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Posts Tagged ‘Metonic cycle’

The Moon and Easter

Tuesday, March 23rd, 2010

… or, “How to Make a Simple Definition Really Complicated”

Today I was chatting with a friend of mine about when Easter is this year, and he cited the well-known (and incorrect) formula: “Easter is the first Sunday after the first full moon after the spring equinox.”

Although this is a pretty good approximation, and it is correct most years, the actual calculation of Easter is surprisingly complicated. The correct definition is that Easter occurs on the first Sunday after the paschal full moon. This is an artificially calculated date that actually does not correspond to any astronomical event. The best description of the paschal full moon is that it is pretty close to a full moon that is usually the first one after the spring equinox!

How did we get into this mess? Why don’t we just celebrate Easter on the same every day each year, as we do with Christmas? And why does the moon have anything to do with it? That is actually a pretty good story that goes way back in time … back before Christ was even born.

[By the way, let me interject that I am not a practicing member of any religious faith. My main reason for being interested in the date of Easter is that I am interested in the ways in which the moon affects our culture. If you are bothered by sentences like "Christ was born," you should mentally add, "according to the Christian religion."]

Let’s start with what the Bible says about Christ’s death. Depending on the book you read, he was either crucified on the date of the Jewish Passover, or the following day. In any case, his resurrection occurred on the Sunday after Passover. Hence, in the early years of Christianity, the practice was to observe Easter on that day.

But determining the date of Passover is itself no easy matter, and that is where the moon comes in. The Jews, like many other ancient civilizations (such as the Babylonians, from whom they borrowed their month names), used a combination lunar-solar calendar. These calendars have the advantage that the new moon always falls on the same day each month; day 1 is the first day after the new moon, and day 14 is (usually) the day of the full moon. Passover was defined as the 14th day of the month of Nisan.

The mischief starts because the lunar cycle is not synchronized to the solar cycle; 365 days is a little bit more than 12 lunar cycles. So if you want the same months to occur at the same time each year (as the Jews did; Nisan was supposed to be the first month of spring, when the barley ripens), you need to insert extra months now and then. In order to prevent your calendar from becoming completely chaotic, it’s nice to have a rule for when to do it.

Fortunately, the lunar and solar cycles do match up very closely every 19 years. Earth takes 19 trips around the sun in almost exactly the time that the moon takes 235 trips around Earth. (The difference is about two hours.) This means that your lunisolar calendar needs to have 12 normal years of 12 months, and 7 long years of 13 months, in each 19-year cycle. (12 x 12 + 7 x 13 = 144 + 91 = 235.) This fact was discovered by the ancient Babylonians and the ancient Greeks; the 19-year cycle is called the Metonic cycle after Meton of Athens. In the Hebrew calendar, it became a standard practice to have long years in years 3, 6, 8, 11, 14, 17, and 19 of the cycle.

This procedure kept the month of Nisan in the spring, where it was supposed to be. However, the Hebrews fiddled with their calendar quite a bit over the centuries; in the early days, the month of Nisan was often determined simply by observing when the barley ripened (a non-astronomical definition if there ever was one!). A controversy arose among early Christians over the facts that (a) the methods used for determining Passover had changed over the years, and (b) in some versions, Passover could occur before the spring equinox. The Nicean council in 325 AD resolved the controversy by adopting the definition that my friend (remember him? See the first paragraph) learned in school.

But that isn’t the end of the story! They didn’t have high-tech computers back then, so Christians continued to use the Metonic cycle of 19 years to compute when full moons would occur. Not only that, they used March 21 as the date of the equinox, which is not always astronomically correct. (For example, this year the equinox fell on March 20.) In other words, they tied the definition of Easter to an approximation of when the full moon occurs and an approximation of when the equinox occurs. This double approximation can result in a date for Easter that is completely different from “astronomical Easter.” The discrepancy arises, in particular, when the full moon occurs very close to the equinox. For example, in 2019 there will be a full moon on March 21, which is not “after the equinox” according to the church but is “after the equinox” according to Earth and the sun. The official paschal full moon that year will be April 20, not March 21, and Easter will be celebrated on April 21 instead of March 24.

