A question about rotatory rotating rotation that rotates

[Thesla]

ok, i don't know if this question belong in here, but here we go:

suppose we are in orbit, we have two bodies: one astronaut in EVA, with an EMU, and a big chunck of a space station, or a shuttle. the astronaut has is not rotating, while the station is slowly rotating on all 3 axis (like around 2:10 in here: https://www.youtube.com/watch?v=phv3VDH4tFk ). the astronaut moves towards the station and grabs it. what happens then? i mean, as he grabs the station his velocity is canceled and he rotates with it, but the station is rotating in all axis, how can he describe such rotation? what does happen with him? my mind is confused.

i tryied making this situation in KSP, but for some reason the kerbal just let go of the ladder. someone has an answer? did anyone understood it at all?

[orcman]

Hey Thesla,

The short answer is: it depends.

Longer answer: Part of the astronaut's kinetic energy (0.5mv^2) will be added to the station's velocity vector (it will alter the orbit ever so slightly), the remainder of their energy will be added to the rotation of station. Exactly how much of each depends on how far away the astronaut grabs the station from the stations' center of mass and the distribution of mass of the station (inertia). If they tumble around like in the clip, things are much harder to calculate, but most likely a larger portion of the energy will go to the extra rotation.

Either way all energy between them stays constant. So if you add up the rotational and kinetic energy of both parts, it will be the same as the sum afterwards - just split a bit differently.

The more probable outcome of the clip is that the astronaut hits the station and is killed (has no real gauge of closing velocity), or tears their suit on some sharp. XD

[Z-Man]

Kinetic energy is not conserved here. "Grabbing" something is an inelastic collision and usually transforms kinetic energy into heat.

What is conserved, though, are linear and angular momentum, and the effects of that are exactly what orcman describes.

[Seret]

the station his velocity is canceled and he rotates with it, but the station is rotating in all axis, how can he describe such rotation?

From the astronaut's point of view he feels a huge yank when he grabs the station, if he manages to hold on (or more likely clip on) then he'll quickly be rotating at the same rate as the station. So from his point of view the station is not moving and it's the horizon that's moving. If it's rotating in three axes it would probably be pretty hard for him to describe how it was rotating without instruments.

[K^2]

You cannot have a rigid body rotating on 3 axes. At any given moment, body rotates about only one axis. The axis of rotation. However, if that axis does not align with one of principal axes of the body, the rotation axis will tumble. You can sort of think of the resulting precession as rotation about two different axes. And even that is pushing it. 3 is right out.

So as far as motion goes, the astronaut is going to move along the same trajectory as a point on the station that he's attached to. Presumably, his mass doesn't affect the inertia tensor much, so he'll be moving along the same exact trajectory that the point was moving on before he grabbed it.

However, as outlined above, due to axis tumbling, that trajectory can be quite complicated.

[lajoswinkler]

That part in Gravity, when they catch on with the destroyed shuttle, is one of the mild mistakes in the movie. When they catch the rotating shuttle craft and their kinetic energy is shared between them and the craft, they'd still feel substantial centrifugal force, so they would need to carefully hold on all the time, yet that isn't really apparent in the scene.

Regarding your question, the resulting motion would depend on how well the astronaut is fixed to the second body, the position of grab, etc. It would be difficult to describe. If it's a proper station, the change would be very weak as the station has a lot more mass.

I, too, did a lot of such experiments in KSP. I'd let a satellite tumble and then, using a Kerbal, try to grab it. It's very difficult