Today is Palm Sunday, the beginning of the week that climaxes with Easter. So Easter Sunday is April 21 – a late Easter, but bot the latest it can be. In 2011 it was on April 24, in 2030 it will again be on April 21, and in 2038 it will be on April 25, really the latest possible.
See the end note about enlarging illustrations.
In this diagram, the red dots are the Full Moons that precede, and predict, the Easter Sundays.
In our Gregorian calendar, Easter Sunday can be anywhere between March 22 and April 25. The nearest April 25 years are 1943 and 2038. The nearest March 22 years are remote: 1818 and 2285.
Easter is the great “movable feast” – great, because many other dates depend on it, Shrove Tuesday, Ash Wednesday, Maundy Thursday, Good Friday, Whitsun – and movable because it depends on astronomical events that shift.
The rule is that Easter is the Sunday after the Full Moon that is next after the March equinox. Well. In 2019, the equinox was on March 20, at 22:01 Universal Time. And the Moon was Full less than 4 hours later, March 21 at 1:42 UT. That was a Thursday, so Easter should have been the next Sunday, March 24 – one of the earliest Easters!
No.
Those astronomical calculations were the kind we can make our computers do with enormous precision and complexity (there are more than 600 terms in the equations to find the position of the Moon). The Easter rule was agreed in AD 325. It assumes that the equinox is on March 21 (astronomically it can be on March 19, 20, or 21 in our Gregorian calendar). And the ecclesiastical calculation uses the Metonic cycle, an ancient Greek discovery that phases of the Moon repeat on the same dates each 19th year, almost though not quite exactly. Tables of Golden Numbers (orders in the Metonic cycle) and Epacts can be read off to give the Easter date. This process can be translated into a short set of equations to use in a program, such as mine, to give the ecclesiastical Easter date.
It agrees remarkably well with the astronomical result, but not always, and this year is one of the exceptions. The equinox, being considered to be on March 21, is on the same date as the Full Moon; so the next Full Moon is April 19, a Friday – Good Friday – and the Sunday after that is Easter.
By coincidence, the spring equinox on Mars this year is only just after Earth’s: March 22, 22 UT. Amusing, and confusing: for a few minutes, looking at my list of dates, I found myself subtracting the wrong equinox from the Full Moon.
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DIAGRAMS in these posts are made with precision but have to be inserted in another format. You may be able to enlarge them on your monitor. One way: right-click, and choose “View image”, then enlarge. Or choose “Copy image”, then put it on your desktop, then open it. On an iPad or phone, use the finger gesture that enlarges (spreading with two fingers, or tapping and dragging with three fingers). I am grateful to know of what methods work for you.
The method for reckoning the date of Easter is traditionally called the “computus”. Eastern Orthodoxy, still on the Julian calendar, has a different computus. A still different algorithm is used to determine the date of Passover, which about one year in eight doesn’t occur in the same lunar cycle as Easter.
I always thought that Easter was the first Sunday after the Easter bunny came out of his hole after hiding to hide all the eggs, The first Sunday after the first full moon after the vernal equinox, despite what Punxsutawney Phil predicted back in February. Because the full moon and equinox were so close this year made it kind of tricky, but Happy Easter to everybody.
You did not indicate on your chart to show the full moon occurring on April 19, 2019!
Yes, a slightly tangled bit of logic about which full moons to mark. I’ve now rewritten it so that if I do this graph again it will mark all full moons after the equinox or in April, with lines from them to Easter Sunday if they are before it.
There appears to be an 11 year cycle with some Easter dates, for example Mar 31 for 2002, 2013, 2024, and Apr 16 for 2006, 2017, 2028. Guy, I know you like cycles. Do you have any idea of the cause of this?
It crossed my mind to look for cycles like that, but I haven’t taken time to do so yet…
In the paragraph after No. I think you meant 20 where you wrote 19 30 21. But where (or what time zone) is the determination for full moon made?
Yes, I did mean that; typo corrected now.
About the calculation of the Moon phase, please see my reply to John Goss.
Indeed it would be interesting to know whether the pre-modern calculators regarded the day as being for the longitude of Greenwich, Paris, Rome, Jerusalem… and whether they took “March 21” as meaning the midnight at th beginning of that day. Or sunrise; or noon (0.5, 12h) as is rather awkwardly used in Julian Dates.
Excellent summary. How is “full moon” determined in the ecclesiastical calendar?
I don’t know. Below is the set of equations I referred to: that is, my Fortran subroutine for finding the ecclesiastical date of Easter, derived from Jean Meeus’s “Astronomical Algorithms”, p. 67-69, in turn based on publications going back to 1876.
The input “argument” of the subroutine is JYR, the year; the output arguments are the month and day. (I use J- to distinguish all quantities that are integers, as opposed to “real” numbers that can have fractional parts. This subroutine uses only integers. MOD means remainder after dividing.)
Of the quantities used internally by the subroutine, JA is from the Metonic cycle. The Full Moon date must be dealt with by the other operations, but Meeus doesn’t explain how. Perhaps you can see how!
I notice now that he gives a list of years in which the astronomical and ecclesiastical results differ (18 of them in 1900-2100), and it includes 1981 and 2038 but not 2019. I don’t understand this. Staring at the dates, I can see no way of not making the astronomical Easter be March 24. There could be ways to interpret the ecclesiastical rule differently (Full Moon pushed back; March 21 equinox meaning the middle of the day?), but they would make that Easter be March 24 also.
John, please tell me whether, when there is a “reply” (like this) to a comment you make, you get an email notification of it.
C Find the date (month and day) of Easter, for the year.
C Meeus, Astr.Algorithms, 67-68.
C Correct only for Gregorian calendar, i.e. 1583 onward.
C For Julian: Meeus p.69.
C JA+1 is the year’s Golden Number,
C i.e. position in the 19-year lunar cycle.
subroutine easter (jyr, jmo,jdy)
ja=mod(jyr,19)
jb=jyr/100
jc=mod(jyr,100)
jd=jb/4
je=mod(jb,4)
jf=(jb+8)/25
jg=(jb-jf+1)/3
jh=mod(19*ja+jb-jd-jg+15, 30)
ji=jc/4
jk=mod(jc,4)
jl=mod(32+2*je+2*ji-jh-jk, 7)
jm=(ja+11*jh+22*jl)/451
jn=jh+jl-7*jm+114
jmo=jn/31
jdy=mod(jn,31)+1
end
Thanks for this. As an undergrad, we were taught a method for calculating Easter.
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