But hold on! There are even more complications to the story! Notice that the church defines the spring equinox as occurring on March 21. But which calendar are you using? The Catholic church, and most Western churches, uses the Gregorian calendar, which first went into effect in 1583. However, the Orthodox Christian church uses the Julian calendar, which differs from the Gregorian calendar by 13 days. Why do they do that? Well, because they’re orthodox. Remember that one of the points of the Nicean council was to base Easter on the way that Passover used to be determined in the time of Christ, not the way it is determined now. Similarly, if we’re using a purely solar calendar to determine the equinox, then we should use the solar calendar that was in use during Christ’s lifetime and during the Nicean council — the Julian calendar, not the Gregorian one. That’s what orthodoxy means. You don’t let things like contemporary customs or the contemporary state of science keep you from doing things the right way, i.e., the way that they have always been done.

Thus, Orthodox Easter (or Pascha) frequently differs from the Roman Catholic Easter. This year, and next year, they are the same. But in 2012 Orthodox Easter will be one week later, and in 2013 it will be a whopping five weeks later (on May 5 instead of March 31).

Interestingly, there has been a move afoot in recent years to bring the Western and Eastern customs into alignment. The problem is especially acute in parts of the world (e.g., the Middle East) where Christianity is not the majority religion and where there are also different forms of Christianity in close proximity. The World Council of Churches has proposed what seems like a sensible compromise: to stick to the Nicean definition of Easter, using the true astronomical full moon and the true astronomical equinox. In other words, to adopt the definition that my friend told me. The nice thing about this definition is that nobody has to learn anything new! And it’s not a complete win for either side. The Orthodox churches would have to change more, but the Catholic church would have to change, too (for example, in the year 2019, as explained above).

However, disputes over matters of faith take a long, long time to resolve, and so I don’t expect to see this one resolved any time soon. I expect that Catholic Easter, Orthodox Easter, and astronomical Easter will remain three different things.

But finally, getting back to the question, “What does the moon have to do with Easter?” I thought the following sentence from the World Council of Churches document answered it very nicely:

“Easter/Pascha has a cosmic dimension. Through Christ’s resurrection, the sun, the moon, and all the elements are restored to their primordial capacity for declaring God’s glory. … Easter/Pascha reveals the close link between creation and redemption, as inseparable aspects of God’s revelation. The Nicene principles for calculating the date of Easter/Pascha, based as they are on the cycles of the sun and moon, reflect this cosmic dimension much more fully than a fixed-date system.”

I hope I have managed not to offend anybody; if you are interested, here are some other sites that discuss the timing of Easter.

Wikipedia is, of course, always a good starting point. This entry on the computus gives you way more information than I have done here. This entry on the paschal full moon is short and to the point.

The World Council of Churches paper, from 1997, is here.

Apparently they’re still talking about it. Here is a pastor’s blog that says (as of 2009) they are getting closer to an agreement.

Here is a page that explains the computation in terms of a formula. Note the prominent appearance of the numbers 19 (the length of the Metonic cycle), 7 (the number of days in a week), 4 (adjusting for leap years?) and 100 (adjusting for the Gregorian calendar). And note a couple of bizarre fudge steps that have no readily apparent explanation.

I find this explanation in tabular format to be much easier to follow. Note that within any given century, the date of the paschal full moon is completely determined by the Metonic cycle.

And what if you just want to know, “When is Easter in 2010?” The answer is that the actual full moon and the paschal full moon are on March 30, and Easter is on April 4.

Tags: 19, Easter, equinox, full moon, Metonic cycle, misconceptions, paschal, Passover, religion
Posted in Just for Fun, Popular culture, Science | No Comments »

New Year, Halos and Blue Moons

Sunday, January 3rd, 2010

A lunar halo.

Here in Santa Cruz, New Year’s Eve brought an unusual coincidence of two astronomical events. One of them was a worldwide event: It was the second full moon of the month, or a “blue moon.”

