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Hmm, yes. Maybe I am just missing something.

Hi @siddartha, I just had a chat with @lemouth who is a particular physicist and professor in physics. The answer is that the astronaut with the jetpack would be able to get to the space station as he is travelling relatively to the space station. To quote him: (the entire system station+astronaut evolves at a given high speed V, and the astronaut is evolving relatively to the space station at a small speed v).

Another answer came from @justtryme90 from the SteemSTEM group on Steemit Chat.

Well when you are up there, attached to the station, you too are moving at 17227 miles per hour. Breaking the tether won't change that as there is little to no molecular resistance in space to slow you down. So you will continue to move in step with the space station. In that case a jet pack should be able to move you around relative to that. However someone else should feel free to correct me if I am wrong. It's an interesting thought, I am not a physicist and its not something I really consider.

Hmm, ya now it makes more sense. I think then astronaut would be able to get back on the space station.

This is certainly correct!

An easier way to think of it is relative speed, sure the space station is going very fast - but if you are going with it, you are also going that fast speed.

The jet pack can only speed you up so fast, you are only going a few miles per hour faster or slower than the station.

It is indeed. It is like a fly flying forward in a car going at 120km

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