Would artificial gravity work in space using centrifugal force?

It does seem to work that way.  There was a movie called 2001: A Space Odyssey, where in the movie travelers to Jupiter were on a space ship just as you say.  It makes a very curious sort of floor layout, where the floor underfoot is a concave curve like walking on the inside of a huge disk.  It would work at any size, but for practical reasons it would have to be pretty big.  In the movie, one of characters jogs around the circular 'tube'.

Yes, you can use centripetal acceleration to create the illusion of gravity in such a system.  This is governed by the equation:

a = v^2 / r

a = Acceleration (gravity)
v = Velocity (of rotating ring)
r = Radius (of ring from center)

In this case, to create Earth gravity, a = 9.81 m/s^2.

You can create an infinite variety of ring sizes and speeds governed only by the maximum tensional properties of the materials that you use.

A very tiny ring spinning really fast will give the same illusion as a very large ring rotating very slowly.  You can play with the equation up there.

Keep in mind, velocity is in (m/s), radius is in (m).

Yes! This would work quite well as a source of artificial gravity. Except that the force you are talking about is not centrifugal force, rather centripetal force.

Centrifugal force is not a force it is a phenomena we experience because of inertia. So, why didn't the rocket scientists at NASA build the space station we have now so it could have artificial gravity using centripetal force?

Here?s why: There are many ways to express centripetal force mathematically. Here?s an easy one: Centripetal force is equal to the mass of the object (you in the space station) times the velocity squared (of the spinning space station) divided by the radius (of the space station). Or: F = mv^2 / r.

To create the situation you describe the centripetal force would need to be equal to your weight. But wait! Weight is equal to mass times the acceleration due to gravity. So we can use this equation: mg = mv^2 / r. Since mass in the same on both sides of the equal sign the mass goes away! This gives us g = v^2 / r. Solving this equation for ?v? we get v = the square root of gr.

Notice that the mass goes away. This means that you would not have to adjust the velocity whenever you change personal or bring in supplies and equipment. (Well, not exactly, as you will see if you keep reading!)

Now we have the velocity. What about the radius? It turns out the radius is the problem! Have you ever heard of tidal effects? Briefly it is this: The force of gravity between Earth and the moon is greater on the side of Earth nearest the moon than on the side of Earth farthest from the moon. This difference in the force of gravity between Earth and the moon is what causes tides.

If we build your doughnut-like space station with a radius that is too small then the centripetal force we feel at our head will be a lot more than the centripetal force we feel at our feet. Imagine what that would feel like. Your head would feel very, very heavy while your feet feel very light. Of course, the blood flow would be affected and the effect would not be good!

Without going into all the math, allow me to just say that in order for these tidal effects to go away the radius of the space station must be roughly a thousand times greater than the height of the average human adult. Yeah! A thousand times! The movie 2001 A Space Odyssey got a lot of the science right but they messed up on this one.

For this space station to NOT be deadly, it would have to have a radius of two kilometers! Two kilometers is one and a quarter miles. This would give you a circumference of nearly 8 miles! Of course, you would not have to build the whole doughnut. You could just build part of a doughnut and the astronauts could live and work in that small section. However, for this thing to turn there would have to be another section of equal mass opposite the working section.

Now, do you see why the rocket scientists at NASA did not build such a monstrosity! It would be cool if they could but a system with two huge masses separated by 2.5 miles of some kind of material would be hugely expensive.

Oh, that velocity? It would have to rotate at about 300 miles per hour. I wonder how such a moving target could be docked to by the supply ships. Oh, I know!  Dock in the middle, a mile and a quarter from the where the astronauts are. But then, whenever an astronaut went down to one part another would have to up to the other portion carrying an equal mass!

Needless to say, such a design is, well, science fiction!