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Hang of Thursdays
05-30-2010, 09:41 AM
But one I'm not able to google a simple answer for.

Suppose you had a giant space station that formed a ring around the earth, say in geostationary orbit, tethered to the earth with space elevators, would that be sufficient for gravity to exist at or near earth levels inside the station?

Albedo
05-30-2010, 10:29 AM
This is a good question, and one I've wondered about before without coming to a definite answer. If the ring is located at geostationary altitude, rotating at orbital speed and you are inside it moving along with it, then you are still in orbit, should be in free-fall and shouldn't feel any net 'downwards' force towards the Earth.

scottVee
05-30-2010, 10:48 AM
What an expensive thing that would be to build. Right now we can't even get a one-mile tether to work without tearing itself apart. Or imagine anything strong enough to act as the anchors for a space elevator. But it's fun to think about.

No, securing something to the earth does not make gravity appear. If your ring was 100 miles up, you'd feel the gravity of the earth at 100 miles altitude, which is near zero.

The main trick to faking gravity is to spin a ship or station and use the centripetal force, which would point toward the center of the spin and feel like gravity. For your ring, using 4000 miles as the earth's radius (close enough) you'd get the centripetal force of

F = m*V^2/r

This is not simple. The ring radius would be 4100 miles, but the rest is a pain. Let's guess that your ring weighs 2 million tons, that's m. The velocity is found by traveling one circumference per day ... 2*pi*4100(miles)/24(hours) = 1072mi/hr. Problem: this is far below escape velocity, so it would crash back to earth. Darn. Let's play with it anyway.

F = (2 million tons) * (1072mi/hr)^2 / 4100 mi

This is a mess of mixed units. Everything should be converted to meters and seconds and grams. And technically we don't want the "force", we want the "equivalent acceleration", since gravity is an acceleration, not a force, so for this the mass is irrelevant (think of gravity as the acceleration felt by each point on the object).

F = (479 m/s) ^2 / (6.6 x 10^6 m)
F = 0.034 m/s^2

Now, one gravity is 9.8 m/s^2. So, such a slow rotation won't produce more than 0.04 G. Not surprising. If the centripetal force was nearly as strong as this (in relation to gravity), we'd all fly off the surface of the earth. Odds are, to get one G of gravity on your giant ring, you'd have to rotate it 60 times faster than the earth, which means you couldn't tether it down, of course.

I haven't done this math in ages, it could be very rusty. But I'm sure other readers will set it straight.

Albedo
05-30-2010, 10:59 AM
No, securing something to the earth does not make gravity appear. If your ring was 100 miles up, you'd feel the gravity of the earth at 100 miles altitude, which is near zero.


Only in free-fall. If you are standing on the top of a 100 mile high building, the gravity is close to 1G (in the realm of 0.95, unnoticably less).

Hang of Thursdays
05-30-2010, 11:05 AM
Thanks guys. That math goes right over my head, but, uh, it sounds right (?).

My thinking was that the centripetal force would supply the gravity, if it's orbiting at the same speed.

Trying a different tack, is there anyway it could work? It's not crucial to the story, but now I'm just curious.

Lhun
05-30-2010, 01:51 PM
A ring-shaped station in orbit that surrounds the whole planet would crash and burn. Literally.
Any object like that isn't gravitationally stable, a tiny disturbance and it just starts falling.
If it's not in orbit but locked to the earth's rotation with towers (some pretty damn strong towers) people inside would experience slightly less gravity than on earth. Because the radius is bigger, the centrifugal force is a little bigger, and the gravity a little weaker, but nothing dramatic at that height.

Albedo
05-30-2010, 04:38 PM
A ring-shaped station in orbit that surrounds the whole planet would crash and burn. Literally.
Any object like that isn't gravitationally stable, a tiny disturbance and it just starts falling.
If it's not in orbit but locked to the earth's rotation with towers (some pretty damn strong towers) people inside would experience slightly less gravity than on earth. Because the radius is bigger, the centrifugal force is a little bigger, and the gravity a little weaker, but nothing dramatic at that height.

But at geostationary height? Assuming you've solved the materials science problem of building space elevators to geostationary height, the problem of maintaining a ring of space stations there would surely be achievable with proper use of corrective thrust. Maybe not a rigid ring, but a continuous chain of stations would serve the same purpose. You could even link them with cables if they were close enough. Would a dense network of self-correcting geostats be any more unstable than the sparse network we've got today?

