The Half-Astrophysicist Blog

The Winter Solstice Eclipse and Statistics

A lot is being made of tonight’s “rare” lunar eclipse that occurs on the Winter Solstice.  Most news reports state there hasn’t been a lunar eclipse on the solstice since 1638 to make the point that this is a rare event.

Which got me to thinking, how often would a lunar eclipse occur on any given date.  Heck, I know one has not occurred on my birthday during my lifetime.

I admittedly don’t know all the intricacies of calculating eclipse frequencies, so this is an exercise in estimation.  Eclipses can occur any month of the year as seen from this list.  Not every eclipse is total however, so let’s restrict ourselves to total lunar eclipses since that is what everyone is making such a big deal about.  They occur about every 18 months on average.  Every 100 years there are about 67 total lunar eclipses.  Let’s assume for a moment (I know this is a bad assumption) that they all occur on  different calendar date.  It would take about 550 years (well 544, but this is an estimate so close enough) for every day of the year to have on eclipse occur on that date.  In reality it will take a lot longer since many dates will have two eclipses occur on them long before the 550 years is up.  So to me, the fact that this hasn’t happened in 372 years just doesn’t seem like that big of a deal to me (although the solstice can vary couple of days adding another layer to the mix, it still seems well within statistical norms).

Now I have made some assumptions here…the most questionable of which is that eclipses are equally likely on any given day.  If this assumption is bad, it could make the winter solstice eclipse a more or less rare event…would take some number crunching to find out.  I found a cool catalog of 5000 years of eclipses from NASA but it’s not in nice form to easily analyze the dates.  However, during 5000 years, there were an average of 69.5 total solar eclipses per century, so my guess was pretty close!

So before you think this is a big deal, take ANY random date of the year and try and find when the last time an eclipse occurred on that date.  I bet it won’t be hard to find a date that has an interval greater than 372 years!  So enjoy it, but remember, statistically speaking, it sure looks like nothing out of the ordinary.

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December 20, 2010 - Posted by | lunar eclipse, Math, Moon

2 Comments »

  1. A nice example of … how pure math can lead you in wrong directions when events are NOT distributed randomly. Eclipses in particular follow several cycles, not just the Saros, and so it happens that 19 years ago and 19 years in the future we also had/will have lunar eclipses similiarly close to the moment of solstice (i.e. within 24 hours) as this year. In 1991 that eclipse was partial, but in 2029 it will be total: welcome to a replay of 2010.

    Comment by skyweek | December 21, 2010 | Reply

  2. Yes, I am aware the Saros cycles and think there are a couple of others. I stated that the assumption is probably valid, although I hadn’t done the math to prove it!

    However, my point was that it is easy to find a random calendar date that has not had an eclipse in several hundred years. A non-random distribution means that it is even easier to find dates on which eclipses have not occurred for a really long time!

    I would love to see a graph of the frequency of eclipses and day of the year…unfortunately, the data wasn’t in a form easy to import into a spreadsheet and I don’t have a grad student to enter the data for me 🙂

    Comment by halfastro | December 21, 2010 | Reply


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