Chasing the Wind

Did you know it’s always close to a full moon on Easter?

The actual determination of Easter is complex. The easiest way to remember it is the first Sunday after the first full moon after the first day of Spring. That means Easter always falls between March 22 and April 25.

It starts to get complicated when it’s not the astronomical full moon, but the eccesiastical full moon which is determined from tables – but even the calculation of the ecclesiastical full moon varies between the Gregorian calendar and the Julian calendar which primarily differ by their calculation of leap year. Western churches use the Gregorian calendar and Eastern churches use the older Julian calendar, so there are some years that Easter is celebrated at different times throughout the world.

And if *that* wasn’t confusing enough, the first day of Spring is actually the vernal equinox. Depending on which side of the international date line you live on, Easter can fall on different dates.

For example, take the year 1962. In 1962, the astronomical Full Moon occurred on March 21, UT=7h 55m – about six hours after astronomical equinox. The ecclesiastical full moon (taken from the tables), however, occured on March 20, before the fixed ecclesiastical equinox at March 21. In the astronomical case, the Full Moon followed its equinox; in the ecclesiastical case, it preceeded its equinox. Following the rules, Easter, therefore, was not until the Sunday that followed the next ecclesiastical full moon (Wednesday, April 18) making Easter Sunday, April 22.

Ow. Oh wait, I found a calculation that will help.

The rule is that Easter is the first Sunday after the first ecclesiastical full moon that occurs on or after March 21. The lunar cycles used by the ecclesiastical system are simple to program. The following algorithm will compute the date of Easter in the Gregorian Calendar system.

The algorithm uses the year, y, to give the month, m, and day, d, of Easter. The symbol * means multiply.

Please note the following: This is an integer calculation. All variables are integers and all remainders from division are dropped.

c = y / 100
n = y - 19 * ( y / 19 )
k = ( c - 17 ) / 25
i = c - c / 4 - ( c - k ) / 3 + 19 * n + 15
i = i - 30 * ( i / 30 )
i = i - ( i / 28 ) * ( 1 - ( i / 28 ) * ( 29 / ( i + 1 ) )
* ( ( 21 - n ) / 11 ) )
j = y + y / 4 + i + 2 - c + c / 4
j = j - 7 * ( j / 7 )
l = i - j
m = 3 + ( l + 40 ) / 44
d = l + 28 - 31 * ( m / 4 )


For example, using the year 2010,
y=2010,
c=2010/100=20,
n=2010 – 19 x (2010/19) = 15, [see note above regarding integer calculations]
etc. resulting in Easter on April 4, 2010.

The algorithm is due to J.-M. Oudin (1940) and is reprinted in the Explanatory Supplement to the Astronomical Almanac, ed. P. K. Seidelmann (1992). See Chapter 12, “Calendars“, by L. E. Doggett.

There. That should clear things up.

Me, I’m sticking to the “first Sunday after the first full moon after the first day of Spring” rule.