Lhun
05-30-2010, 05:56 PM
An individual object in orbit is stable, because any small perturbation will only change the orbit a little. If it is a rigid ring around the centre of gravity instead, any small perturbation will send it falling down. You can't suspend a rigid ring or sphere around a centre of gravity without constant adjustments because gravity is an attractive force. If one part of the ring is slightly closer to the centre, not only does it get a stronger gravitational pull, it also pushes the other part farther away, weakening the pull on the other side.
How many individual objects you can have in orbit is a different question, mostly determined by how much of a collision risk you are willing to take. Tethering them together would only increase that problem, and i don't see for what purpose you'd want to do that in the first place.

dclary
05-30-2010, 07:14 PM
Put a tiny little black hole at the location where you want the gravity well to exist. Everyone in the space station will be pulled in that direction, simulating gravity.

Lhun
05-30-2010, 07:35 PM
Remember that a black hole generates the same gravitic field that any other object of the same mass would. Using black holes to generate gravity for space stations orbiting a planet would be ... spectacular.

dgiharris
05-30-2010, 08:29 PM
Not quite sure what is going on in this thread but some of the physics is wrong.

Assuming the material science problem is solved, and you were able to build a rigid ring around the entire earth at GSO, that ring would be INCREDIBLY STABLE.

The force of gravity is an attractive force. Draw a circle representing the earth and draw a bunch of arrows around the earth pointing to the center.

Now draw a ring around the Earth that is outside the arrows. All of those arrows serve as a giant stablizing force, pulling along the ENTIRE circumference of the ring towards the center of the earth. That combined with the structure's rigidness would provide for a stable system.

Or put another way, think of a bicycle wheel with all those spokes radiating from the center. That is pretty much what you would have.

The mass of the ring structure (inertia) combined with the constant equidistant pull of the Earth's gravity on the rings, would combine to form an incredibly stable structure provided that structure is equidistance from the earth at all sides. Combined with a few stablizer thrusters and you have a stable self correcting system.

As for gravity. The force of gravity falls away at 1/r^2 so no, you wouldn't feel any gravity from the earth. But as mentioned above, you could simply spin the station.

Also. you don't need to be at GSO. Again, if you were able to build a rigid ring system, then you could bring it in much closer to the Earth. GSO is 42,000km away so that would be a HUGE ring. Much simpler to just bring it in closer to low Earth Orbit something like 3,000km which would be orders of magnitude smaller and use less materials!!!

lastly, as for spinning the station. That is a trivial matter. Objects in space whip around at fantastic velocities. Velocity in space is trivial. You simply accelerate the object and eventually the station will spin at the rate you want it to spin. I would guess that it would probably take around a month or so of nice slow acceleration for the ring to reach the desired velocity so that you'd have gravity (http://en.wikipedia.org/wiki/Centripetal_force).

And as an aside, a ring system around the planet has a lot of benefits. You'd have virtually infinite power moving through the Earth's Magnetic field not to mention the benefit of space's vaccum for manufacturing (semiconductor and nanotechnology and anything else that uses a clean room). The vaccum of space is about a million times cleaner than the cleanest clean room on Earth. And i'm sure there would be countless other benefits.

p.s. all this works for a 'loose' ring system as well held together by cables. But a rigid system would be more stable IMO. ONly downside to a rigid system is that you generate stresses which would decrease the lifetime of the station. but, since this is the future, we'd have nanotechnology and fixing stress fractures (as well as monitoring the structure) would be trivial.

Lhun
05-30-2010, 09:19 PM
Not quite sure what is going on in this thread but some of the physics is wrong.

Assuming the material science problem is solved, and you were able to build a rigid ring around the entire earth at GSO, that ring would be INCREDIBLY STABLE.Far from it.

The force of gravity is an attractive force. Draw a circle representing the earth and draw a bunch of arrows around the earth pointing to the center.

