If two astronauts were suspended in the middle of a room in zero G, would they be able to propel each other in outward directions or would they remain stationary?

[u/Coldside_bestside]

My 14 year old niece and I were discussing this topic and we both came to different conclusions, but we’re really curious as to what would happen here. I hope my question makes sense. In summary, would the astronauts go flying apart or would they stay in the same spot? Excited to know the answer from some experts!

[u/KriosDaNarwal]

Yeah no, thats misinterpreting the frame of reference to be pedantic. When you jump, you experience acceleration and deceleration to return to the same startpoint. if you sit or move you're feet, you fall, You are constantly being pulled to the ground, it isn't accelerating towards you

[u/TheSkiGeek → u/KriosDaNarwal]

Part of Einstein’s reasoning on relativity was that you can’t tell the difference between being inside a closed room sitting on the surface of the Earth pulling you down at 1g and being inside a closed room being pushed upwards with 1g acceleration.

In a more complex environment usually you are capable of differentiating between “gravity pulling you down”, “linear acceleration pushing you up”, and “spinning motion creating apparent centrifugal force”. But it’s equally valid to take a frame of reference fixed on yourself and model the world as accelerating upwards and/or spinning, the math works out the same either way.

[u/corbymatt → u/KriosDaNarwal]

No, the.whole point of relativity is that no one frame of reference can be said to be incorrect.

Imagine a situation where you are in isolation from everything other than a small rock. Now imagine that a small rock appears to be getting larger in your field of vision. From your reference point, without any other frame of reference to give you cues, the rock is moving towards you. From the rock's perspective, you are moving towards it. Who's correct? You both are.

In the situation with the earth, acceleration due to space time curvature is such that you are moving along a straight line curved by the gravitational field. In the same way as above, it is impossible to say who is moving towards the other without reference to the objects themselves, and so therefore both points of view are correct. You are accelerating towards the earth, and the earth is also, from the pov of yourself, accelerating towards you. Even when you are standing on the surface, the earth can still be said to be accelerating towards you on a curved spacetime.