Simulated Gravity with Centripetal Force
(and a lack of centripetal force)


We tend to feel like weight (the force of gravity) is acting on us only when we can feel the floor pushing back up on the bottom of our feet.  That's why when we are in free fall we feel like we are weightless because nothing is pushing on the bottom of our feet.  It also explains why when you are in an elevator and it accelerates downward, you feel like you weigh less than normal because the floor doesn't push as hard against your feet.  (There are other factors that go into feeling weightless that have to do with your body not having to apply a force on your guts to keep them in place...but that has to do with feeling weightless not with simulating gravity.) 

As we look toward the possibility of living in space for long periods of time (whether traveling or just staying in orbit around the Earth) we find that humans don't function as well in weightless situations.  We get upset stomachs and in general we need a floor to push against us so we can move around an be productive.  The question then arises, how do we create artificial gravity, or how do we simulate it? 

The only way to create a nearly realistic feeling of weight would be to create a spinning space station or shuttle.

space station animation (21k)If a station was created like the one at the left, while it is spinning, the wall of the space station would apply a center seeking (centripetal) force on the person to keep them traveling in a circular path.  The wall of this station has to exert that force (which also happens to be a normal force) because if it didn't, the person would continue moving in straight-line motion.   That's what things do in the absence of a net force.  " Up" would be seen as toward the center of the station.

 

The acceleration felt by the astronaut would be the centripetal acceleration which is described by the formula centacc.gif (1164 bytes)   The faster the space station spins the greater the centripetal acceleration felt by the person.  The larger the radius of the space station the smaller the centripetal acceleration.  By adjusting the rotational velocity (v) of the space station we could literally adjust the amount of the simulated gravity.  If adjusted  to just the right velocity, the centripetal acceleration would equal the the acceleration due to gravity on Earth (ac = g) which means we would be simulating the amount of gravity felt on Earth.   Any person in the space station would feel the same amount of force pushing on the bottom of their feet as they would if they were standing on Earth.

The formula for this centripetal force would be centrfrm.gif (1286 bytes) The faster the space station spins the greater the centripetal force needed to keep the person in  a circular path.  The larger the radius of radius of the space station the smaller the centripetal force.  When ac = g  then
Fc = w

This method would work well for simulating the force on the bottom of the feet but what about the forces on things that are not attached to the "floor" of the station.   Would things not touching the floor (an apple, a baseball hat, or your internal organs) seem to have weight or not.  If the your internal organs don't seem to have weight then we will have that oogy feeling we are trying to avoid.

 
spacestation animation with apple (21k)Consider the case of an apple held by the astronaut.  In order to be kept in a circular path, the astronaut will have to exert a  centripetal force on the bottom of the apple.  This force will feel like the "weight" of the apple.  (true weight can only be caused by gravity) So the astronaut will be fooled into thinking that the apple has weight.  Since the apple is an object not touching the floor and seems to have weight then we could say the internal organs of the astronaut would also seem to have "weight."  We wouldn't have that oogy feeling.

What happens if the astronaut drops the apple?  Notice that when the apple is released, there is no longer a net force acting on it.  So in the absence of a net force in continues on in the same direction and speed (constant velocity) that it had the instant it was released.  From our point of view the apple moves in a straight line when released.  From the astronaut's point of view (accelerated reference frame) the apple seems to drop in a straight line toward the floor.  It seems to be pulled to the floor as if by gravity.  The astronaut is fooled by what he sees into believing that there is gravity.  The only time an oogy feeling comes over the astronaut is when he or she looks out the window and see the stars rolling around.   It would be best to build this station with few windows... or make sure they are all covered with curtains.

We have to make sure that we are not fooled into believing that somehow centrifugal force is pushing the apple down or out away from the center.  Centrifugal force is a ghost force...it does not exist! 
Centrifugal force is not a force at all, it's a lack-of-centripetal force.

1998 Science Joy Wagon