Apologies if this has been asked and answered recently; I don’t know the appropriate scientific terms to run an accurate search. I’m not even sure if I can word my question here accurately.
It has been years since I read Rendezvous With Rama. The premise is that a giant tube-shaped spaceship had been given a spin, and cities and farms can exist on the inner surface, with centripedal force substituting for gravity.
But it seems to me, it can’t behave just like gravity if an object was introduced into this tube at the center. The object would drift freely, unaffected by the gravity-like force, and possibly eventually drift into the spinning wall. It would never “fall” like an object would if dropped into a singularity like a planet or a moon.
Right? Or do I have this completely wrong? I never took any classes in physics or even excelled at math so I’m not at all sure about how it works.
I’m not a physics major either, but I believe you’re correct about an object introduced into the center of the spacecraft. But objects on the surface of the tube will have lots of momentum imparted by the spin of the cylinder. If they jump into the air their motion will mimic gravity.
Are you OK with objects on the surface behaving like they are in a gravity well and just have a problem with objects introduced externally into the cylinder?
You’re right - and if you move fast enough in the direction opposite to the rotation, you should be able to jump and take off (air resistance notwithstanding).
Or if you run move fast in the same direction as the tube is rotating, you get heavier.
The earth and the moon are not singularities. They can be treated as point particles for calculations if the other object is outside the perimeter. But that’s not the same as being a singularity.
Once you are inside the perimeter, things get a bit trickier. Makes for a good final exam question for Physics 101.
Well, a planet or moon aren’t singularities…not sure what you were trying to say there but they aren’t that. Certainly at the center of the rotating cylinder there would be no 'gravity…that area would be in free fall with zero ‘gravity’. There are tons of articles on the internet about this, but here is one on the physics from Wired FWIW (I’m sure one of the physics 'dopers will be along to explain it in more detail soon).
(there are some helpful diagrams in the article if you want to take a look)
Right. Spinning simulates a planet’s gravity at the inner surface, not at the axis.
However, if there is an atmosphere inside the cylinder, frictional forces between the atmosphere and an object near the axis will tend to cause the object to move away from the axis, faster and faster. This happens in Rama, actually - someone is using a human-powered airplane at the axis - which works fine, until he drifts away from the axis, and experiences spin-induced gravity caused by the spin of the atmosphere (friction will keep the atmosphere moving with the cylinder walls).
Correct. This is explicitly considered in Rendezvous with Rama, where they travel using low-powered aircraft (skybikes) near the center (but a bit outside), where it takes very little lift to keep aloft.
There was a similar incident in an episode of Babylon 5, which is a rotating O’Neill cylinder similar to Rama. A character jumps from a transport tube running along the cylinder axis. He is initially floating weightlessly, until the rotating atmosphere starts causing him to pick up speed and move along with the cylinder’s rotation. He starts to drift “downward” (toward the cylinder rim), picking up speed until he is danger of smashing into the cylinder rim with lethal force.
I wondered about that w.r.t. the baseball game set on the space station in Interstellar. I don’t think any baseballs there will follow anything close to curved Terran trajectories…
This scenario also played out in Schlock Mercenary. There, a character spirals out from the center due to air resistance, and eventually smacks into a structure on the surface. Howard Taylor, the author, states that the speed at collision (though not the direction) would be the same as terminal speed in a uniform gravity field equivalent to the surface of the cylinder. I haven’t actually checked that calculation (between here and there lurks a messy differential equation), but it sounds plausible.
That’s ringing a bell. Dang, I’m going to have to read this book again. I read most of Arthur C. Clark’s novels before I ever picked up one of Larry Niven’s. That must have been thirty-five years ago!
He jumps from a moving monorail near the axis towards the ground.
Ivanova says “He’s more or less weightless, but the ground is moving at 60 mph. If we can’t catch him, he’ll be killed by the impact.” So he is moving steadily, not picking up speed. So the collision would be like jumping off a 60mph train - not much vertical speed, but the horizontal speed is the problem.