Now draw a ring around the Earth that is outside the arrows. All of those arrows serve as a giant stablizing force, pulling along the ENTIRE circumference of the ring towards the center of the earth. That combined with the structure's would provide for a stable system.It is unstable exactly because it is an attractive force. A repelling force would provide for a stable system, because any variation is self correcting. If any part of the ring gets closer to the center it will be repelled stronger, and since the opposing part has to be farther away (since the ring is rigid) it will be repelled weaker. As a result the ring gets a net push in a direction, until it is in a stable equilibrium again, with the repelling force in the middle.
With an attractive force, the exact opposite happens. Any part getting closer to the centre will experience strong attraction than the opposite side, pulling it even closer and so on. Even the tiniest perturbation will result in the whole structure crashing sideways into the planet. It is the exact opposite of a self-correcting system.

efkelley
05-30-2010, 09:42 PM
I'm still not sure what function such a station would serve. In most human endeavors the function defines the form. Other than looking pretty, why would you do this?

Practicing to build a Ringworld maybe? Which would have the exact same issues, by the by.

dgiharris
05-31-2010, 12:02 AM
Far from it.
It is unstable exactly because it is an attractive force. A repelling force would provide for a stable system, because any variation is self correcting. If any part of the ring gets closer to the center it will be repelled stronger, and since the opposing part has to be farther away (since the ring is rigid) it will be repelled weaker. As a result the ring gets a net push in a direction, until it is in a stable equilibrium again, with the repelling force in the middle.
With an attractive force, the exact opposite happens. Any part getting closer to the centre will experience strong attraction than the opposite side, pulling it even closer and so on. Even the tiniest perturbation will result in the whole structure crashing sideways into the planet. It is the exact opposite of a self-correcting system.

Not sure what I was smoking, you are right. It would be unstable

But...

How unstable? I would think that if you got the system stable to begin with, and you had thrusters to counter perturbations before they built up sufficient momentum to offset the balance, then i'd think you'd have little to fear from any one side getting to close to the earth before you could correct it.

Given the distances involved and the force of gravity vs the structure's mass, its not like the ring could be sucked into the earth in a matter of seconds or minutes or even hours. I think the runaway effect of a perturbation pushing the structure to one side of the Earth would need weeks or months to build up sufficient momentum, and in all that time the thrusters would be able to correct.

Mel...

dgiharris
05-31-2010, 12:23 AM
I'm still not sure what function such a station would serve. In most human endeavors the function defines the form. Other than looking pretty, why would you do this?

Practicing to build a Ringworld maybe? Which would have the exact same issues, by the by.

Believe it or not, a ring around the planet would be of enornomous benefit to mankind.

As mentioned in my earlier post, you'd have virtually an unlimited source of clean energy. In fact, you'd have so much energy from moving through the Earth's Magnetic field that you could literally beam the energy down to the planet's surface (in microwaves, RF waves, or lasers) and power entire continents with clean energy.

Then there is the manufacturing aspect. Alot of our modern technology requires cleanrooms in order to build. Cleanrooms are VERY expensive depending on the rating. For instance, at Intel, it costs them approximately $1000 per square foot of space PER MONTH for some of their cleanrooms. Add up all the companies that utilize cleanrooms and it literally costs TRILLIONS of dollars to maintain cleanrooms on Earth. But in space, you'd get cleanrooms that were 1000 times cleaner and 1000 times cheaper to maintain.

There are a lot of technological advantages to constructing things in space in vaccum or zero gravity (especially in the medical field since gravity is a huge impediment to growing organs in petri dishes.)

ANd lets not ignore the obvious recreational appeal of living in space. Millions of people would kill to live on the moon or in a space station.

THere are probably a million other applications that I can't imagine. Remember, human beings are creative.

There was a time when people thought the telephone would be useless or that personal computers would never appeal to the commercial market.

I view the industry of Space in the same light. A lot of people say, "Why do we need to go to space? What's the point?"

A lot of people forget how much of our current technology comes from the Space Race and how dependant we are on Space (GPS and Communication satellites anyone???)

Eventually, as we become a space fairing race, we will see the utility of building such a structure (especially with overpopulation). That day (building a ring around the Earth) is probably 500 - 1000 years into the future.

thothguard51
05-31-2010, 01:04 AM
I too have to question the reason for such a structure. For manufacturing or science purposes. Get real. The cost and materials of such a structure would far out weight any benefits. Remember, one of the reasons Star Fleet shrunk the ships to the Voyager model was because of cost...

Of course, if such a structure was built, would it cast a perpetual shadow on certain land masses of the planet below? Would the people in those land masses revolt against the nations that built this structure? Would vegetation, wildlife, insect and even microbes be affected because of the perpetual twilight? Would oceans and other bodies of water be affected and what about the life in them?

