once the cord goes taut and doesn’t stretch or move any longer
Does the climax of the movie ‘Gravity’ violate simple physics?
Ethan Siegel

Hi Ethan, thanks for writing amazing stuff as always.

In this case, I’m not sure if this premise is correct. If you watch the clip for that part closely, you will see that the last time we see an open take of them and the station, not only they are rotating compared to the ISS (which makes your theory possible), but they are also still going further away from it (1:17 in the clip below):

This means that the cord holding Sandra Bullock was still stretching when he is about to let go, and pulls her back once he does let go, giving the impression that he gains speed, while he is actually staying at the same speed compared to the ISS.

What do you think?

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