Moondark for March: Algebra of Easter
The Sunday after the Full Moon following the Spring Equinox is Easter. Of civil and Christian holidays observed in this country, this is the most movable. In 2005, Easter will be Sunday, March 27th. And although this simple explanation works for this year, it isn’t the whole story.

In 1582, the Pope instituted calendar reforms resulting in the eponymous Gregorian calendar, the system used around the world today. Ten days were deleted, October 15th followed the 4th, restoring the vernal equinox to about March 21st. To better match the Earth's revolution, century years (multiples of 100) were no longer leap years unless evenly divisible by 400 (which, incidentally, is why 2000 was a leap year). In addition, new tables of the Full Moon were adopted for the calculation of Easter.

Accordingly, Easter is defined to be the Sunday following the ecclesiastical Full Moon that falls on or next after March 21st. The 21st is defined as the vernal equinox, even though it does not necessarily fall on that date. The ecclesiastical (or Paschal) Full Moon may differ from the astronomical as well, although adopted reforms henceforth keep calendars and astrophysics roughly in synchronization. Importantly, rules allowed Easter to be determined simply for practical purposes long before orbits were known to sufficient accuracy. 

The earliest possible date is March 22nd, and the latest is April 25th, and April 19th is the most common date over the long term, although March 31st, April 15th and 20th occur most frequently (five times each) in this century. Astronomical and ecclesiastical rules yield different dates only 18 times in 1900-2100, most recently in 1981 and not again until 2038. And because adopted rules and astronomical phenomena can differ, full moons can occur on Easter Sunday, as happened most recently in 1998. Easter Sunday's Full Moon can even be eclipsed, and this will next occur on April 5th, 2015. Amazingly, the cycle of Gregorian Easter dates takes 5.7 million years to repeat.

In Greece, Easter will be celebrated five weeks later on May 1st, 2005. The 1582 calendar reforms were rejected by the Eastern Orthodox churches, and they have continued to use the Julian calendar and traditional lunar tables to calculate Easter. In this century, the Julian Calendar is 13 days behind the Gregorian, and Easters can coincide or differ by one, four or five weeks. Differences between these calendars are still accruing, and starting in 2437 the two Easter dates can differ by as much as six weeks, and they can no longer fall on the same date after 2698. Calculation of Julian Easter is algorithmically somewhat simpler, and the cycle of dates is much less complicated, repeating every 532 years.

Of course the dates of Easter so far off into the future are of little practical importance and only computable if churches maintain their current practices. One alternative fixes the date as the second Sunday in April, i.e., between the 8th and 14th. Another proposal uses the astronomical  equinoxes and full moons at the Jerusalem meridian. While advocates argued this be initiated for the new millennium, no church has adopted this proposal.

Whenever Easter falls, things are sure to be looking up for star gazers. While the days grow rapidly longer and the nights shorter, low temperatures are no longer bone-chilling. Winter’s familiar bright stars—Aldebaran, Rigel, Betelgeuse, Sirius and Procyon—are fading into the western twilight. The sky overhead seems empty in comparison. But those with telescopes know to wait patiently for the dark of the Moon and look more deeply. The spring sky is filled with enough galaxies to last until our home, the Milky Way, returns with summer’s hazy nights.

A Google.com search will yield innumerable pages related to dates of Easter, calculator applets and calendrical systems in general. In hardcopy, good sources include the Explanatory Supplement to the Astronomical Almanac (1992), and any of the books by astro-calc-guru Jean Meeus: Astronomical Algorithms (1991) Chapter 8, Mathematical Astronomy Morsels (1997) Chapters 59 and 60, and More Mathematical Astronomy Morsels (2002) Chapter 25, all published by Willmann-Bell

The full moon will rise just two days before Easter Sunday this year...
Moondark is written by Doug Miller, published online, and printed in the Delmarva Star Gazers' Star Gazer News. Last revised on 20 Feb 2005. Text and images copyright © 2005 by Douglas C. Miller, All Rights Reserved. This material may not be reproduced in any form without prior permission.