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§126
The new moon nearest to the spring equinox is the first month of
the year. The first month will always be either the new moon just
before the spring equinox, or it will be the new moon just after it.
One way of determining this is to compute the equinox Julian date and time
and find the difference between it and the Julian date and time of the
respective new moons, taking the nearest as the first month. A new
moon is measured from sunset on the evening of the crescent.
§127
In the first century c.e., the day of the new moon was determined by eyewitness
observation. When two witnesses had seen the new moon in the west,
just after sunset, that day, beginning with that sunset, would be declared
the new moon day. The new moon was declared when the new crescent
was first seen in the west after the conjunction. The Sanhedrins
calendar council, called the Beth Din, was responsible for cross-examining
the witnesses. Jerusalem was the prime location of observation, although
the council would take testimony from witnesses who traveled to Jerusalem
in those cases in which the seeing conditions were not good at Jerusalem.
In no case was the month ever made to be longer than 30 days, or shorter
than 29 days. If there was any doubt whatever, due to poor conditions,
it was the practice of the Jewish people to observe two new moon
days, and two feast days for each feast day, in order to be sure of observing
the correct day.
§128
This program (which is available free on this site) can be considered
an electronic eyewitness which computes with utmost precision the location
of the moon and sun on the day or days in question, and then it determines
if the moon could be seen based upon two factors (a) the size of the lighted
portion of the moon, and (b) the amount of twilight competing with the
crescent just after sunset on the day or days in question. The mathematical
relationships between these two values can no doubt be improved with continued
examination of actual documented cases in which witnesses have seen the
new moon after sunset.
§129
The lighted portion of the moon is directly proportional to its apparent
angular distance from the sun, which is quantified by a value called the
arc of light herein designated as AL. The amount of twilight working
against the arc of light is directly proportional to the length of time
the moon stays above the horizon after sunset. This is quantified
by a value called the arc of vision, herein quantified by AV. When
the AV is small visibility of the new moon is unlikely. When the
AL is small, visibility of the moon is not as likely. It was determinged
by a French astronomer named Danjon that if the arc of light was less than
7 degrees, the moon in no case could be seen. This is due to the fact that
the lunar mountains shade out all light hitting the moon near the terminator
as viewed from the earth. When this condition occurs on the day preceeding
visibility, this program will post PR: < 7. Many times
it happens that even though the arc of light is substantial, the moon sets
before the sun. This condition is posted as S>M, i.e. sun greater
than moon (in altitude) for the day preceeding visibility.
§130
The formulae relating the arc of vision and the arc of light are
§131
For example if AL = 8, then AN= 10.75. If the AV>= 10.75
or AV < 12.75, the program will designate the new moon as AMB, i.e.
ambiguous The AMB designation is placed on any AV that is within 2 degrees
of the arc of vision needed. The day will be listed as the
new moon day, however. It will be clear that the next day is to be
observed also as the new moon day.
§132
If the designation is AMBpr, this means the previous day came within one
degree of meeting the formulaes criteria for visibility. In that
case the preceeding day should be observed with the day listed as the new
moon day.
§133
The arc of light and arc of vision are computed without refraction, which
amounts to about 33' of arc at sunset. Please take this into account
when using other software to check on this program. The reason for
not computing the atmospheric refraction is that the arc of light is used
to measure the visible portion of the crescent, which is not changed by
the refraction. Refraction will reduce the arc of vision at sunset.
Refraction will increase the arc of vision the nearer the observation time
is to moonset. This effect of 33' is within the Ambiguity parameters
of the program. which are two degrees when AV>AN and 1 degree when AV<AN.
Improvements will need a better theory.
..
§142
(1) The most common calendar error of Passion Chronologists is to intercalate
the luni-solar year incorrectly, hence those who place a Wednesday Passion
in 31 c.e. do so only by having Aviv a month late. Such is the error
of the World Wide Church of God. (2) Sir Robert Anderson, The
Coming Prince, goofted in selecting 32 c.e. for the Passion, since
that year has no useful Passover dates. (3) Another popular mistake
is to retrocalculate the modern Rabbinic Calendar or some variation of
it (see history above). (4) Another error is to place the new moon
at the conjunction.
.
§142.1
The fixed calendar was established ca. 359§142.91
c.e., so it is clear that neither Yayshua or other Jews used it in the
first century. Yet this is the calendar that is used throughout most
of the Jewish world today. Obstensibly, the fixed calendar was instituted
as a measure to unify Judaism at a time when many Jews were observing the
moon locally. Hence it could often happen that the calendars and
feast dates of two separated communities could disagree. But instead
of unifying Judaism, the fixed calendar fueled the schism between the Rabbinite
and Karaite Jewish sects, as the Karaites wanted to follow the scripture
more literally, and the Rabbinite Jews wanted to follow the authority of
the Rabbis' tradition.
§142.2
It is probable that the Rabbis who introduced the fixed calendar not only
wanted to unify Judaism, they wanted it unified under their authority.
They wanted to ordain the feast days, fasts, and new moons. According
to Feldman (see note 1), and Arthur Spier (The Comprehensive Hebrew Calendar)
only a new Sanhedrin has the authority to reform the calendar. This
is also the opinion of most other Rabbinic Jews.
