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See this Wikipedia page for Harmonices Mundi, a book by Kepler (yes, he was the one to discover the three Kepler's laws). The author writes:

He found that the difference between the maximum and minimum angular speeds of a planet in its orbit approximates a harmonic proportion. For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion. Venus only varies by a tiny 25:24 interval (called a diesis in musical terms).

Can anyone explain why this is the case physically (possibly with mathematical formulae)? Or is it just a coincidence?

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It’s a coincidence.

He also thought the spacing of the planets was related to nested Platonic solids. It isn’t.

His three laws, not his numerology, are why he’s rightly famous.

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  • $\begingroup$ Disappointing, but expected. $\endgroup$ – Ma Joad Nov 25 '19 at 7:36
  • $\begingroup$ As with most attempts at numerology, the coincidence usually goes away when you get more accurate measurements. $\endgroup$ – probably_someone Nov 25 '19 at 10:02

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