this post was submitted on 01 Dec 2023
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I summarized it above, there's an extra rotation included when the outer circle moves along the inner circle, essentially falling a bit with every roll forward. If the outer circle rolled along a straight line of the same length as the circumference of the inner circle, it would only roll 3 times, but moving around the circle instead adds exactly one extra rotation. That other gent says this is used in calculating orbits too, where you're also moving forward while constantly falling
I read an article about it. Everybody is doing a shit job of describing what happens. The outer circle naturally makes a full rotation as it travels around the inner one, as the path it follows goes around a full 360°, so that counts as one of the rotations it ends up making, which is in addition to the 3 due to travel around the circumference.
thank you, that was the comment that explained it for me
Thanks for letting me know! It was too frustrating to not share.