Assuming there are exactly 365 days per year, how many rotations about its axis does the earth make in one year?
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2$\begingroup$ @RewanDemontay eh, I'm kinda on the fence. It definitely has a "single definitive answer", but might be considered "textbook". $\endgroup$– user46002Commented Apr 10, 2019 at 22:51
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3$\begingroup$ 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.) $\endgroup$– Rubio ♦Commented Apr 10, 2019 at 23:03
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1$\begingroup$ 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. $\endgroup$– hexominoCommented Apr 10, 2019 at 23:15
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1$\begingroup$ @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. $\endgroup$– Jac FrallCommented Apr 10, 2019 at 23:17
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1$\begingroup$ Related puzzle about coin rotating around a set of coins: puzzling.stackexchange.com/questions/56787/… $\endgroup$– PreshCommented Apr 11, 2019 at 2:36
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2 Answers
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Answer
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.
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2$\begingroup$ 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 $\endgroup$– PreshCommented Apr 11, 2019 at 2:32
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1$\begingroup$ @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. $\endgroup$– jarnbjoCommented Apr 11, 2019 at 17:12
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2$\begingroup$ @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. $\endgroup$– PreshCommented Apr 11, 2019 at 20:05
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2$\begingroup$ But only because earth is a prograde planet (otherwise it would have been 364) $\endgroup$– RetudinCommented Nov 24, 2020 at 7:03
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Half jokey/ half serious answer:
Exactly one rotation. Assuming the axis in question is the one through the gravitational center of the Earth/Sun system. One rotation around that axis is the definition of a year.
Or worse:
Something like .000000004 rotations around the Milky Way galactic center.
Mama never told me not to play with axes
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$\begingroup$ Objects don't rotate around external axes, they revolve around them. It's a misuse of terminology to say the earth rotates around the sun. $\endgroup$ Commented Jun 13 at 20:02