The usage of the term “blue moon” to mean the second full moon in a calendar month actually stems from a mistake in Sky and Telescope magazine in March 1946! This article on Sky and Telescope‘s website explains how the confusion arose. However, as the authors note, the new definition is “like a genie that cannot be forced back in the bottle.”

How often do blue moons occur? That is a very interesting question that you can figure out for yourself if you look at the chart on the bottom of page 2 of the article. The chart reveals an interesting fact that the authors do not mention: blue moons happen on a 19-year cycle.

To see this, notice that 1999 began with blue moons in January and March. Nineteen years later, the year 2018 will begin in exactly the same way. Why is that? Well, 19 is sort of a magic number for moon-lovers. It turns out that 19 solar years are almost exactly equal to 235 lunations. (A “lunation” is the time between one full moon and the next.) So that means if you have a full moon on December 31 this year, you will most likely again have a full moon on December 31 nineteen years from now.

There are only two things that can mess up this pattern. First of all, there is a tiny 2-hour discrepancy between 19 solar years and 235 lunar months, which eventually (over a period of twelve 19-year cycles) will move the full moon forward a day. The other discrepancy results from Leap Day. If you look again at the Sky and Telescope diagram, you’ll see that the blue moon of 2001 (in November) does not match the blue moon of 2020 (in October). According to our 19-year rule, they should be in the same month each year, but the blue moon in 2020 gets pushed forward a month because of the extra day that is inserted in February that year.

This 19-year cycle was very important in ancient times, because many cultures used both a lunar and a solar calendar. To bring the two into rough correspondence, you need 7 intercalated or “extra” months every 19 years. (That is, in 19 years there are 19 x 12 “regular” months, plus 7 “extra” months, for a total of 235.) The rule was discovered by Meton of Athens in 432 BC, and is therefore known as the Metonic cycle.

Unlike the Athenians, we use a purely solar calendar. The “months” in our calendar are no longer lunations; they are merely convenient fictions. For that reason, also, the Metonic cycle no longer has any direct effect on your life — unless you happen to be the kind of person who pays attention to blue moons!

By the way, there is one other intriguing thing about that Sky and Telescope chart. I have said that there are 7 “extra” full moons every 19 years, and so you would think there would also be 7 blue moons. But actually, that isn’t quite correct! If you look at the chart, you will count 8 blue moons from 1999 through 2017! Where did the extra one come from?

The problem is, once again, February. In 1999 there were no full moons at all in February, and therefore we had two in March as well as two in January. Thus, from 1999 through 2017 (the current Metonic cycle) we will have 8 months with an “extra” full moon and one month (February 1999) with none. In other words, we will have a NET of 7 “extra” full moons, just as we are supposed to.

**************

As I mentioned, there was other wonderful astronomical phenomenon on New Year’s Eve. This one was local, rather than global. When I went outside at ten minutes before midnight, I was stunned to see a beautiful, huge halo around the moon — just like the one in the photo at the beginning of this post. (By the way, that is not my photo. It was taken by an Aussie photographer named Anthony James, who kindly gave me permission to post it in my blog. Click here to see his Flickr page, which specializes in beautiful nighttime imagery.)

A lunar halo is much easier to understand than a blue moon. It is formed in the same way as a rainbow, by the refraction of light off of ice crystals or drops of water in the atmosphere. That night was very misty and cloudy here in Santa Cruz. In fact, according to the newspaper, we weren’t supposed to be able to see the moon at all that night. However, by 11:50 PM enough of the haze had evaporated that the moon was very clearly visible. However, there were no stars — it was as if everything in the sky had been turned off except this enormous eye looking back down at me.

That’s really what it looked like — an eye, or the photographic negative of one. The lunar halo looks like the iris and the moon looks like the pupil (white, instead of black!). I think that Anthony’s picture gives you some idea of the effect.

What an incredible night–a blue moon, an eye in the sky, and the beginning of the year, all at once! I’m certain that combination will never happen again in my lifetime.

Tags: eye in the sky, Flickr, lunar calendar, Metonic cycle, Sky and Telescope, solar calendar
Posted in Just for Fun, Popular culture, Science | 2 Comments »

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