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Every 39.88 minutes 10 degrees ($\frac{360^\circ}{36}$) of arc passes over the zenith. It can also be stated that the 36th harmonic of the rotation period of the earth (1435.8 min) is equal to 39.88 min. Note the similar relationships with the rapidly rotating planets:

  • Mars, rotation period of $\frac{1477.2 min}{\text{harmonic of }37} = 39.92$
  • Jupiter: $\frac{595.8}{15} = 39.72$
  • Saturn: $\frac{639.6}{16} = 39.98$
  • Uranus: $\frac{1035}{26} = 39.81$
  • Neptune: $\frac{966.6}{24} = 40.28$

For the slowly rotating planets, and the Moon, the numbers are larger, but still very close to 39.88:

  • Mercury: $\frac{3520.2}{88} = 40.00 \text{ } (88 = 22 \cdot 4)$
  • Venus: $\frac{14582.4}{368} = 39.63 \text{ } (368 = 23 \cdot 16)$
  • Pluto: $\frac{9223.2}{232} = 39.76 \text{ } (232 = 29 \cdot 8)$
  • Moon: $\frac{39343.68}{992} = 39.66 \text{ } (992 = 31 \cdot 32)$

The questions are: Are these relationships well known? Are they factors in other planetary phenomena?

peterh
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    Voting to close: it seems like all you've done is divide planetary rotation period in days by 39 or so and then used that as your divisor on the left side. –  May 24 '18 at 19:02
  • True. The odd thing is that all the results are integers within a few seconds. Coincidence? –  May 24 '18 at 19:11
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    See, how well this site supports Latex! :-) Just type $5\cdot5$ and you get $5\cdot5$. – peterh May 24 '18 at 19:29
  • I'm voting to close this question as off-topic because it's about coincidental numerical relationships, not astronomy. – HDE 226868 Jun 03 '18 at 00:28

2 Answers2

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I'm very sorry for you, but this is just (mathematical) probability at work and no (astronomical) pattern. I'm on mobile right now so I can't do a full analysis, but note that if you divide Mercury's period (3520.2) by 89 instead of 88, the result is 39.55. Still pretty close to 39.88. In other words, the larger the numbers get, the easier is to find a 'divisor' close to 39.88.

Glorfindel
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So you divide the rotation periods of the planets by any number you need it to be for the end result to be 40, and wonder why the result is 40?

Circular argumentation works because circular argumentation works. It's just not meaningful in any way.

AtmosphericPrisonEscape
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