<p>From the same <a href="https://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html" rel="nofollow noreferrer">NASA page</a>:</p>

<blockquote>
  <p>The recurrence of solar eclipses is governed by the <a href="https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html" rel="nofollow noreferrer">Saros</a> cycle. For more information, see <a href="https://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html" rel="nofollow noreferrer">Periodicity of Solar Eclipses</a>.</p>
</blockquote>

<p>which then goes on to say:</p>

<blockquote>
  <p>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.</p>
</blockquote>

CC BY-SA 4.0
2018-07-19T10:32:43.397Z
2018-07-19T10:32:43.397Z
Mick
<p>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)</p>

<p><a href="https://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html" rel="nofollow noreferrer">NASA has published the list of the count of solar eclipses</a> (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:</p>

<p><strong>Hypothesis</strong>: </p>

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

<p><strong>Question</strong>: 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.</p>

CC BY-SA 4.0
2018-07-19T10:24:06.443Z
Are you familiar with the Saros Cycle?
Dr Chuck
CC BY-SA 4.0
2018-07-19T10:33:00.617Z
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?
Mick
CC BY-SA 4.0
2018-07-19T11:50:28.887Z
Crossposted from https://physics.stackexchange.com/q/418408/2451
Qmechanic
<the-sun><orbit><solar-eclipse>
The total number of solar eclipses in a century repeats roughly every 6th century
Nilotpal Kanti Sinha
# The total number of solar eclipses in a century repeats roughly every 6th century

(Asked by: username_0 on 2018-07-19)

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](https://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html) (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.

**Tags:** the-sun, orbit, solar-eclipse

> **Comments:**
> **username_1**: Are you familiar with the Saros Cycle?  
> **username_2**: 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?  
> **username_3**: Crossposted from https://physics.stackexchange.com/q/418408/2451  

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## 1 answers

### Answer by username_2 on 2018-07-19. Score: 2

From the same [NASA page](https://eclipse.gsfc.nasa.gov/SEcat5/SEcatalog.html):

> The recurrence of solar eclipses is governed by the [Saros](https://eclipse.gsfc.nasa.gov/SEsaros/SEsaros.html) cycle. For more information, see [Periodicity of Solar Eclipses](https://eclipse.gsfc.nasa.gov/SEsaros/SEperiodicity.html).

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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