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There are dozens of places where you can see how often total eclipses occur at the same location on average. My question is, how often do eclipses occur at any given place, if we include partial eclipses (but not penumbral lunar eclipses)? Which includes:

  • What is the average time between two solar eclipses of any type (at a given place)?
  • What is the most time between two solar eclipses of any type?
  • What is the average time between two lunar eclipses including partial eclipses?
  • What is the most time between two lunar eclipses including partial eclipses?

And even when it comes to total eclipses, no one bothered to talk about the extremes. So

  • What is the most time between two total lunar eclipses?
  • What is the most time between two total solar eclipses?

OK, for this one I guess the answer isn't available, see Counting from the 21st century forward, what place on Earth will be last to experience a total solar eclipse?.

The reason I'm not asking about the least time between eclipses is, that after a quick look on eclipse lists it's obvious that any kind of eclipse(not taking in account penumbral lunar eclipses) can repeat after six months.

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  • $\begingroup$ I don't have much of a reference, but a slide deck I have says it's about once every 400 years. $\endgroup$
    – Greg Miller
    Commented Dec 9, 2023 at 3:17
  • $\begingroup$ @GregMiller Not clear to what you refer. $\endgroup$
    – George Lee
    Commented Dec 10, 2023 at 15:33

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Jean Meeus, in his excellent Mathematical Astronomy Morsels, p. 91, says:

We then, finally, obtain the following mean frequencies for any given point at the Earth’s surface:
  a total eclipse once in 375 years,
  an annular eclipse once in 224 years,
which, by combination, gives an annular or a total eclipse every 140 years for a place chosen at random. Because our results are based on a sample of observable eclipse, they are subject to uncertainty of about 16 years’ standard error for total eclipses, 7 years for annular, and 4 years for both. Further error may arise because of the limited number of points on the Earth’s surface used in the analysis.

(emphasis in original)

He also points out that this is an average and that some places sometimes get to see two eclipses in a much shorter time (barely more than 9 years between the eclipses of May 2142 and June 2151 for Antwerp [Belgium]).

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    $\begingroup$ Including Lunar and partial eclipsies would make this much less, I'd guess that the total eclipse are just a rounding error compared to the frequency of partial solar and lunar eclipies. $\endgroup$
    – James K
    Commented Dec 9, 2023 at 13:50
  • $\begingroup$ Including lunar eclipses, we get approximately one eclipse every two or three years, if I remember correctly. $\endgroup$
    – Pierre Paquette
    Commented Dec 9, 2023 at 14:11
  • $\begingroup$ My question was what is if we include partial eclipses, not just annular (But I didn't asked to include solar and lunar eclipses in the same calculation). $\endgroup$
    – George Lee
    Commented Dec 10, 2023 at 15:38
  • $\begingroup$ As for the shortest time between two total/annular eclipses, it's 6 months, as I stated in my question, see texashighways.com/travel/…. But I'm not sure if this still holds if we exclude annular eclipses. $\endgroup$
    – George Lee
    Commented Dec 10, 2023 at 15:44

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