# Earth rotation discrepancy

Some time ago, I discovered that planet earth's sidereal rotation period equals 23 hours, 56 minutes, and 4.1 seconds (see for example this Wikipedia article). The sidereal rotation is the rotation of a celestial object around its axis. Thus, earth takes a little less than 24 hours to rotate around its own axis.

Now I wondered how it could be that our clocks measure 24 hours for one day instead of only 23 hours, 56 minutes, and 4.1 seconds. Though the difference seems quite small, we just need to do some basic maths to uncover the ominous effects of that situation:

• after 10 days, the difference between clocks and earth rotation equals ~39,5 minutes
• after 30 days, the difference equals almost two hours
• after half a year, midnight would be around noon

As you can see, there must be some flaw in this logic. We would most probably have realized if at midnight the sun would be at the highest point on the sky.

So, what do you think is the reason that our clocks work fine, although earth seems to rotate a little bit too fast?

Note: I do already know the answer to this puzzle but I am interested about your approaches.

• Probably should've added an answer rot13(Vf vg orpnhfr bs gur bccbfvgr qverpgvba bs gur ebgngvba naq eribyhgvba bs Rnegu?) – Abbas Aug 22 '19 at 6:35

## 2 Answers

I'm thinking that it's due to that the earth is not only making rotation but also revolution.

In short, in a year, the earth is making "an extra rotation" due to Coin Rotation Paradox. Therefore it adds $$24/365$$ hours which is roughly $$4$$ minutes so that the midnight is still midnight~

• That's the correct answer. Thank you for the link to the "Coin Rotation Paradox" - I was not familiar with that term before. – Spark Fountain Aug 22 '19 at 7:01
• Astronomers distinguish between the siderial day, where a given "fixed star" is over the same meridian on two successive occasions, and the solar day, where the sun is over the same meridian on two successive occasions. The explanation above also explains the distinction between the solar and siderial days. – Jeff Zeitlin Aug 22 '19 at 11:08

The Earth is moving in relation to the Sun, so one spin around the planet's axis in relation to the Sun is slightly longer than the sidereal rotation period.