# Spin vs Gravity

How could a rotating/doughnut space station provide gravity? I’m trying to figure it out using my physics from school but I’m getting nowhere.
The way I’m trying to figure it out is like so;
The loop formed by the floor of the space station keeps them moving in a circle, the reaction between feet and floor provides a centripetal force right? But then what stops them from floating back off the floor? Are they continually moving in a straight line and therefore colliding with the floor as it moves “up” in front of them?
There are probably large holes in my theory (like what is up or foward in zero gravity) but I am anywhere near the facts?

I’m sure someone will come along with a more detailed answer, but here goes:

The donut shaped space station is a hollow ring. The residents walk inside the outer edge of the donut. They are kept there by the centrifugal force of the spin of the donut. If they climb “up” a ladder from the “floor” of the dunut toward the hole in the donut their body feels lighter because of the decrease in spin. At the center of the donut (or if the space station were a solid sphere instead) a body would be weightless.

You can see this work by tying a half full (or half empty) water bottle on a string, and spinning it lariat-style above your head. The water will be pushed to the point of the bottle farthest from you. Similarly, if you roll an automobile tire with rainwater in it down a hill, the water spreads out evenly all over the inside of the tire, rather than staying at the bottom.

I’m not a physicist, but I think you got the gist of it. The centripital force pulling you in is provided by the “floor” of the spinning space station.
The floor being the surface pointing towards the axis of rotaion, hopefully enclosed by the space station.

But I have a question for someone who does know more:
Is the following scenario posible?

In the spinning station, you jump in the air, facing the direction you are spinning(you’re spinning with the station, remember?). While in the air, you use some jets or boosters to accelerate you backwards, so that you are no longer moving with the spin of the station. Seeing as you’re no longer moving relative to the axis of rotation, you wouldn’t move towards the walls(the floor), and the space staion would spin around you. From the refrence frame of the person in the station, you would be levitating over the ground, whizzing forward. At least, thats what I would like to happen.

Hmm…sounds like fun to me, and a great way to move quickly around a really big space station, the only energy you expand is the initial boost, the energy needed to counteract air drag, and the boost needed to start moving again.

Ok, I’ve had enough thinking for today.

Go to the nearest amusement park. Take a ride on ‘The Rotor’.

Experiment over.

I’m getting ready to pack up and head home, so I’ll keep this short. I’m sure a doper in a differnt time zone will be able to add more.

2x4 is close, just upside down. There are many threads in GQ about centripetal vs. centrifugal force. In short, there ain’t no such animal as centrifugal force.

When an object spins (a point about the outer edge rotates about an axis), there is a force acting on that point and is directed towards the center of the circle (the axis). Thus, in the space station described, people would actuall walk in the inside floor (with feet towards the center of the donut, and heads pointing away from center. Any physics book with a section on Rotational Dynamics will have simple equations you can use to determine what radius of the station and angular velocity combination is needed to produce a “gravitational” force equal to Earth’s. I don’t have any physics books here at work, and I’m too lazy to derive it now.

Get a book of freshman physics and look up fictitious forces in a rotating coordinate system. The simple expression for the fictitious force is m times v squared divided by the radius of the circle that is the floor you’re standing on. There’s a gravity gradient very different from a real gravitational field, and there’s the fictitious Coriolis force, too, but the Centrifugal force will do a pretty good job of pinning you to the floor in a gravity-like fashion. And yes, it sort of acts like the floor is a board coming up to stop your otherwise straight-line motion.

Spritle,
You’re confusing reference frames. To the object being spun it “feels” as if you’re being pulled toward the center. The difference is based upon the acceleration frame of reference.
Regarding the earth, we have gravity here due to its Mass, not due to its spin.

Think of it this way. According to Newton a moving object will continue to move in a straight line unless acted upon by a force. In other words, if you are to keep moving in a circle, you need a force that supplies a centripetal acceleration or else you will fly off in a straight line. The floor of the space station is what supplies this centripetal force.

Ignoring air drag, if you were to jump in such a manner as to nullify the instantaneous linear velocity (v = w*r) supplied by the moving floor you would hover above it and in the frame of an observer on the floor you would appear to zip backwards (assuming the observer was facing in the direction of spin)

Yes, centrifugal force is a fictitious force. On the other hand, so is gravity, according to General Relativity. Who cares? To a person in the appropriate reference frame, however (standing on the surface of the Earth, or at rest relative to a spinning space station), it acts just like a real force, so you might as well treat it that way.

spritle, the centripetal (towards the center) force in the space station example is the force of the floor on the feet of the people in the station: It’s the force that causes the person to travel in a circle, instead of a straight line. Of course, in the (rotating) frame of reference of the space station, the person isn’t moving in a circle, or moving at all, so centripetal force is only relevant to a person outside the station, in a non-rotating reference frame, looking in. If you try to walk around on the inner wall of the torus, all that you’re likely to get is a concussion from falling onto the floor (or the floor coming up to hit you, depending on your reference frame).

So, let me get this straight…

If we have a space station that is essentially a big bicycle wheel spinning in space, I’m inside the hollow created by the tire. As I have understood it my whole life, the “ceiling” would be where the wheel spokes meet the wheel rim. The “floor” would be the inside of the tire tread. The force that holds us on this floor is what we think of as centrifugal force.

