Geometry question about the radius of star trails

I have a project going related to Flat Earth debunking, but I want to get some geometry right first.

It is commonly observed that star trails near the poles are circles, while a star trail right on the celestial equator is a straight line, since it is a great circle on the celestial sphere. I have some pictures that demonstrate this, including some basic calculations for predicting the pixel radius of the star trails near the poles: https://astronomy.stackexchange.com…s-the-equation-for-the-radius-of-a-star-trail

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