Friday, 29 March 2013

Why Is Easter In March?

A couple of evenings this week, those nice people at South West Trains cancelled the last train from Andover to Basingstoke, and put on every commuters' ultimate nightmare - the rail replacement bus service. Which stank. I think just beforehand it had been used to host a chainsmokers' convention.

Hence, I get to Basingstoke at 1/4 to midnight, hang around for a slow train to Southampton Central, get in about 20 to 1, no buses that late, and walk home.

Wednesday morning I was hurrying home and it was quite cloudy, with a full moon shining through a gap in the cloud.This wasn't any old full moon - this was the Paschal Full Moon, the first one of spring.

In an earlier post (keep it open in a new tab or window as I will refer to it later) I mentioned the calendar reform by Ugo Boncompagni which gave us the Gregorian calendar we all know and love today.

For the Roman Catholic Church it was/is important that Easter was celebrated on the right day.

In my previous post I looked at the different types of lunar months, and the important one for this is the synodic month of 29.530589 days.

The average year length in the Gregorian calendar is 365.2425 days. 19 years will be 6,939.6075 days on average. It depends how many leap years there are in those 19 years - there will be 4 or 5, so 19 years will be 6,939 or 6,940.

235 synodic months is 6,939.688415 days - very close to 19 years. So, if you have a full moon (or perhaps, the Paschal Full Moon) on a day one year, it is likely to be on the same day 19 years later. This is called the Metonic cycle.

The Jewish calendar is a luni-solar one, with most years having 12 months, but 7 out of every 19 having 13 months. Hence 235 months every 19 years.

If you have a copy of the 1662 Book of Common Prayer there will be tables about using the Golden Number to calculate Easter. The Golden Number is found by:

  • Take the year (2013)
  • Add 1 to it (2014)
  • Divide by 19 (106, remainder 0)
  • The Golden Number is the remainder - if the remainder is 0, then the Golden Number is 19.
  • So, this year has a Golden Number of 19. One table will give the Paschal Full Moon for each number (really an ecclesiastical Paschal Full Moon, as the real one could be a day different due to leap years). And we see the date given as 27 March - with Easter being the following Sunday (31 March).

    12 synodic months is 354.367068 days, so if you have a full moon on one date one year, you should expect one about 11 days earlier the following year (if you onserve meteor showers, then it is best for the peak to be near new moon - useful advice I got once is that if a new moon is on a particular date one year, it should be on a near-enough date 3 years later). So, we should expect the Paschal Full Moon to be about 11 days earlier from year-to-year, so Easter should be about a week (or maybe a fortnight) earlier each year.

    Except when you have an earlyish Paschal Full Moon, 13 synodic months is 383.897657 days, so you should then expect the Paschal Full Moon to jump about 19 days later the following year.

    A Golden Number of 1 gives the Paschal Full Moon (ecclesiastical) as 14 April. This is a Monday, so Easter is the following Sunday - 20 April.

    Actually, the real Full Moon is on 15 April, when there is a total lunar eclipse.

    What was the problem that Boncompagni wanted to sort out?

    The British Empire didn't switch from the Julian calendar to the Gregorian until 1782, and there is a dating convention of writing [OS] for "old style" for Julian calendar dates and [NS] for "new style" for Gregorian calendar dates.

    The vernal equinox is often on 7 March[OS]/20 March[NS]. This year the full moon was 14 March[OS]/27 March[NS]. And this highlights what the problem was.

    Under the Julian calendar, with an ecclesiastical vernal equinox remaining 21 March, this week's full moon was still a winter one.

    The next full moon is 12 April[OS]/25 April[NS] - and under the old calendar this would be the Paschal one, the first of spring. And Easter would be 15 April[OS]/28 April [NS].

    Hence, Boncompagni's problem that people could be celebrating Easter incorrectly as the Sunday after the second full moon of spring.

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