James Fortune wrote:[color=blue]
>
jafortun@oakland.edu (James Fortune) wrote in message[/color]
news:<a6ed3ce7.0411041105.7262c1e9@posting.google. com>...[color=blue][color=green]
> > Trevor Best <nospam@besty.org.uk> wrote in message[/color][/color]
news:<4187f60b$0$1158$db0fefd9@news.zen.co.uk>...[color=blue][color=green][color=darkred]
> > > Isn't Easter the first sunday after the first full moon after the[/color][/color][/color]
first[color=blue][color=green][color=darkred]
> > > day of spring? How does the function know the moon phase?[/color]
> >
> > I'll see if I can track down the documentation others have written
> > about C.F. Gauss' computations.
> >
> > James A. Fortune[/color][/color]
Easter Function explanation Part I
The information for this post is contained in "The Oxford Companion to
the year."
The reason this is taking so long is that I have to go through a ream
of information (literally) to extract the pertinant information
necessary to understand C. F. Gauss' calculations. I decided to try to
infer all the pieces of the puzzle using the information in the
Companion rather than look up the final explanation in another source.
I will try to avoid the confusion of earlier times caused by dealing
with the rates of the Earth on its axis, the Moon around the Earth and
the Earth around the Sun. Note that the time from a new Moon to a new
Moon is easier to observe than its period of revolution around the
Earth. A culture living on any planet revolving around a star and
having one moon would almost certainly face the exact same issues. I
apologize to the authors in advance if I paraphrase any of the
information incorrectly.
In order to assist in computing Easter it is advantageous to construct
a lunar calendar. Since some cultures already use a lunar calendar
much is known about adjusting them to the solar year and keeping the
vernal equinox date at about the same day each year. An Athenian
astronomer named Meton (c. 432 B.C.) observed that 235 lunar months is
roughly equivalent to 19 solar years. I.e.,
235 lunar months = 6939.68865 days
19 solar years = 2939.6018 days
based on what we know now that the period from a new moon to another
new moon is 29.53059 days and a solar year = 365.2422 days. This
observation is referred to as the Metonic Cycle. In addition to a
constructed lunar calendar it is also advantageous to consider the
differences between the Julian calendar and the Gregorian calendar.
The Julian calendar acts as a bridge between the Gregorian calendar in
use today and our constructed lunar calendar. Since 365.2422 is close
to 365.25, the Julian calendar is one in which a leap year occurs each
and every four years. The Julian calendar, after a few bumpy starts
has been kept continuously since 8 A.D. The book notes that this start
date conveniently makes leap years divisible by four. The difference
of 11 minutes 12 seconds kept accumulating each year until people
recognized in the 13th century that the difference between the calendar
and the true positions of the sun and moon were getting beyond
acceptable limits. The Council of Trent in 1563 authorized the papacy
to correct the calendar. Pope Gregory XIII started his reform in 1579
and adjusted the calendar in 1582. The Gregorian calendar includes a
correction to make up for the drift caused by the Julian approximation
plus new leap year rules to get closer to the 365.2422 value.
James A. Fortune
It is a curious fact that the same side of the moon always faces the
Earth. It's not what you'd expect. There's no apparent physical
reason for it to be that way. Some have theorized a dumbbell-shaped
core of the moon as a possible explanation of why the moon always
presents the same aspect. -- Wayne Noss