I finally got a clear night and managed to capture some star trails. I couldn't get to a really good location for a full sky view that wasn't blocked in some way, that will have to wait for spring.
I made sure that Polaris was centered in the frame so there would be no barrel distortion.
Tom never said how long the star trails need to be for his procedure, but hopefully these are long enough.
As you can see, these are circular. They are not oval, they are not massively distorted, they do not look anything like the bridge pictures that were shown.
I made no distortion corrections to this image. It's not warped in any way. I did crop it and removed the horizon.
Overall I'm pretty happy with this, it shows what I wanted and is just in general, pretty to look at. I never took star trails perfectly centered before, I always tried to frame the picture to be interesting. So this was fun.
This experiment proves (if only to myself) that star trails are indeed circular. I know the camera, lens, setting and everything done to this image so there can be no doubt in my mind. If anyone has questions, feel free to ask.