While a ring type station would be a good idea, the ring does not have to orbit the world it was created from. It should be situated away from the planet in such a manner that it does not affect the suns or moons influences on the planet below.

To build a structure this large, there would have to be benefits that far outweigh the cost in labor and materials. Such as a world wide plague in which the survivors have to get off world. IMHO.

Lhun
05-31-2010, 02:21 AM
Not sure what I was smoking, you are right. It would be unstableYou're in good company. Larry Niven made the same mistake.
How unstable? I would think that if you got the system stable to begin with, and you had thrusters to counter perturbations before they built up sufficient momentum to offset the balance, then i'd think you'd have little to fear from any one side getting to close to the earth before you could correct it.It's not so unstable that it would crash in seconds, but the constant firing of thrusters is a problem, since you constantly waste fuel just to hold position. And the problem is bigger than for a normal orbiting object, since any satellite (for example) that drifts out of position, there's no active force pushing on it. It just sits on a slightly different orbit, waiting for a push back to the right orbit. But the station builds up gravitic pull, and not only do the thrusters have to move it back, they have to work against gravity while they're doing that. The total mass won't be negligible either, you'd burn huge amounts of reaction mass all the time.
Building a "normal" station, is most likely the better alternative, no matter what the purpose of the ring is supposed to be. Similar to how Banks Orbital are a much better design than Nivens Ringworld.

As mentioned in my earlier post, you'd have virtually an unlimited source of clean energy. In fact, you'd have so much energy from moving through the Earth's Magnetic field that you could literally beam the energy down to the planet's surface (in microwaves, RF waves, or lasers) and power entire continents with clean energy.While you can generate electricity this way, it's not necessarily free. The energy comes from the earth's magnetic field slowing down the station's rotation. It works out if you have locked the station to the surface of the earth, it's no problem, but if the station isn't, you again have to constantly fire thrusters.

I view the industry of Space in the same light. A lot of people say, "Why do we need to go to space? What's the point?"Another possibility is that technology will have progressed us to a post-scarcity economy. Given the technology necessary to build such a station that's not an unreasonable premise.
I too have to question the reason for such a structure. For manufacturing or science purposes. Get real. The cost and materials of such a structure would far out weight any benefits. Remember, one of the reasons Star Fleet shrunk the ships to the Voyager model was because of cost...http://img139.imageshack.us/img139/2182/qft.jpg (http://img139.imageshack.us/i/qft.jpg/)
Seriously. If it's on StarTrek, it's more likely to be stupid, or outright wrong than a good idea.

Of course, if such a structure was built, would it cast a perpetual shadow on certain land masses of the planet below? Would the people in those land masses revolt against the nations that built this structure? Would vegetation, wildlife, insect and even microbes be affected because of the perpetual twilight? Would oceans and other bodies of water be affected and what about the life in them?Short answer? No.

efkelley
05-31-2010, 07:12 AM
digharris, I see what you're saying, but I think that all of these things could be accomplished through good old-fashioned space stations. And a fair bit cheaper than an artificial ring.

Also, in order to cast any appreciable shadow, this thing would have to be HUGE.

Ah, Lhun, we have to give Mr. Niven a little credit. He addressed all these concerns (and more) and explained it away with 'we don't fully understand all the engineering involved'. This was at a time when hand-waving was perfectly acceptable. Although, I think that was in Ringworld Engineers and not the original.

Lhun
05-31-2010, 01:20 PM
Although, I think that was in Ringworld Engineers and not the original.Because he was made aware of the mistake by people who read the first one and complained. ;)

efkelley
06-01-2010, 06:21 AM
Oh sure 'people' complained.

We all know it was you. ;-)

Lhun
06-01-2010, 06:23 AM
Hah, i'd love to be able to claim credit for that, but i'm not old enough. Wasn't even born in 1970.

efkelley
06-01-2010, 06:52 AM
Time machine.

Plus 'Engineers' was 1980.

Pthom
06-01-2010, 10:26 AM
Build it like a bicycle wheel. Many tethers, which like spokes, are all in tension. Don't attempt this, however, unless you have some incredibly strong material. No, steel isn't strong enough. But assuming you have the material to build the ring in the first place...