All the way up to this point I have been lead to believe that Special Relativity only describes uniform motion. If a ship turns around the motion is not uniform so Special Relativity shouldn’t be able to accurately describe what happens. Surely under Special Relativity, once two observers pass each other they will never meet again. (If they do, at least one of them has changed speed and/or direction)

Maybe General Relativity can be used to deal with a change of direction (acceleration), but I haven’t got that far yet!

I think you’re right Paul, because what if the ship literally does not change it’s velocity but instead simply arcs back to Earth. Surely that would be counted as constant velocity motion. The affect of Gravity and universal expansion must be the factors that vary the velocity.

A change in direction is a change in velocity.

Based on what we have learned so far, the first example seems to contain a contradiction: According to the astronauts on the rocket, they covered 4.25 lightyears in 3.19 years, I.e., they were going faster than the speed of light.

Thanks for the advice of dividing and multpling of gamma. I also had a confusion, so I paused the video, First figured out why it got divided and then rememberd this N = YM (N-nomal, Y-gamma, M-moving) . When I resumed the playback, you just solved my problem. Coincidence!
And ship reached proxima in 3.19 years due to lorentz contraction.

Thanks for the advice of dividing and multpling of gamma. I also had a confusion, so I paused the video, First figured out why it got divided and then rememberd this N = YM (N-nomal, Y-gamma, M-moving) . When I resumed the playback, you just solved my problem. Coincidence!
And ship reached proxima in 3.19 years due to lorentz contraction.

The Earth moved and came back, while the rocket remained at rest. I don’t see how this is not a valid perspective. Otherwise, the Earth gets a preferred frame of reference and that breaks one of the postulates.