[net.religion] Date of Easter ?

bill (04/12/83)

Joe P. quotes the Book of Common Prayer on the
date of Easter, and he is of course correct.  What
he didn't say is that Easter is NOT determined
by the time of the ACTUAL full Moon, but rather
by a mathematical approximation known as the
"Paschal Full Moon".  The tables in the Book
of Common Prayer are constructed according to
this rule, rather than the best known astronomical
rule.  Given time, the rule for the Paschal full
Moon will diverge more and more from the time
of the actual full Moon (although the error is
only a few hours at present).

People often wonder that Passover sometimes comes a
month later than Easter.  This is an interesting
question because the two festivals were originally
related, and the "Easter Rule" was intended
at first to cause them to coincide.  According
to the Hebrew calendar, Passover starts on the
15th day of the Hebrew month Nisan.  All months begin
at New Moon, and in ancient times the Vernal Equinox always
occured within Nisan.  The method used to calculate the 
moment of New Moon is really quite accurate - it dates back 
to the Babylonian exile (being identical to the rule
used by the Babylonians) and after all that time, is
only a few hours off.

The discrepancy arises because the Hebrew calendar uses
a different rule to estimate when the Vernal Equinox
occurs than does the Gregorian calendar.  The Gregorian
calendar is very accurate - the error is one day in
about 3000 years.  The Hebrew calendar uses an
approximation known as the Metonic Cycle to estimate
the date of Vernal Equinox (a Solar calendar concept)
relative to the lunar calendar.  According to the Metonic 
Cycle, there are 235 lunar months in 19 years, and this 
is a pretty good approximation.  It is not exact, however, 
and at the present time it predicts the Vernal Equinox 
a few days late.  As a result, several times during the
19 year cycle, the beginning of the month of Nisan
is postponed to the new moon AFTER the actual Vernal
Equinox.  An extra "intercalary" or "leap" month
is inserted.  (These leap months are added routinely
in years #3,6,8,11,14,17 and 19 of the Metonic
cycle, since 19 years * 12 months falls seven months
shy of 235 months.)  When this happens, Passover will 
be a month later than Easter.  This discrepancy will 
become worse and worse with time.  

If my notes are correct, at the present time
3 years out of 19 have Passover a month later than
Easter.  They are the 8th, 11th and 19th years of
the cycle, so not every year which has an intercalary
month will have this discrepancy between the dates of
Easter and Passover.  (The latest cycle began with its 
year 1 in 1978-9, so the next year in which this will 
happen should be 1986). 1000 years ago, Easter always 
came a few days after Passover.  In the future the 
discrepancy will become more and more obvious, as the 
two calendars slip more and more out of phase.

What is remarkable about all this is the accuracy 
with which the ancients were able to determine
the lengths of the fundamental astronomical cycles
that went into this calculation.  When one realizes 
that the rule for Passover is of the order of 2500
years old, and only now is getting noticeably out
of phase with the actual astronomical events it
attempts to track, you really have to give the
people who made up the rules a lot of respect.

		Bill Jefferys  (-!hao!cires!nbires!un-ngp!bill)
		Astronomy Dept
		University of Texas