To get to my next point about Arthur Christmas I needed to know how fast an arbitrary point on the Earth is moving, as the Earth rotates. This required me getting out a sheet of paper and doing some sketches, so, I figured it’s worth a side article to explain what I was doing.
The first thing was that I simplified stuff. In particular, I decided the Earth is near enough a sphere that I’m not bothering with the fact that it isn’t. The difference between an actual sphere and the geoid is not worth bothering with unless you’re timing the retrofire for a ballistically-reentering space capsule. That’s … actually fairly close to the problem I want, about how long it might take the reindeer and sleigh to get back to Arthur Christmas and Grand-Santa, but that’s also too much work for the improvement in the answer I’d get.