When is Easter Anyway?


Easter date worksheet

In January, I have posted my investigation of the difference between the dates of Christmas celebration in western and eastern Christianity.  If you think, that was confusing, hold on.

The short answer to the question “when is Easter?” is straightforward.

Easter Sunday is the first Sunday after the first full moon on or after vernal equinox. — www.timeanddate.com

This has to do with the Jewish Passover holiday which is based on the Hebrew moon calendar.

Let’s use this definition.  The equinox is on March 20th.  It’s an astronomical event with a fixed (or almost fixed) date.  The next full moon after March 20th in 2015 is on Saturday, April 4th.  Therefore, in 2015, the Easter Sunday is on April 5th.  Easy.  Right?  Why then Eastern Orthodox Christians celebrate Easter on Sunday, April 12th in 2015?

It was an interesting quest for me to figure this out.  As I mentioned in my post about Christmas dates, Eastern Orthodox Church uses Julian calendar for its celebrations.  Gregorian calendar is 13 days ahead of the Julian calendar (at least, until 2099).   My first thought was that Julian equinox is 13 days after the Gregorian equinox, on April 2.  But that’s not true.  In Julian calendar, the date of equinox is set to March 25th which is April 7th in Gregorian calendar.  Then I thought, to get the Orthodox Easter date, I need to find the full moon date after April 7th which is May 3rd, 2015.  Apparently, that doesn’t work because Orthodox Easter is on April 12th in 2015.  What’s wrong?

It turns out that the Orthodox Church uses ecclesiastical full moon to calculate the Easter date, not the astronomical full moon.  Ecclesiastical full moon used to determine the Easter date is called paschal full moon.  The paschal full moon is calculated based on golden number:

Golden Number = (year mod 19)+1 — www.webexhibits.org

The number 19 has to do with Metonic cycle: the dates of Lunar phases repeat every 19 years.  The Julian date for the paschal moon is simply tabulated.  It turns out, the equinox date is not used for this calculation at all (or, rather, the equinox date is accounted for in the table).

Golden number Full moon Golden number Full moon Golden number Full moon
1 5-Apr 8 18-Apr 15 1-Apr
2 25-Mar 9 7-Apr 16 21-Mar
3 13-Apr 10 27-Mar 17 9-Apr
4 2-Apr 11 15-Apr 18 29-Mar
5 22-Mar 12 4-Apr 19 17-Apr
6 10-Apr 13 24-Mar
7 30-Mar 14 12-Apr

www.webexhibits.org

Let’s try this for 2015.  2015 modulo 19 = 1.  In 2015, golden number is 2.  Julian paschal moon date is March 25th, which is April 7th in Gregorian calendar, and the first Sunday after April 7th is April 12th.  As you see, the paschal moon date April 7th calculated using the golden number table is 3 days after the astronomical full moon on April 4th.

For 2016: Golden number is 3, Julian paschal moon date is April 13th, which is April 26th in Gregorian calendar, and the first Sunday after April 26th 2016 is May 1st 2016 which is correct.

In 2016, Orthodox Easter is more than a month after the western Easter which is on March 27, 2016.  Let’s check this, by the way. Full moon after March 20, 2016 is Wednesday, March 23rd, 2016, so, first Sunday after that is March 27, 2016.  Good.

In 2014, Orthodox and western Easter dates both fall on April 20th.  Let’s check again.

Orthodox: golden number is 2014  modulo 19 = 0.  Golden number is 1.  Julian paschal moon date is April 5th, 2014 which is Friday, April 18th, 2014 in Gregorian calendar.  The Sunday after that is April 20th.  Western: full moon after March 20, 2014 is Tuesday, April 15th, 2014, and the first Sunday after that is, again, April 20th.

Finally, it seems that I got it right.  I think, it’s easier than the tax return, after all.

For the geeks, here is the “full monty”: http://en.wikipedia.org/wiki/Computus

Merry Christmas! Again?


You may think that Christmas season is finished.  Not so fast.  January 7 is the Christmas day by the Eastern Orthodox Church calendar, so this is the high time for Christmas celebrations in Eastern Europe — Russia and Ukraine, in particular.  Ever wondered why?  Read on.

The story begins with the Solar System.  Most people know that Earth year is approximately 365 days.  By the age of 4 or 8 years, most people learn that the year is approximately 1/4 day longer than 365 years.  The accrued extra day is added as Februrary 29th every 4 years.  The “long” year is called leap year. Almost every year that can be divided by 4 is a leap year. The calendar accounting for the extra day every 4 years was introduced by Julius Caesar in 46 BC and is, therefore, called Julian.

By the age of 100 or 200, most people learn that the year is approximately 0.008 days shorter than 365 and 1/4.  The accrued missing day is taken away by skipping 3 leap years every 400 years.  Each year that can be divided by 100 is not a leap year unless it can also be divided by 400.  Years 1900 and1800 are not leap years. Year 2000 is a leap year. Of course, most people do not live to the age of 100 or 200 and never learn that most centennial years are not leap.  The calendar accounting for the missing leap years was introduced by Pope Gregory XIII in 1582 and is, therefore, called Gregorian.  They do have to know a thing or two about science, those Popes.

The “approximately” does not end there.  Of course, there are more decimal places in the length of the year calling for more adjustments, but most of the people do not live long enough to notice.

By 1582, the 0.008 days every year have accrued 11 days.  Gregorian calendar corrected Julian calendar by skipping 11 days in October 1582:

Calendar for October 1582 (Spain)

Atheists are not the only people who think that Pope is no authority to them.  Protestants and Americans have not adopted Gregorian calendar until September 1752.  By the time they decided to switch, they had to skip 12 days:

Calendar for September 1752 (United States)

(as if there were United States in 1752).  When I learned UNIX commands in college, I was surprised to find out that UNIX “cal 1752” command produces this:

Screenshot from 2015-01-06 13:34:10
Output of “cal 1752” Linux shell command.

You may be surprised to learn that Eastern Orthodox Church is still using Julian calendar for its holidays!  Now, the difference is 13 days!  So, Orthodox Christmas is on December 25, except that December 25 “old style” falls on January 7 “new style”.  For the same reason, the anniversary of The Great October Socialist Revolutiona major holiday in the Soviet Union, was celebrated on November 7.  When the revolution happened, it was October 25th, but when the Soviet Union converted to Gregorian calendar in 1929, the date moved to November 7th. Julian calendar was still in use until 1930 in the Soviet Union.  In year 2100, another leap year will be skipped adding to the schism separating Eastern Orthodox Christians from the rest of the world.  Starting from year 2101, Orthodox Christmas will move forward another day — to January 8th.  I wonder, how well this change will be received.

In case you wonder, yes, they celebrate the New Year “old style” on January 14 in Eastern Europe.  It’s called “the old new year“.