The Purpose of the Hebrew Calendar Rosh HaShanah Dehiyyot (Postponements of the First Day of Tishrei)
Bookmark or cite this page as <http://www.sym454.org/hebrew/postpone.htm>
by Dr. Irv Bromberg, University of Toronto, Canada
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Menu of Topics:
- Introduction to the Rosh HaShanah Postponement Rules
- Molad Zakein
- Lo ADU Rosh
- Third Rule
- Fourth Rule
- Frequencies of Rosh HaShanah Postponements and Weekdays
- The Visibility of the New Lunar Crescent on Rosh HaShanah
- The Net Effect of the Rosh HaShanah Postponements
- Summary
Introduction to the Rosh HaShanah Postponement Rules
As shown in this chart of the
Traditional Hebrew Calendar Rosh HaShanah status 96 KB, relative to the Hebrew weekday of the
molad of
Tishrei, in about 39% of years
Rosh HaShanah is
not postponed, in about 47% of years it is postponed by one day, and in the remaining approximately 14% of years
Rosh HaShanah is postponed by two days.
Traditionally the moment of the molad is
expressed in terms of the number of hours since sunset, which I call
"Talmudic Temporal Time". This method has the advantage that the Hebrew
weekday is directly and easily determined by calculating the number of
days elapsed since the epoch of the Hebrew Calendar + 1 (because that In
comparing actual lunar conjunctions to the moments of the traditional molad, where the moladRosh HaShanah was on Yom Sheini = Monday), then divide by 7, and add 1 day to the remainder, which is the Hebrew day number of the week.
To compare molad moments to actual lunar
conjunctions for astronomical evaluations, however, it is necessary to
subtract 6 hours from the traditional molad moment so that it is expressed in terms of the civil time (but then the weekday will be wrong for all molad moments between sunset and midnight).
The
Rosh HaShanah postponement rules are an innovation of the
fixed arithmetic Traditional Hebrew calendar. They did not apply to the
original observational lunar crescent calendar. Instead, the
observational calendar varied the month lengths to be 29 days if the new
lunar crescent was seen at sunset at the end of the 29th day, or 30
days otherwise. On the other hand, the
Talmud Bavli mentions in tractate
Rosh HaShanah page 20A that the Court (
Sanhedrin
calendar committee) used to intimidate visible crescent witnesses to
withdraw or confuse their testimony or to disqualify them if otherwise
Rosh HaShanah
would be sanctified on Wednesday or Friday (see rule #1, below).
Likewise, the Chinese calendar, based on astronomical algorithms for the
longitudes of Sun and Moon, varies the length of months from 29 to 30
days depending on the computed moment of the actual lunar conjunctions.
The Traditional Hebrew Calendar has constant month lengths, but
something has to vary to accomodate the non-integral mean length of the
molad (representing the mean lunar cycle), which equals 29 days 12 hours 44 minutes 1 part (each "part" equals 3+
1/
3 seconds =
1/
18 of a minute), and this is accomplished by adjusting the lengths of the two months after the
previous month of
Tishrei, that is
Cheshvan and
Kislev, according to the following four rules:
1. Molad Zakein: If the molad of Tishrei falls on or after noon then postpone Rosh HaShanah to the next day.
This is the second-most-commonly invoked postponement rule, but
logically should be checked first because its invokation can cause
Rosh HaShanah to be postponed to a disallowed weekday (which in turn will be handled by the second postponement rule). The Hebrew term
molad zakein literally means "old
molad".
For example, this is the reason for postponing from Monday to Tuesday in Hebrew year 5786.
Note that noon coincides with
3/
4 of the day elapsed, because Hebrew calendar days start at sunset. Therefore, rather than explicitly checking the timing of the
molad moment,
German Mathematician
Johann Carl Friedrich Gauss (Gauß) pointed out that this postponement rule could be bypassed simply by adding
1/
4 day to the moment. If the original moment had been past noon then adding that
1/
4 day would automatically advance the
molad moment to the following day.
Traditionally, this postponement was considered necessary to ensure the visibility of the New Moon on the first day of
Rosh HaShannah. In reality, it doesn't ensure that, see below for my astronomical analysis of the visibility of the lunar crescent on
Rosh HaShanah. Remy Landau states that this postponement is to ensure that the calculated time of any
molad does not exceed the first day of any month in the Hebrew calendar, see <
http://hebrewcalendar.tripod.com/#11>.
