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We know that on a longer time scale (millions of years) the orbits of planes are unstable and it is impossible to make predictions about eclipses millions of years into the future. But on a shorter scale, the behaviour of orbits can be considered to be fairly stable. I was studding the distribution of the number of solar eclipses in short time scale (thousands of years as opposed to millions of years)

NASA has published the list of the count of solar eclipses (total + annular + partial) every century from 1999 BC to 3000 AD. When we plot count of eclipses against the century (-19 for 1999 BC to 1900 BC, +30 for 2900 AD to 3000 AD) we get a curve which roughly looks like a sine wave. I fitted a sine curve on this data and obtained a good fit with $R^2 = 0.9$. Since a sine function is period function with a period of $2\pi$ it means that the number of solar eclipses in a century should roughly repeat every $2\pi$ century or 6th century (6.28th century to be precise). Example: For the 6 century cycle starting from the first century AD we have (1AD, 248), (7AD, 251), (13AD, 246), (19AD, 242) etc. Generalising this, for any time period $T$ instead a century, we have the hypothesis:

Hypothesis:

The number of solar eclipses in a time interval of length $T$ has a quasi-period of $2\pi T$.

Question: Is it possible to provide a theoretical justification to this empirically observed trend? I am more interested in why should the quasi-period be $2\pi T$ rather than just why there should be a quasi-period.

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    $\begingroup$ Are you familiar with the Saros Cycle? $\endgroup$ – Dr Chuck Jul 19 '18 at 10:24
  • $\begingroup$ That's quite interesting. NASA has also published the solar eclipses by date. Have you analysed that data to validate the hypothesis? And what are the residuals on the $R^2$ fit? $\endgroup$ – Mick Jul 19 '18 at 10:33
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    $\begingroup$ Crossposted from physics.stackexchange.com/q/418408/2451 $\endgroup$ – Qmechanic Jul 19 '18 at 11:50
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From the same NASA page:

The recurrence of solar eclipses is governed by the Saros cycle. For more information, see Periodicity of Solar Eclipses.

which then goes on to say:

The periodicity and recurrence of eclipses is governed by the Saros cycle, a period of approximately 6,585.3 days (18 years 11 days 8 hours). It was known to the Chaldeans as a period when lunar eclipses seem to repeat themselves, but the cycle is applicable to solar eclipses as well.

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