Yeah, I disagreed with Ivanova’s analysis of the situation when I first saw the scene. As he falls he will be accelerated by the moving air he’s passing through. This will actually decrease his horizontal (circumferential) velocity relative to the ground. But the centrifugal force imparted by that velocity will increase his downward (radial) velocity as he falls. It would probably be worthwhile to do an exact analysis of the physics of the event, given the station radius (420 meters), rotational speed, and some reasonable assumptions about how much force is imparted by the moving air during his descent. I’ve read that the air density wouldn’t change very much from the axis to the ground, but that could use some analysis too.
It was a kick in the guts, but that was also the storyline that had the titular character (Sergeant Schlock) walking grenades across a city block and missing his target because “shooting in a rotating reference frame is hard”
Since we’re in GQ, I’d just like to emphasize the fact that RwR is an excellent book. Most of Clarke’s stuff is top notch, and that is one of the best of the bunch.
That can’t be right. In the limiting case where there’s no atmosphere, the person is going to smack into the wall with whatever radial velocity he started with in the radial direction, and in the circumferential direction a speed (relative to the wall) of just the speed of the wall (v= ωr). But terminal velocity with no atmosphere is infinite. So the two quantities can’t possibly be the same.
I’m not very confident in my intuition about the limiting case of a very thick atmosphere, but it seems like the person would be generally be rotating at almost the same angular speed as the wall (and atmosphere), very slowly ‘sinking’ towards the wall while being continually accelerated up to the speed of the new more outer layer of air, so it would hit the wall with only a small velocity difference in either direction.
The problem is even worse than you think. It can’t behave “just like gravity” no matter where the object is located, at the center or otherwise. The farther away from the center you get, the less noticeable the discrepancies are. But there are there. Here are some examples:
You visit a recreation tower built by rock climbers, for fun. The tower points straight toward the center of the tube. Since the top of the tower is slightly closer to the hub than its base, people at the bottom are spinning a larger circle than people at the top. So, as you climb up, you feel as if there’s a mysterious force pulling you toward the East. And then, as you climb down, you feel it again but now it’s pulling you toward the West.
The second time you climb the tower, you decide to rappel down. You strap on a harness, clip in, and step over the West side of the tower. As you rappel down, the tower moves away from your feet and you find yourself dangling in mid air at a crazy angle. Your rope is attached to the top of the tower, the tower is straight up and down, yet you at the end of the rope are not touching the tower.
The rappelling instructor hauls you back up and lectures you for ignoring the sign which clearly says “Rappel on East side only”. Rappelling down the East side, you feel strangely heavy and have to push your feet off the tower much harder than you’d expect.
Your home is on the opposite side of the tube. You usually walk East to get there. But today you decide to walk West. You realize you’re behind schedule so you start running. Suddenly you feel lighter. The faster you run, the lighter you feel. You find yourself taking huge leaping bounds, ten times bigger than a normal walking stride. Then you realize you dropped your wallet a little ways back and you have to stop and turn around to go get it. Running West, you find that, the faster you run, the heavier you feel.
You finally get back to your house and you need a shower. All the walls in your bathroom point straight up (toward the center of the tube). The walls are closer together at the ceiling than they are at the floor. You turn on the shower head. As the water drops fall down, they curve slightly toward the West. The East wall of your shower hardly gets wet at all. Down at the very bottom of the shower enclosure, the West wall remains completely dry.
And I have even gotten started on playing baseball.
True- in a rotating structure the acceleration is NOT identical to gravity. A falling (or rising) body will act very much like it’s in gravity if the rise or fall is tiny compared to the radius of the rotation. But once it becomes a significant fraction of the radius strange things happen. Taking the inner surface as “stationary”, a rising or falling body seems to be mysteriously deflected spinward or antispinward. This is called Coriolis force. And inversely a body moving spinward or antispinward will experience a vertical force making it heavier or lighter.
So yes, if you pay attention aboard a rotating space station, you will see significant departures from a static gravity field.
