## Saturday, April 23, 2011

### How is the date of Easter determined?

Many people, if they know at all, believe that Easter falls on the Sunday after the first full Moon following the Vernal Equinox. That's what I used to think myself.  The details, however, are a bit more complicated and, as we'll see, the Church doesn't calculate the date of Easter the way an astronomer would.

As I've written before, the Vernal Equinox is the half-way point between the Winter Solstice and the Summer Solstice - the times when the Earth's Northern Hemisphere has its maximum tilt away from or toward the Sun.

So the Equinox is when the Earth's axis of rotation is neither tilted toward nor away from the Sun - technically that occurs where the plane of the ecliptic passes through the celestial equator at a right ascension of zero hours (don't worry if you don't understand this).

From the perspective of us on Earth, the Vernal Equinox is when the Sun passes over the Equator (in the winter, the Sun is over the Southern Hemisphere, in summer, over the Northern).  The Vernal Equinox generally occurs around March 20 (although not always because our civil Gergorian calendar does not perfectly align with astronomical events).

For the 1,000 year span of time from 1500 to 2499 CE, the date of the Vernal Equinox in Universal Time (UTC) has the following distribution on the Gregorian Calendar (yes, I know the Gregorian calendar wasn't invented until 1582, but we need to make this assumption to compare dates):

March 19 =   7.1%
March 20 = 66.4%
March 21 = 26.5%

An astronomer calculating the date of Easter would use the actual date and time of the Vernal Equinox which, between 1500 and 2499 CE, ranges from 12:28 UTC on March 19, 2496 to 20:42 UTC on March 21, 1503 (I think it's just a coincidence that the earliest date of the Vernal Equinox is near the end of my 1,000 year range and the latest date is near the beginning!).

Since Easter commemorates an event which occurred in Jerusalem, I suppose one could use the precise time of Easter in that time zone which is 3 hours ahead of the UTC time (doing so would shift 122 of the dates to the next day giving 4.0% on March 19, 60.4% on March 20, and 35.6% on March 21).

Full Moon over Jerusalem

What about the date of the first full Moon after the Vernal Equinox?  Astronomers can calculate this very accurately as well.  This year, for example, the Vernal Equinox fell on Sunday, March 20 at 23:21 UTC.  Full Moons this year fell on Saturday, March 19 at 18:10 UTC and Monday, April 18 at 02:44 UTC.  As you can see, the March full Moon was just a hair early so Easter had to fall on the Sunday after the April full Moon which is April 24 (the latest possible date of Easter, by the way, is April 25).

Let's look at another example, however.  In 1962, the Vernal Equinox occurred on Wednesday, March 21 at 02:30 UTC.  The full Moon occurred on the same date at exactly 07:56 UTC.  That was the first full Moon after the Vernal Equinox.  Easter should have been the following Sunday, March 25.  Instead Easter fell on April 22 that year, two days after the next full Moon on April 20.  Why?

It has to do with how Protestant and Roman Catholic churches calculate the date of Easter (Eastern Orthodox churches do things differently to further complicate the issue).  The ecclesiastical rules for calculating Easter are as follows:

1.  Easter falls on the first Sunday following the first ecclesiastical full Moon that occurs on or after the day of the vernal equinox;

2.  this ecclesiastical full Moon is the 14th day of a tabular lunation (days since the new Moon); and

3.  the Vernal Equinox is fixed as March 21.

This results in Easter never occurring before March 22 or later than April 25.

So, even though the Vernal Equinox can occur on March 19, 20, or 21, the church fixes it on March 21 (the date it occurs only 36% of the time in Jerusalem as we've seen).   Also, what's up with the phrase "ecclesiastical full Moon" seen in the definition?  How's that different from an ordinary full Moon?

The ecclesiastical full Moon is also called the Paschal Full Moon after the Hebrew pesach or Passover.  The date of Easter was first officially set for the Church by rules developed in 325 CE at the First Council of Nicaea convened by the Emperor Constantine. This was based on the Julian calendar.  When Pope Gregory XIII developed the modern-day Gregorian calendar in 1582, however, the rules for determining the date of Easter were also updated with the new calendar system.

Basically, tables were drawn up dividing 19 calendar years into 235 lunar months of 29 and 30 days each (the cycle of lunar phases is 29.531 days).  This is based on an ancient cycle known as the Metonic Cycle after Meton of Athens (although the ancient Babylonians knew of it as well).  The dates of the full Moon on these tables is as much as 2 days off from the date of the full Moon in the sky since it's an approximation.

Here are the dates for the Paschal Full Moon as computed for the present 19-year Metonic cycle compared to the astronomical dates of the full Moon.  Note that they don't always correspond.

So the date of Easter is set by two approximations - the Vernal Equinox is artificially set to March 21 and the full Moon date is determined by tables calculated by a procedure dating back to ancient times!  There are some algorithms (see here and scroll down) to calculate this if you're interested (it's a relatively easy programming task with a computer).

Eastern Orthodox churches calculate Easter much in the same way but they use the Julian calendar which the rest of the world abandoned hundreds of years ago since it doesn't do leap year calculations accurately and is thus quite a bit off from our modern calendar.

The funny thing about all of this is that there's no compelling theological reason for the complexity of Easter other than Church tradition.  There have been a number of reforms suggested over the years (e.g. celebrate Easter on the second Sunday in April) but given the number of different denominations involved, it's doubtful any of them could agree on the color of the sky, let alone the date of their most sacred holiday.

#### 1 comment:

1. It really doesn't matter because the point of Easter is to celebrate the life, death, and resurrection of Jesus Christ, not to calculate the exact day. Just like our Christmas isn't the exact day of birth of Christ.