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I know that the astronaut starts floating off into space. But I wanted to know that why does he start floating in space, even though the spaceship has mass. So if the spaceship has mass, then shouldn't it exert a tiny gravitational force towards the man, but why does he start floating away from the spaceship?

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Well, the astronaut doesn’t necessarily float off into space. This would only happen if they are pushed away from the ship. If we do make the assumption that they are moving away from the spaceship at the time their tether breaks or, at least that their tether is broken and they push/are pushed off the ship, then they would indeed move away through space.

It is true to say that the ship exerts a gravitational force on the astronaut which attracts them to the ship. This force, however, is incredibly small (gravity is the weakest of the four fundamental forces unless one, or both, of the bodies is/are very massive, which implies planet-like mass. That is not the case for the astronaut or the spaceship). This means that the attraction of the astronaut to the spaceship is negligible and not going to help the astronaut in a meaningful way.

To go further, I might suggest alternative ways to save the astronaut. Astronauts usually have a sort of jet-pack attached to their suits, which would allow them to manoeuvre back. In the case they don’t, they could throw something (maybe a heavy tool) in the direction they are travelling. Conservation of momentum would result in them moving in the opposite direction of the object they threw (hopefully, for them, back to the spaceship)

Hope that helps :)

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  • $\begingroup$ How much oxygen do they have? Would just waiting until you arrive from the other side be anywhere close to having a chance to work? $\endgroup$ Sep 30, 2021 at 11:27
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    $\begingroup$ Well, they have enough oxygen for many hours (around 16), but remember that the spaceship is also moving around earth (I’m assuming that’s the context). That means the astronaut is only moving around the Earth a little bit quicker than the astronaut so it would take a while to catch up. An even bigger problem is that if they fell out, they might not follow the exact same path as the spaceship around earth and when they caught up, they’d be even further away. $\endgroup$
    – UnrulyTank
    Sep 30, 2021 at 11:34
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    $\begingroup$ I’ve just done some maths: if we assume this spaceship is the International Space Station, then the astronaut would have to move around 2670 km/h quicker than the spaceship to catch up within 16 hours... I don’t think that is really realistic, because to accelerate the astronaut to that speed, the international space station would also lose quite some momentum. $\endgroup$
    – UnrulyTank
    Sep 30, 2021 at 11:40
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"I know that the astronaut starts floating off into space" is not right in every instance, if the a. is not moving relative to the space ship, she will not float away, if she is moving to the spaceship, she will do so after the tether breaks. Only if she is moving away she will continue moving away. It is true that there is a very small gravitational attraction to the ship, but like every mass there is an "escape velocity" which is very low for a small mass. If you move away from earth with about 11km/s the earth will never catch you again, so if you escape from the small mass of the space vehicle some cm/s are enough .

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