Centrifigul force, as M-W explains it is:

Etymology: New Latin centrifugus, from centr- + Latin fugere to flee – more at FUGITIVE
Date: circa 1721
1 : proceeding or acting in a direction away from a center or axis

Are you guys saying that’s not so?

To be absolutely correct there is no such thing as centrifugal force. An object naturally moves in a straight line, and it requires a force to alter the path from a straight line. The force that does the altering is centripetal not centrifugal.

But in the rotating frame of the observer it sure feels like a real force and for what it’s worth I think the term has value and I also feel that only real pedants want to ban its use.

What do pedants call centrifuges? “That thing with the fictitious name that uses a fictitious force to seperate liquids” seems kind of unweildy.

To continue with the possibilities raised by askol and Ring:

If you were in a car inside the station and drove in the direction of the spin, would you gain “weight”? If you drove opposite to the spin, would you “weigh” less? And if you pitched a ball in the direction of spin, would it be a “sinker”, while if you pitched in the opposite direction you could throw a “riser”?

I know there have been SF books about life inside space stations, but have effects such as these been explored in any books?

Those postings that there is no such thing as centrifugal force are ignoring Newtwon’s Third Law (for every force there is an equal and opposite force). On such a rotating space station, the force the station exerts on your feet is centripedal, the force your feet exert on the floor is centrifugal. These are, of necessity, equal in magnatiude and opposite in direction. The equation for it is a=v^2/r, where a = acceleration, v = velocity and r = radius. Since the circumference is 2pi*r, and the acceleration due to gravity at earth’s surface is 32.2 ft/sec/sec, it follows that to convert gs to RPM, the equation is…

RPM = [60 * Sqrt(32.2 * g * r)] / [2 * pi * r]

Thus, to provide 1g of acceleration, a 200’ diameter space station must spin at about five and a half RPM.

Yes.

I don’t know - it hurts my brain to think about it. It would seem that you’d hit the floor in either case since the only effect on the ball is the plus or minus linear velocity imparted because you are spinning i.e. the ball would be free to follow a straight path because its not connected to the floor.

Other than physics texts I have never seen one.

The weird effects inside space stations haven’t been explored enough in sf. I only know of one story that mentions it. I can’t recall the story or the author, but it’s in the anthology “great Science Fiction by Scientists”.

To answer So Far So Good’s questions – yeah, if you drive in the direction of the spin you WILL increase “gravity”, since your velocity is increasing while the radius remains fixed. Imagine how it feels when you go around a vertical loop in a roller coaster. And if you drive against the spin you will decrease your perceived gravity.

One easy way to figure out what really happens without having to deal with the cross-products involved in calculating Centrifugal forces and Coriolis forces is to imagine everything happening in a stationary reference frame – things move in straight lines. It’s only because you imagine your rotating reference frame inside the space station to be “inertial” that the effects of rotation seem weird.

So now toss your baseball “horizontally”. Regardless of whether you throw toward the direction of spin or away from it, it’s going to try and move in a straight line – which means it’s going to drop towards the floor. I guess, then, in either case you have a “sinker” (I’m not familiar with baseball slang).

Not quite. If the ring is spinning clockwise:

Away from spin: The ball moves in a straight line (let’s ignore air for the moment) and sure enough hits the rim (assuming it’s not thrown at the exact same rate as . However, the ring (and the thrower) have now moved on a fair bit. Imagine throwing it from 6 (on a clock) and the ball moving towards 5. By the time it gets there though, the whole wheel has spun and it actually hits 4 (which is where 5 was previously). From the pitcher’s point of view, he reckons he hasn’t moved, so he sees it curve up from 6 to 4.

Spinwards: Again, from 6, straight to 7. However, by the time ball gets there, 6 has moved to 7. The ball hits the ground right in from of him.

I think that’s right. Apply proper baseball terminology to taste…

Any overall force applied to your body feels like gravity, especially when it’s to your feet. Going up in an elevator, for example, gives you a little boost in weight as it accelerates. Conversely, your weight goes down when it moves down. So the centripital force applied to your body through the floor of the space station feels like gravity. And this force is just enough to change the straight-line course your body’s momentum would dictate it go. It wouldn’t cause your body to free-float, however.

If you were to jump in such a space station, you wouldn’t float away, because your body isn’t headed straight to the hub because of your jump, but rather it’s still going on a straight-line course tangeant to the stations circumference. So in a second or so, your body’ll meet back up with the floor of the station. And because of your frame of reference, it’ll seem like an on-Earth jump, not a free-float in space.

In order to negate the centripital gravity effect, you’d have to run as fast as the angular velocity at the radius of the station. This would basically make your body stay still in respect to the hub, and you’d be in the same freefall as the station as a whole. Eventually (probably very soon), the air in the station would slowly accelerate you with enough momentum that the gravity effect would affect you again.

dylan73:

Quite right. That’s what I get for posting my afterthoughts without thinking them through.

Larry Niven’s “Ringworld” deals with them somewhat, but on a MUCH larger scale.