§142.3
When the fixed calendar was set up ca. 359 c.e., the calendar
makers used 3761 b.c.e. as their starting point. Tishri 3761- Tishri
3760 marks year 1 of the W.E. (world era). The world era begins precisely
10/6/3761 b.c.e. at 11 p.m. 11 min. 20 seconds. That moment is called
Molad Tohu, which means "formless birth," i.e. so named because in Rabbinical
reckoning it was 6 months before creation which was in the spring of 3760
by their computation. I should point out that the equinox of Nisan
in the spring serves as the starting point for the solar year, which points
up a great inconsistency in the fixed calendar, and that is the Bible ordains
Aviv (Nisan) as the first month (Exodus 12:1-3), and the fixed calendar
makers recognize this by using the T'kufah (equinox) of Nisan as the starting
point for their solar year, yet they make the calendar year begin with
the 1st of Tishri!
§142.4
All the Moladoth (or conjunctions) of the fixed calendar are determined
by adding 29 days 12 hours 44 minutes, and 3 1/3 seconds, or a multiple
thereof to the Molad Tohu. Keep in mind that 29d 12h 44m 3.33s is
only the average length of a lunation. The real conjunction can deviate
as much as 15 hours from this average.
§142.5
Hence, when the fixed calendar makers say, or when the modern calendar
says that the molad, i.e. conjuntion was at such and such a moment, they
do not mean the real conjunction, but only what the conjunction would be
based upon averages. An actual conjunction, for all practical purposes
never comes exactly 29d 12h 44m 3.333sec after the previous one.
§142.6
In point of fact, the length of a lunation is now 29d 12h 44m 2.8sec, and
after a few thousand years, the molad of the fixed calendar will deviate
greatly from the actual molad. The fixed calendar thus does not depend
upon current observations (or calculations) of the position of the moon
or the sun. In fact, the actual position of the sun and moon has
been of no use to the fixed calendar since 359 c.e. and probably ealier,
i.e. 249 c.e. Yet, God ordained the sun and moon to fix the times
and seasons in Genesis.
§142.7
Starting with Molad Tohu at 3761 b.c.e. at 10/6, at 11h 11m 20 sec p.m.,
29d 12h 44m 3 1/3 sec are added to obtain the next Molad (even though it
wasn't the actual moment of the conjunction, but only an average guess).
There are 12 lunations (or months) in the common year. Hence to obtain
Molad Tishri of the year 3760, i.e. the start of the second year, 29d 12h
44m 3 1/3sec are added 12 times to Molad Tohu. For Molad Tishri
starting the third year, another 12 lunations are added. However,
at least every 3 years a leap year of 13 lunations length must be used.
For this the fixed calendar uses the Metonic cycle. According to
the Metonic cycle the third year must be 13 lunations in length, hence
29d 12h 44m 3 1/3sec is added 13 times.
§142.8
The above pattern is repeated adding 12 lunations for the 4th year, and
12 more for the 5th; 6th = 13 mon., 7th = 12mon, 8th = 13, 9th = 12, 10th
= 12, 11th = 13, 12th = 12, 13th = 12, 14th = 13, 15th = 12, 16th = 12,
17th = 13, 18th = 12, 19th = 13 months. That is, in the first 19
years, years 3, 6, 8, 11, 14, 17, and 19 are 13 months, and years 1, 2,
4, 5, 7, 9, 10, 12, 13, 15, 16, and 18 are 12 months. After 19 years
the pattern repeats, being the same in the 20th year as in the first year.
Using this method, any molad can be computed up to the present and beyond.
§142.81 Of course 19 years with its 12 common years, and 7 leap
years requires 235 lunations to complete (12*12 + 7*13 = 235). But
235 * 29d 12h 44m 3 1/3sec = 6939d 16h 33m 3 1/3 sec, which when divided
by 19 gives a year length of 365.246822 days, which is in excess of the
true value 365.2422001, since the inception of the fixed calendar has caused
the cycle to run ahead of the sun some seven days. This in turn causes
the months of the whole year to be 1 month out of phase with the first
century method about 1/4 of all years, since 7/29.5 is about 1/4.
§142.82
For example the molad beginning the 40th year is determined by adding up
the correct number of lunations of 29d 12h 44m 3 1/3 sec to Molad tohu.
Two 19 year cycles = 38 years complete, plus 1 year equals 39 years complete,
which is the start of the 40th year. But 38 years is 235*2 lunations.
The 39th year is year 1 of the cycle, hence it is 12 lunations long.
Therefore:
10/6/3761 11h 11min 20sec plus (235 * 2 + 12) * 29d 12h 44m 3
1/3 sec brings us to the molad beginning the 40th year, i.e. molad tishri
for the 40th year.
Typically it is easiest to convert the Molad Tohu to the Julian
day and fraction thereof before adding lunations to this benchmark.
Then one will be able to compute the Julian day no. of molad tishri.
§142.83
At this point the day of the week for molad tishri would also be determined,
and then the following rules applied:
§142.91
"The Phase Method of determining the beginning of a month described in
the preceeding pages, prevailed until the time of Abbaye and Raba (middle
of 4th century), when it was replaced by the fixed calendar Method which
makes use of a Mean Conjuntion or Molad to determine the beginning of a
month" (Rabbinical Mathematics and Astronomy, W.M. Feldman, pg. 185).
§142.92
"The Hebrew Calendar: A Mathematical Introduction," by John A. Kossy, ed.
by Herman L. Hoeh, Ph.d., first edition, Ambassador College Press, (c)
1971, 1974. If anyone wants to pursue this, I suggest writing to
John B. Bowers, 1141 W. Shaw Ave #201, Fresno, CA 93711. When and
how the Metonic Cycle was set, adjusted, or readjusted prior to 359 c.e.,
when the Fixed Calendar was introduced is a matter of historical interest,
not theological, since the Fixed Calendar was not used in Yayshua's day
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