Stephen P. Morse , San Francisco
1. What are the rules for calculating Easter?
Easter falls on the first Sunday following the Paschal Full Moon.
The Paschal Full Moon is the first Full Moon on or after March 21.
2. How is the Paschal Full Moon Determined?
Originally it was done by observation. Today it is defined by
an Ecclesiastical table-driven algorithm that approximates the occurrence
of the first Full Moon on or after March 21.
3. What calculations are used here for determining the Paschal Full Moon?
This website approximates the occurrence of the Paschal Full Moon using the rules of the Jewish calendar. The Jewish calendar is a solar/lunar calendar with each Jewish month starting with the New Moon and the years being synchronized with the seasons. The yearly synchronization is obtained by using a 235 month cycle since such a cycle consists of 19 Jewish years, which is very close to 19 solar years. The Ecclesiastical calculations also use the 19 year cycle, and for the same reason.
This suggests a very simple way to approximate the Paschal Full Moon. Since each Jewish month starts with the New Moon, halfway between two month-starts will be the Full Moon. So we simply need to check halfway into each Jewish month until we find the first one that occurs on or after March 21. That would be the Paschal Full Moon.
However there is a problem with the method just described. The calculations of the Jewish calendar start by computing the New Moon for each month. That is called the molad of that month. But then the actual start of the month is sometimes delayed by a day or two past the molad so that certain holidays don't fall on certain days of the week. For example, if Yom Kippur fell on a Friday, there could be no food preparation for Saturday resulting in two consecutive days of fast.
So a modified version of the above method is used. The calendar
rules for computing the molads are used, but the delay rules are not applied.
This results in each month starting precisely with the New Moon.
4. Why did you do what you did rather than using the Ecclesiastical calculations?
My goal was purely for research. I wanted to determine how close the Ecclesiastical calculations for the Paschal Full Moon compares to the same calculations made using the rules of the Jewish calendar. As you can see, they are very close. Here is a table comparing the two over a 21 year period. Note that they are identical 16 times, and the other 5 times they differ by only one day.
The secular dates shown in this table are for the Gregorian calendar.
However there will be times when the error could be a month. It happens infrequently but
it does happen. For example, in 2019 the Paschal Full Moon based on the Ecclesiastical
calculations is on April 18 whereas it is on March 21 using the Jewish Calendar calculations.
5. How does this relate to the date for Passover?
Passover always starts on the 15th day of the Jewish month of Nisan. As such, it would always be close to a Full Moon (it would be even closer to a Full Moon if not for the intentional delays added -- see question 3). Nisan usually falls around the vernal equinox and thus the Full Moon of Nisan is often the first one on or after March 21. If that happens, and if no delays were used that year, the start of Passover would come extremely close to the Paschal Full Moon. Thus it is no accident that Easter and Passover are usually very close together.
However, due to gradual creep in the Jewish calendar (see the Jewish
Calendar Creep section on the Jewish Calendar Rules
page), for very high years Passover will start to deviate significantly
from the vernal equinox. At that time, Passover and Easter will no
longer come close together.
6. What is the purpose of the Gregorian/Julian radio button?
The Gregorian calendar is the calendar in common use today. It differs from the Julian calendar which preceded it by the rule for determining leap years. Specifically, under the Julian calendar a leap year occurs in every year that is divisble by 4, whereas in the Gregorian calendar the leap year does not occur in years divisible by 100 unless they are also divisible by 400. In addition to changing the rules for leap years, the introduction of the Gregorian also caused a change in the calculation for the Paschal Full Moon.
The switch from the Julian calendar to the Gregorian calendar occurred at different times in different places, ranging from 1582 for most of Catholic Europe to 1929 in China.
The Gregorian/Julian radio button will change the calendar dates as
well as change the algorithm for computing the Paschal Full Moon.
It should be noted that you can set the button to Gregorian and enter a
year preceding 1582. In that case the dates shown are what the Gregorian
dates would have been if we extended the Gregorian Calendar back far enough.
Similarly if Julian is selected and a year is entered that is later than
1929, the dates shown are what the Julian dates would have been if we never
switched to the Gregorian calendar.
7. When I specify year 65000, why does Passover come out in 65001?
The Jewish calendar is slowly creeping through the seasons. See the section on Jewish Calendar Creep on the Jewish Calendar Rules page. The creep causes Passover to occur later and later each year and eventually come after December 31st. That first happens in the Gregorian year 59917. Beyond that, it oscillates back and forth for a few centuries, and eventually settles down to being in the next year. After another 80,000 years or so, it will slip to the second following year, etc.
Of course, in spite of the creep, I could have attempted to display the Passover that falls in the Gregorian year you specified. But that presents a problem since not every year has a Passover. Indeed there is a Passover in every Jewish year, but not necessarily in every Gregorian year. For example, Passover for the Jewish year 63676 will fall on December 12, 59916. The next Passover will be in the Jewish year 63677 and that will fall on January 1, 59918. So there will not be any Passover in the Gregorian year 59917. Furthermore, there will be two Passovers in the Gregorian year 59918 -- January 1 and December 21.
So rather than displaying the Passover in the Gregorian year you specify,
I count that number of Passovers and display the Gregorian year that it
occurs in. For example, suppose you specify the Gregorian year 2007.
Rather than displaying the Passover that occurred in the Gregorian year
2007, I display the 2007th Passover since the Gregorian year 0 (assuming
that there always were Passovers as well as Gregorian years going all the
way back). For Gregorian years below 59917, they are one and the
-- Steve Morse