive.