Artificial gravity and diameter

I was watching a show on the human future in space recently, and the narrator was saying that in order for a space station to be able to generate artificial gravity, it would have to rotate (obviously) and be at least a mile in diameter. I understand the rotation part, but why the specific diameter?

Theoretically, it could be smaller, but I can see a practical problem with smaller sizes.

It’d be great if someone would double check my math here, but if I threw it together right…

With a one mile radius, the station would make 1 rotation every 44 seconds. That’s still pretty fast, but it is reasonable.

With a half-mile radius, the station would make 57 rotations per second! I sure as heck wouldn’t want to try to dock with that. Make sure not to look out the windows…

Wait, there is no way that that is right… I know I did something wrong. Nevermind that. :slight_smile: I’ll try again when I’m thinking it through better, if someone else doesn’t get to it first.

What we’ve got here is your basic “uniform circular motion”, according to my physics textbook. In UCM, the body moving in a circle is subjected to an acceleration equal to the square of the velocity divided by the radius of the circle (v^2/r).

Now, assuming we want to be the same weight on the station as we do on earth, let’s let the acceleration be equal to the acceleration of gravity on earth, which is about 32 feet per second per second. With a radius of one mile, or 5,280 feet, we wind up with a velocity of about 411 feet per second, or 280 miles an hour. At that speed the station would make one revolution in 80 seconds or so.

As you can tell from the calculations, the larger the radius, the faster the station has to spin to get the same acceleration. But since the radius is larger, the period of rotation is also slower (if you’re confused, think of tires on a car: small tires have to spin faster than large tires at the same speed). To the people inside, I doubt it would matter much, but it would be hell for someone to dock with that sucker if it was only a hundred feet in diameter.
– Sylence.

“A friend of mine once sent me a post card with a picture of the entire planet Earth taken from space. On the back it said, ‘Wish you were here’.” - Steven Wright

Yeah, DSC, I saw the same program on Discovery (I think). The space station would be a mile in diameter and would be built about as far out as Jupiter’s orbit.

According to my (questionable) calculations using Sylence’s formula, the “rim” of the station would travel at 188.499 mph to simulate Earth’s gravity. The circumference would be 16588 ft. Docking would be done at the “hub” of the station where, of course, there would be zero gravity. Their main concern was Solar radiation.

I don’t know how they arrived at “one mile in diameter.” I think the idea was to build a starship to travel to another solar system. To do this, you’d need a lot of room for materials, people, and life support to assemble the ship. I guess a mile in diameter is a good round number. (No pun)

“After two six packs, all these things will become clear.”…Ron

Something else to consider:
Approximating gravity with “centrifugal force” works only locally. Obviously, if you walk halfway around the station, “down” will rotate 180 degrees. If the placement of your feet differs by x feet and the station has a diameter of d, your legs will experience a “downs” varying by an amount proportional to 2x/(d*pi). Also, your head will experience less “centrifugal force” than your feet. There are other strange things, such as Coriolis forces, that result from the strictly local nature of “down”. The larger the spaceship, the larger the area in which local, rather than global, effects will predominate.

" ‘Ideas on Earth were badges of friendship or enmity. Their content did not matter.’ " -Kurt Vonnegut, * Breakfast of Champions *

Diameter…three reasons:

  1. Obviously, the bigger the diameter, the more inside space you get.

  2. Things with a larger diameter do not have to spin as fast (i.e., as any RPM) to get the same centrifugal force (=“artificial gravity”).

  3. Smaller spinning objects produce more Coriolis force. Try throwing a Nerf ball to someone on one of those carnival rides where you stand on the inside of a spinning cylinder… it’ll go off to the side.

Just throwing in another formula here: The centriptal acceleration can also be calculated as a=r*w^2 where w is the angular velocity in radians/time. I wanted to use a lower-case omega instead of ‘w’ but I’m kinda limited here.

According to “Colonies in Space”, the important part was the effect the spin rate would have on the people inside. The dizzyness people feel when spinning is due to Corialus(sp!) effect, which in turn is a function of the spin rate, or RPMs. The greater the diameter of the station, the slower the RPM rate need to get 1 gravity at the rim. A mile gives a spin rate of about once a minute, which was considered acceptable.

I knew I was spelling “Coriolus” wrong, but it wasn’t in my dictionary!

I do not think that a space station a mile in diameter is feasible. It would be too susceptible to space debris. Artificial gravity would not be a requirement for a space station, just a nice feature.

If they outlaw outlaws, only outlaws will be outlaws

The lastest and greatest designs ared ring shaped, they are tethered capsules spinning like bolas.

If you ever want to go home, it is. Significnt bone decalsification happens in only months when consantly exposed to zero Gs.
Unfortunatly its theorized that artificial gravity also has adverse health effects. Due to the steep gravity gradiant, and the Coriolus effect.

Since you brought it up, I think you mean “Coriolis”

Aura…that’s not how Corey O’Luss spelled it. :wink: