Human max speed in open space

Question

Suppose you are an astronaut forgotten in the middle of nowhere, between our solar system and proxima centauri's. Now, you are out of fuel. I heard that with some kind of movements, someone in free space can actually acquire velocity, i.e. accelerate. Kind of like when you played swing as kid, acquiring more velocity with swinging legs back and forth. My first question is:

1. What is the maximum acceleration from one such optimal movement?

2. Then, is there a limit to the attainable speed through repeating such movements frenetically?

3. Finally, as a bonus, how much time to get back to earth with optimal trajectory?

Sorry for the question list but I think they are linked.

Newtonian as well as curved spacetime answers are appreciated and welcome.

Answer 1

You cannot change your linear or angular momentum in open space at all. You need something to transmit it to. if you swing your legs your body will rotate in the opposite direction while you swing, and stop when you stop swinging. If you are out of fuel there is no way to accelerate. Only by releasing mass you could change momentum, as Bender well shows you, if there is nothing external with which you could interact.

As for the max. speed, there is none (if you consider non relativistic speeds). You can go as fasta as you're going in the beginning unless you interact with something.

Answer 2

You can't just acquire velocity (and hence momentum) without an equal and opposite momentum going to something else. So you are wrong that there are things you can do to acquire velocity. Unless you want to leave parts of yourself behind or are capable of stealing momentum from, say, an electromagnetic field.

However, if you are an extended body in a curved spacetime that is capable of moving your parts around, it is potentially possible to translate yourself, even though you don't pick up a velocity. The effect is quite small, and you can search for "swimming through spacetime" for details.

Unlike a velocity build up you'd have to do each translation from scratch, and the less curvature, the less of an effect. Every analysis I've seen assumes you have perfectly rigid parts, and can freely move them however you want. Real human parts are not perfectly rigid and it will require effort to move them, if you were an astronaut caught light years away from earth the translations would be very small, and you'd stop translating when you stopped moving your limbs so you would surely die before you made it anywhere close to Earth, and once you died you'd stop travelling (this is different than picking up velocity where your corpse might some day arrive).