Okay, this one gave me some pause.
Most of the people around me probably understand that the earth rotates around its axis (the imaginary north-south line), and the moon orbits around the earth (although, to be more precise, the earth/moon pair actually rotates together around their common center of gravity, which is actually located inside of the earth but seriously distant from the earth's center), and the earth/moon system orbits around the sun.
I was reading about the ancient Egyptian and Babylonian mathematicians and astronomers, who made astoundingly careful and accurate measurements and analysis and predictions despite having no telescopes and only dripping-water clocks with which to measure time intervals. They knew the earth was round 3000 years ago, had a pretty fair idea of its size, and they knew that the moon's orbit around the earth was not a perfect circle but had an apogee and a perigee which they measured to an accuracy which is downright astounding. They knew that the earth's orbit around the sun took somewhere between 365 and 366 days and they could accurately predict the change in the time of the sunrise from day to day as winter passes to summer and back. (They also knew Pythagorus' theorem when all the Greeks were still living in caves and wearing animal skins.)
I got to thinking about this and that day thing ... that the day is 24 hours long and the year is between 365 and 366... and then I realized that what we call a "day" is not exactly a 360 degree rotation of the earth around its axis but something just a little bit different than that, on account of the action of the earth orbiting around the sun.
So your pop quiz today is this: how much difference in time does this orbiting have and does a 360 degree rotation of the earth (so that a star, other than the sun, has returned to its exact same longitude in the sky as the night before) take a little longer or a little less than 24 hours?
I never learned this. I had to compute it. I'm lazy, I only worked it out to the minute, but if you get the concept right then you can find the numbers and plug them in to the formula and get it right to nanoseconds if you wish. But I do find its interesting, just a little bit more than Jerry Springer ....