John Harper <John.Harper@vuw.ac.nz>

The "popular" rule (for Roman Catholics and most Protestant
denominations) is that Easter is on the first Sunday after the first
full moon after the March equinox.

The actual rule is similar, except that the astronomical equinox is
not used; the date is fixed at March 21.  And the astronomical full
moon is not used; an "ecclesiastical" new moon is determined by
adopted tables based on the Metonic cycle, and "full" is taken as the
14th day of that lunation.  There are auxiliary rules that make March
22 the earliest possible date for Easter and April 25 the latest.  The
intent of these rules is that the date will be incontrovertibly fixed
and determinable indefinitely in advance.  In addition it is
independent of longitude or time zones.

The popular rule works surprisingly well.  When the two rules give
different dates, that occurs in only part of the world because two dates
separated by the international date line are simultaneously in progress.

The Eastern Churches (most Orthodox and some others, e.g., Uniate
Churches in Palestine) use the same system, but based on the old
(Julian) calendar.  In that calendar, Easter Day is also between March
22 and April 25, but in the western (Gregorian) calendar those days
are at present April 3 and May 8. Whenever the Gregorian calendar
skips a leap year, those dates advance one day.

Some Eastern Churches find both movable feasts like Easter and fixed
ones like Christmas with the Julian calendar; some use the Julian for
movable and the Gregorian for fixed feasts; and the Finnish Orthodox
use the Gregorian for all purposes.

To explain the Eastern system one must begin with the Jews in
Alexandria at the time of the Christian Council of Nicaea in 325, who
appear to have been celebrating Passover on the first "full moon"
after March 21, as specified by the 19-year Metonic cycle and the
Julian calendar (with its leap year every 4 years, end of century or
not). The Bishop of Alexandria was made responsible for the Christian
calendar; he specified that Easter be the Sunday after that Passover.
Eastern Christians still say that Easter must follow Passover, but
that Passover is the one that is meant, not the Passover defined by
the present Jewish calendar.

Subsequently the Jews reformed their calendar (in 358 or in the early
6th century according to different sources; possibly at different
times in different places), in order to improve the fit between
astronomy and their arithmetic, but the Christians did not follow
suit.  In 1996, for example, Passover was on April 4 but the Orthodox
Easter was on Sunday April 14, not April 7 (which as it happens was
the Western Easter.)

The Eastern Easter is 0, 1, 4, or 5 weeks after the Western
Easter. The Western Easter can precede the (modern) Jewish Passover,
as in 1967, 1970, 1978, 1986, 1989 and 1997, and can even coincide
with it, as in 1981.

Much of this information was taken from the Explanatory Supplement to
the Astronomical Ephemeris, page 420, 1974 reprint of the 1961
edition.  There is more in the Explanatory Supplement, specifically a
series of tables that can be used to determine the Easter date for
both the Julian (Eastern and pre-1582 Western) and Gregorian
calendars.  However, the Explanatory Supplement is misleading on the
subject of the Eastern Easters, though its tables are correct.

Jean Meeus has published a program to compute Easter in "Astronomical
Algorithms," also see below.  Simon Kershaw has written one in C,
available at <URL:http://www.ely.anglican.org/cgi-bin/easter>.

The most easily available published source for what the Jews 
and Christians were doing in ancient Alexandria appears to be Otto 
Neugebauer's "Ethiopic Easter Computus" in his _Astronomy and History 
Selected Essays_, Springer, New York, 1983, pp. 523--538. 

John Harper acknowledges the help of Archimandrite Kyril Jenner, Simon
Kershaw, and Dr. Brian Stewart concerning Eastern Easters.