# How many times does the earth rotate per year?

Assuming there are exactly $$365$$ days per year. How many rotations about its axis does the earth make in one year?

• @RewanDemontay eh, I'm kinda on the fence. It definitely has a "single definitive answer", but might be considered "textbook". – Hugh Apr 10 '19 at 22:51
• Our guiding principle is roughly presented here - Are math-textbook-style problems on topic? - the general idea is that a problem with a "Clever or elegant solution, often an "aha" moment; Unexpected problem statement; or Unexpected or counterintuitive result" might be a good puzzle. I'd be inclined to let this pass, given that to folks who have never really thought about it, the result is likely to be surprising. (Having said that, it's trivially solvable without actually resorting to math, making it, well, less puzzle and more trivia.) – Rubio Apr 10 '19 at 23:03
• I also have some sympathy for this question - I have actually thought about posting this riddle, in some form, before but it's difficult to make it sound enticing. Needless to say, the result is not immediately obvious. – hexomino Apr 10 '19 at 23:15
• @hexomino I agree. This was something I actually thought about today and figured out. When I typed it out though, it doesn't seem enticing at all. Maybe someone can transform it into a more wordy puzzle. – Jac Frall Apr 10 '19 at 23:17
• Related puzzle about coin rotating around a set of coins: puzzling.stackexchange.com/questions/56787/… – Presh Apr 11 '19 at 2:36

366

Explanation

As the Earth revolves around the Sun it has to turn slightly more than a complete rotation each day to account for the extra angular distance that it has traveled. Over the course of a year, this will add up to an extra sidereal day over the number of solar days.

• Is this phenomenon related to the "coin rotation" paradox? I would love a reference that relates the two, but nothing about sidereal days explicitly mentions the coin rotation paradox: en.wikipedia.org/wiki/Coin_rotation_paradox – Presh Apr 11 '19 at 2:32
• @Presh It is more or less the same principle. The Wikipedia article you are linking to relates the coin rotation paradox to the movement of the moon around the earth, but it could just as well had been the earth's movement around the sun. – jarnbjo Apr 11 '19 at 17:12
• @jarnbjo: Thanks. I am considering a video on my YouTube channel (MindYourDecisions) so I try to be careful. Since the answer works for flat coins, perhaps even the flat-earthers will agree about the answer. – Presh Apr 11 '19 at 20:05