Stanford Torus - What happens when you jump up?

[Koloss]

Dear Community,

The title says it all: What happens when you jump up inside of a Standford Torus?
As it is rotating with 1 RPM the gravity - while standing - is roundabout 0.9 to 1.0g. What happens when you jump up? There can't be gravity, right? So you will be floating in the air?

I'm starting to get a headache while thinking about this! :lol: Please help me!

Greetings,

Chris

 

[Urwumpe]

Dear Community,

The title says it all: What happens when you jump up inside of a Standford Torus?
As it is rotating with 1 RPM the gravity - while standing - is roundabout 0.9 to 1.0g. What happens when you jump up? There can't be gravity, right? So you will be floating in the air?

I'm starting to get a headache while thinking about this! :lol: Please help me!

Greetings,

Chris

The question is: How are you jumping up? Are you jumping up in the rotating frame? Then you still have the sideways speed but at a shorter radius: effectively you will jump less high than possible on Earth, because the acceleration by "centrifugal force" will push you back to the rotating wall faster than gravity would (because your acceleration outwards increases with reduced radius at the same lateral speed: a = v²/r)

While gravity acceleration would stay constant for short distances (See: Galileo), the acceleration by centrifugal force would increase.

1g = v1²/r1
2g = v1²/(r1/2)

Now, of course: Rotating frame. In reality it would get more complicated than that simple relation, because you have conservation of rotational impulse. But the simplification approximates it well enough.

If you are jumping up with a counter-spin component, you will continue to float through the torus until you collide with a wall again or get to the rotation axis.

Or in other words: When you start floating you stay in motion.

 

[Artlav]

Here is something to help your imagination:

Look closely at his trajectory when he does a step or a jump.
He floats in a straight line until the collision with the floor.

So, once you leave the floor in the jump, you are moving in a straight line, with approximately the rim speed of the rotation.
However, the floor is curved, so you will eventually intersect it.
Getting-close-to-it-ness have the appearance of gravity, in the way the distance reduces itself.
A jump cuts you across the circle, on a chord.

 

[boogabooga]

Wait, so did they SPIN Skylab?

 

[jedidia]

No. He's just colliding with the floor because it slopes upwards and he's carefull not to push up. The principal would remain the same in a rotating frame, just that you don't have to produce your forward momentum by yourself.