[styrophone]

I think this thought experiment assumes the astronaut is spinning around an axis orthogonal to their belly. From the cartwheeling astronaut's perspective, the other one is also cartwheeling in their own plane.

[SomeStupidPoint]

But if you tuck in your knees and the other guy spins differently, that's a sign you're the one spinning, no?

[styrophone]

Yeah, the choice of a non-inertial reference frame for this example is a little confusing to me too. I also haven't been able to find an independent mention of the spinning astronaut experiment.

[dogma1138]

No because you technically performed an action which changes the system.

Relativity states that there isn't a measurement you can take if you change the system however it's a different story.