I think another important thing to consider is the lack of atmospheric particles in space. Things moving at very high velocities within the atmosphere are hitting a lot of molecules in the air creating friction, re-entry burn, etc. Basically, that’s what gives the appearance of instability at high velocity, but in space where there are little-to-no particles to cause that friction, vehicles moving at very high velocity won’t show that same instability.
It’s moving 17,150 mph relative to *us*, but what matters for docking is how quickly it’s moving relative to the ISS. We are completely irrelevant at that point. At the point of docking, they’re basically moving at the same speed relative to us, so their speed with respect to each other is basically 0. It’s like if you’re in a car and your friend’s car pulls up next to you. You guys can be driving as fast as you want, but you can still do things like pass stuff back and forth between the cars without having to take their speed relative to the road into account. This is basically the whole idea behind reference frames. In their view, it’s the road that’s moving quickly, and that’s perfectly valid. Neither of those reference frames us any more valid or right than the other. Physics is the same in both of them. That’s the beauty of relativity.
You can extend the same idea to the Earth. The Earth is orbiting the Sun, the Solar System is moving through the galaxy, the galaxy is moving in our local group, our local group is moving with respect to other clusters. That’s a *ton* of motion, but everything seems still here.
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