Forces resulting from rotation of a spacecraft.

Main Question or Discussion Point

In Sean Carroll's "From Eternity to Here", pages 69-70, the author says that people in a sealed spaceship out in space can tell when they accelerate (they are pushed "down" to the floor say by a rocket firing at the rear of the craft), or when they rotate (an object perfectly positioned at the centre of the axis of rotation stays where it is, but any object off the axis of rotation is "pulled" to the hull of the ship).

When they don't accelerate or rotate, an object released (placed) anywhere in the spaceship stays where it is (I assume).

I have a question about the "pull" that results from rotation. Imagine a cyclindrical spacecraft is going some direction, and if it rotates, it does so around the long axis of the cylinder.

If the spacecraft rotates at some constant rate, is the "pull" present whether or not there is an atmosphere present?

Presumably with the artificial atmosphere in a spacecraft, if it is constantly rotated, the astronauts and anything else in the capsule are "pulled" to the periphery.

Now imagine they get into spacewalking suits (with some air supply etc), open the hatch for a minute so the atmosphere inside the capsule is identical to that outside in "empty" space. They close the hatch and continue on. One of the astronauts, who is stationary with respect to the capsule, say halfway between the centre and hull of the cylinder, releases a marble in front of him. It stays stationary in front of him.

At this point, a rocket is fired which sets the capsule rotating at some constant rate. Are the marble and astronaut "pulled" to the hull of the capsule?

Or does the astronaut get dizzy because he suddenly sees the capsule rotating around him, while he stays "where he was"? (With the marble also staying where it was.)

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I don't see why the astronaut would get "pulled" unless the hull/ air imparts some speed onto him.

It's just a case of poor wording. Carrol probably means that an object that is fixed with respect to the spaceship at some radius r != 0 (ie. not in the centre) would feel a force pushing it towards the outer rim of the rotating spaceship.

I.e. he is talking about objects that rotate together with the spaceship.

Obviously, if the object is floating weightlessly somewhere inside the spaceship, it would not get pushed towards the outer rim of the spaceship.

I haven't read it, but I'm assuming he just worded it a bit imprecisely.

D H
Staff Emeritus
What you are missing here is that the object is positioned so that it's velocity is zero with respect to the (rotating) vehicle.

Suppose you are standing on the surface of the Earth. You tie a rock to a rope. You grab the other end of the rope and start spinning around so that the rock is spinning with you. (Think of a hammer throw in sports.) From your perspective the rock is not moving. It's velocity with respect to your eyes is zero. It is the land and sky behind the rock that appear to be moving from your perspective. Now you let go of the rope. What you see is that the rock will initially goes flying away straight away from you and will then starts curving to the left or right depending on which you are spinning.

What an inertial observer sees is something quite different. They see you as spinning around in circles and the rock flying in a circle around you. When you let go of the rope an inertial observer will see the rock go flying off in a straight line with whatever velocity it had at the instant you let go of the rope.

So, back to the spacecraft. Suppose the spacecraft has an axis running along the central axis of the cylinder and you are tethered to the axis. You hold an object at arms length and let it go. If the spacecraft isn't rotating or accelerating the object will stay where you left it. If on the other hand the spacecraft is rotating (and hence, so are you), when you let go of the object it will initially appear to start moving straight away from you and then will curve off from this straight line trajectory.

An inertial observer will see the object in circular motion up to the moment you release it and will then see it move along a straight line trajectory.

What you are missing here is that the object is positioned so that it's velocity is zero with respect to the (rotating) vehicle.

Suppose you are standing on the surface of the Earth. You tie a rock to a rope. You grab the other end of the rope and start spinning around so that the rock is spinning with you. (Think of a hammer throw in sports.) From your perspective the rock is not moving. It's velocity with respect to your eyes is zero. It is the land and sky behind the rock that appear to be moving from your perspective. Now you let go of the rope. What you see is that the rock will initially goes flying away straight away from you and will then starts curving to the left or right depending on which you are spinning.

What an inertial observer sees is something quite different. They see you as spinning around in circles and the rock flying in a circle around you. When you let go of the rope an inertial observer will see the rock go flying off in a straight line with whatever velocity it had at the instant you let go of the rope.

So, back to the spacecraft. Suppose the spacecraft has an axis running along the central axis of the cylinder and you are tethered to the axis. You hold an object at arms length and let it go. If the spacecraft isn't rotating or accelerating the object will stay where you left it. If on the other hand the spacecraft is rotating (and hence, so are you), when you let go of the object it will initially appear to start moving straight away from you and then will curve off from this straight line trajectory.

An inertial observer will see the object in circular motion up to the moment you release it and will then see it move along a straight line trajectory.
I believe the OP is asking something somewhat subtler than that, to wit if they are NOT rotating, and there is no mechanism (like air resistance) to make them rotate, then is there any apparent force at all?

Ie., what the inertial observer sees is actually a spacesuited astronaut (or a rock, it doesn't matter) in a vacuum filled cylindrical compartment, not on the "surface", but not (necessarily) on the axis, either. I'll assume for the moment that this compartment is stationary, but even if had some translational motion it shouldn't matter. Then, the compartment is suddenly spun up--while the astronaut/rock is floating around. What the OP is asking, then, is whether the astronaut would feel any force pulling him or her towards the ground (or so I interpreted his/her question), or in the inertial frame whether the astronaut would start moving towards the wall.

I should rather think the answer is "no", there needs to be some sort of mechanical connection for them to feel that "force".