Determining The Date of Easter
The calendar is very important for a society so that it can determine when things should be done. In the ancient world, knowing the time to plant crops was vital; and in modern times the calendar enters every aspect of our lives, telling when to celebrate, when to work, and when to pay our bills.
Our calendar is based on the sun with the fundamental units being the day (determined by the rotation of the earth with respect to the direction of the sun) and the year (determined by the rotation of the earth around the sun).
Not all calendars have been determined by the sun. For example the Moslem calendar is moon-based; whilst the Babylonians based their calendar on a combination of the sun and moon.
In our calendar, a hint of a moon-based system remains with the "month", although the average month is a few days longer than the rotation of the moon around the earth.
A further remnant of a moon-based system is the determination of the date of Easter. Many people know the definition of Easter as "Easter Sunday falls on the first Sunday after the Full Moon on, or after, the March Equinox".
But this definition hides a number of problems and can require quite accurate knowledge of the orbit of the moon. The first problem is the need to define a longitude on earth for which Sunday is determined. For example, at the instant of Full Moon it may be Sunday in Sydney but still Saturday in London giving rise in certain circumstances to a different date for Easter. A second problem arises from the variabilities in the orbit of the moon which is perturbed by the sun and the major planets. The exact orbit of the moon was not known precisely until recent times and it would be difficult if the date of Easter changed as our knowledge of the moon's orbit changed.
To obtain consistency in the date of Easter, the Church at the Council of Nicea decided to define Easter with respect to an imaginary moon - known as the "ecclesiastic moon". Also, the date of equinox was fixed at March 21 even though it can vary slightly from this date. With this definition, the date of Easter can be determined in advance without further astronomical knowledge. But the sequence of dates varies significantly from year-to-year with Easter Sunday being as early as March 22 and as late as April 25. In fact, the exact sequence of Easter dates repeats itself approximately every 5,700,000 years in our Gregorian calendar.
The Eastern Orthodox churches decided not to follow the above definition and they determine Easter in another manner, sometimes leading to a difference in the date of Easter between churches.
For those interested, the following table lists the date of Easter Sunday up to the year 2010.
The following is an algorithm by which the date of Easter may be calculated.
|the year x||19||-||a|
|the year x||100||b||c|
|b + 8||25||f||-|
|b - f + 1||3||g||-|
|19×a + b - d - g + 15||30||-||h|
|32 + 2×e + 2×i - h - k||7||-||L|
|a + 11×h + 22×L||451||m||-|
|h + L - 7×m + 114||31||n||p|
Then n is the number of the month (3 = March; 4 = April) and p + 1 is the day of that month upon which Easter Sunday falls.
Astronomical Algorithms, Jean Meeus
Man and the Stars, Robert Hanbury Brown.
Material prepared by Richard Thompson