Imagine you're in a spacecraft that uses centripetal force to simulate gravity. What happens if you jump?

I would think you would drop back down. If the speed of the rotation stays constant the force of fake gravity should also stay the same. It would be different I suppose the sweet spot would be where people are expected to be the majority of the time.Since there is no resistance in space there would need to be a counter rotation on the part of the ship that isn’t gravity charged otherwise the other part wouldn’t turn.

I made a little sketch to convince myself that when you jump straight upward you will actually follow a linear path since there are no forces on you. Once your feet leave the floor (which has been pushing up on you until you jujmped) there is no circular motion until you land, when it resumes again. Your previous trajectory was tangent to the circular curve of the ship. The jump launches you on a chord of this circle that will land you ahead of where you would have been without jumping.

The apparent gravity should feel weaker as you approach the center of rotation. If the spaceship rotates with a constant angular velocity ω then acceleration equals Rω^2. Constant ω means acceleration is proportional to distance. As R decreases from its initial value (the floor) to zero (the hub), acceleration will fall similarly.

I can’t help recalling images from the movie “2001: A Space Odyssey” where the guy is running laps inside the ship.

@gasman beat me to the punch. So just a vote. What he said. The only variable I would add is that might be just slightly off if the ship had just begun rotating and the atmosphere inside it had not yet been accelerated by friction to the rotational speed of the cylinder. To be very precise, as in hair-splitting precise, the air inside would never reach the cylinder’s rotational speed. It would approach it on an asymptotic curve, so for purposes of measurement it would have virtually no effect after the craft was well underway.

Centrifugal force is due to your desire to move in a straight line while being forced into a circular path. When you are in a rotating spaceship, the only reason you are moving in that circular path is the hull of the ship your are standing on that forces you into it. Your body wants to move in a straight line. When you jump up, you temporarily stop moving in that circular path and instead move in a straight line (think hammer throwing), until you hit the circular hull again.

This article might help:

http://en.wikipedia.org/wiki/Artificial_gravity#Rotation

“Artificial gravity levels vary proportionately with the distance from the centre of rotation. With a small radius of rotation, the amount of gravity felt at one’s head would be significantly different from the amount felt at one’s feet. This could make movement and changing body position awkward.

Effects produced by the Coriolis effect also act on the inner ear and can cause dizziness, nausea and disorientation. Experiments have shown that longer periods of rotation reduce the Coriolis forces and its effects.”

An alternative to a rotating spaceship is one that flies alternating wide curves, following the path of a wave.

If you like this question I highly recommend James Gleick’s short book Newton.

Isaac Newton and his contemporaries were pondering this kind of question (what if you dropped through a hole through the earth?).

Prior to Newton, people were just guessing

The astounding thing to me was that Newton figured out the math, Alone. Nobody was even close. Through sheer superhuman brainpower he figured out the mathematics of planetary orbits in the late 1660s, and it’s the same math which allows NASA to calculate its launches to Mars and beyond.

@jaytkay Isaac Newton has always fascinated me. Thanks for the book recommendation. I will add that to my “to read” list on Goodreads.com.

And while Newton’s contribution to the math required to chart a trajectory to Mars cannot be minimized, it is worth noting that had Einstein not added relativistic equations to it, we would miss Mars by millions of miles.

@ETpro Interesting. I know that the GPS system wouldn’t work without relativistic calculations carried out to atomic-clock precision.

It’s true that standing “upright” puts your head closer to the hub than your feet. The blood pressure gradient is physiologically bad for you – with enough gradient I’d expect swollen feet and lightheadedness! The larger the radius of rotation, the smaller the head-to-foot gradient, which is proportional to 1/R, so larger, more slowly rotating wheels are better for generating human-friendly 1g.

I think when you jump up from the floor, you drift a little forward but always land upright, because even though you now float in a straight line, your body is still rotating synchronously with the ship; your angular momentum doesn’t change; no torque is applied (if you jump in an ideal way). So when you land on the floor your head should still be pointed toward the hub.

Coriolis forces will tend to pull you forward as you move toward the hub – until some tangential velocity is shed. That’s why jumping lands you forward. If the effect is strong enough (with small R) I’m sure it could be very annoying. Anyone know if these details have ever been described in a sci-fi novel?

@Mariah, once again GQ!

Thanks so much, everybody! I got the information I need, although obviously the discussion is still interesting.

This is for a sci-fi story I am writing about a society living on a spacecraft. I foresaw the force differential from feet to head and it has gotten some coverage – the society calls it “radius sickness” and it is somewhat of a problem for them.

Good luck with your story!