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Easter Astronomy

Being neither Christian nor Pagan I’m not inclined to pay much heed to Easter (except of course for the days off work and the chocolate eggs) but it does present an opportunity to talk about a little astronomy. Did you know, for example, that the date of Easter changes each year, and that it depends on the phase of the Moon?

The Venerable Bede

The Venerable Bede, a Northumbrian Monk, wrote, in his book “The Reckoning of Time” (725CE):

“The Sunday following the full Moon which falls on or after the [Spring] equinox will give the lawful Easter”

So that all seems fairly straight forward: wait till the Spring Equinox; wait till the next full Moon; wait till the next Sunday; and voila, Easter.

However complications arise because:

(a) the ecclesiastical date of the Spring Equinox does not always match the astronomical date; and

(b) the ecclesiastical date of the Full Moon does not always match the astronomical date.

Why is this?

Put simply the ecclesiastical Spring Equinox always falls on 21 March, whereas the astronomical Spring Equinox, that is the point in the year when the Sun passes from the southern to the northern celestial sphere, can occur on 19, 20 or 21 March (and occurs most often on 20 March), and so the starting date for the computation of Easter is often out.

Also the ecclesiastical date for the Full Moon takes no real account of the actual phase of the Moon, instead it refers to the 14th day of the lunar month in which the New Moon occurs between 8 March and 5 April, which can differ from the date of the Full Moon by up to three days. This is referred to as the Paschal Lunar Month, the word “Paschal” deriving from the Hebrew word for Passover, a Jewish festival commemorating the Exodus.

The table below shows how these two dates vary over the next decade, and how that effects the date of Easter.

 Year (A)
Date of Ecclesiastical Spring Equinox
(B)
Date of Astronomical Spring Equinox *
(C)
Date of Paschal Full Moon on or after A **
(D)
Date of Astronomical Full Moon on or after B
Date of Sunday on or after C (Easter) Date of Sunday on or after D
(Astronomical Easter)
 2011  21 March  20 March  18 April  18 April  24 April  24 April
 2012  21 March  20 March  8 April  6 April  8 April  8 April
 2013  21 March  20 March  30 March  27 March  31 March  31 March
 2014  21 March  20 March  15 April  15 April  20 April  20 April
 2015  21 March  20 March  4 April  4 April  5 April  5 April
 2016  21 March  20 March  24 March  23 March  27 March  27 March
 2017  21 March  20 March  12 April  11 April  16 April  16 April
 2018  21 March  20 March  1 April  31 March  1 April  1 April
 2019  21 March  20 March  19 April  21 March  21 April  24 March
 2020  21 March  20 March  9 April  8 April  12 April  12 April

* Despite these dates being all the same, the date of the astronomical Vernal Equinox can vary between 19, 20 and 21 March, but occurs most often on 20 March. Over the next 100 years it will fall on 19 March only 4 times, and on 21 March only 20 times.

** The dates of the Lunar Months (there are 13 Lunar Months in one Solar Year) repeat on a 19 year cycle, called the Metonic Cycle. 2011 in the 17th year in that cycle; in 2014 we’re back to year 1. The dates for the Paschal New Moon can be found in calculation tables.

So you can see that, despite the fact that the Ecclesiastical Spring Equinox date doesn’t match the Astronomical Spring Equinox date on any year over the next decade (and only matches it in 20 out of the next 100 years), plus the fact that the date of the Paschal Full Moon often doesn’t match the date of the astronomical Full Moon, the dates of Easter calculated using the Ecclesiastical and the Astronomical methods only differ on one year in the next decade – 2019CE, when those who are so inclined will celebrate Easter on 21 April, but when, according to Bede, the Sunday after the full Moon after the equinox actually occurs on 24 March!

Maybe I’ve got too much time on my hands…

[Please note that throughout this post I have calculated and referred to the dates of Gregorian Easter, that celebrated by the western Christian churches. Eastern Orthodox Christians calculate Easter using the Julian calendar, which is currently 13 days ahead of the Gregorian calendar, i.e. on 21 March (the Spring Equinox) the Gregorian calendar reads 3 April.]

  1. Mockingbird
    July 7, 2011 at 06:18

    The site you linked to, showing the ecclesiastical new moons, is correct, but your computations of the ecclesiastical full moons are in error. Here is a corrected list of PFMs:

    2011 April 17
    2012 April 7
    2013 March 27
    2014 April 14
    2015 April 3
    2016 March 23
    2017 April 11
    2018 March 31
    2019 April 18
    2020 April 8

    As you can see the PFM is normally within a day of the astronomical full moon referred to universal time. It is an average moon, but the average it is based on is reasonably accurate.

    • July 7, 2011 at 07:13

      Thanks for your comment, but my understanding of the Ecclesiastical Full Moon is that it is by definition 14 days after the Ecclesiastical New Moon, which is how I calculated column C above. I’d happily stand corrected if you can tell me why this isn’t the case, and how you calculated your dates.

  2. Mockingbird
    July 8, 2011 at 03:50

    The ecclesiastical new moon does not correspond to the day of the conjunction. It is formally the day that the new waxing crescent first becomes visible. (In the case of the northern hemisphere’s paschal crescent, because of the configuration of the ecliptic and the equator when sun and moon are near the vernal equinox, the new paschal crescent is in fact often visible on the evening before the tabulated day, right on schedule.) In other words, it is the first day of the new lunar month, so that the 14th day is obtained by adding 13, not 14, to the date of the ecclesiastical new moon.

    Your dates, except for 2013, are correct for the 15th day of the Easter-month, and your next-to-last column correctly states that Easter will be the Sunday on or after the 15th of the moon. But this contradicts the wording at the head of column C, which describes the 14th, not the 15th. For the 14th may fall on March 21st or after it, but the 15th must fall after it, never on it. And your use of the 15th as the “full moon” in column C is inconsistent with your (traditionally correct) identification of the 14th as the paschal full moon in the preceding text.

  3. April 18, 2014 at 07:53

    You both have too much time on your hands, interesting though. I’d prefer it if they’d decide on a suitable day and stick to it, like Christmas.

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