The
Talmud Bavli, in tractate
Rosh HaShanah page 20B explains that if the
molad
occurs after noon then there is no way that the new lunar crescent will
be visible at the coming sunset (six hours later), but it will be
visible at the following sunset. This noon cutoff time led Rabbi
Zerachiah ben Isaac Ha-Levi Gerondi (the
Baal HaMaor,
1125-1186 AD) to assign the meridian 90° east of Jerusalem as the "date
line" in Jewish Law, but this was partially based on the
incorrect assumption that the traditional
molad moment refers to the meridian of Jerusalem. As I have shown on my web page "
The Molad of the Hebrew Calendar" at <
http://www.sym454.org/hebrew/molad.htm>, the original historical reference meridian of longitude of the traditional
molad was actually midway between the Nile River and the end of the Euphrates River, which, according to the logic of the
Baal HaMaor,
would shift the "date line" to about 94° east of Jerusalem, or almost
130° east of Greenwich, passing east of Korea, through the middle of the
southern island of Japan, the Philippine Sea, the Java Sea west of New
Guinea, the Timor Sea north of Australia, and just west of Darwin,
Australia. Another problem with the interpretation of the
Baal HaMaor
is that although in his own era the world was understood to be a sphere
with times of day differing between meridians of longitude, in the era
of the sages of the
Talmud it was thought that the world was
flat, during the night Sun was "outside" the celestial sphere, and
during rising or setting Sun moved through "windows" (or tunnels)
between the outside and inside of the celestial sphere such that sunrise
and sunset occurred at the same moment for the entire world. These
concepts are discussed as such in that section of the
Talmud and
by its commentators. In those days there was no understanding of time
zones or meridians of longitude, therefore the noon cutoff time
specified in the
Talmud could not have had any relationship to any concept of a "date line".
The
Baal HaMaor also claimed that the selected cutoff time
ensures that "somewhere in the world" the actual lunar conjunction will
correspond to the traditional
molad moment. However, there is
nothing special about that particular cutoff time that ensures any
higher probability of that statement being true, in fact it would be
equally true for any alternative cutoff time. Even so, of what relevance
is it?
Furthermore, the reference meridian for the traditional
moladot
is drifting eastward at an accelerating rate, so are we to learn that
the International Date Line is also drifting eastward at the same rate,
to remain 90° (6 hours) ahead of it?
If the "date line" were to pass through populated lands then it would be possible to almost completely avoid
Shabbat by taking a step to the east across the line as
Shabbat starts west of the line, waiting for
Shabbat to end west of the line, then taking a step back to the west across the line as
Shabbat starts east of the line. Conversely one could observe two consecutive days of
Shabbat by staying to the west of the date line at the start of
Shabbat, then as
Shabbat is ending west of the line taking a step east across the line where it will be near the start of
Shabbat.
Such examples make it obvious that the international date line must
never pass through populated lands, and led Rabbi Avrohom Yeshaya
Karelitz (the
Chazon Ish) in 1941 AD to extend the
halachah
date line to the eastern coasts of Asia and of Australia. Nevertheless
that extension still leaves the problem that a person swimming at a
coastal beach, or boating in that region, will be crossing the line.
Perhaps such a date line should be extended to the
continental shelf?
For more information about the date line controversy see Willie Roth's essay at <http://koltorah.org/old/ravj/The International Date Line and Halacha.htm>, and "The Sabbath, the International Date Line and Jewish Law" by Rabbi Yehuda Shurpin at <http://www.chabad.org/library/article_cdo/print/true/aid/1736567/jewish/The-Sabbath-the-International-Date-Line-and-Jewish-Law.htm> (cancel the print command if you wish).
There is some commentary debate as to whether the cited
Talmud text refers to the actual lunar conjunction or the mean conjunction as estimated by the Hebrew Calendar
molad arithmetic. In the era of
Hillel ben Yehudah the
molad of
Tishrei was on average 4+
1/
5 hours late with respect to the actual mean lunar conjunctions but today it is on average 6 hours late,
as shown in this chart 316KB (see also the last paragraph on this page), although today an individual
molad moment can be as much as 16 hours late and in the era of the
Talmud a
molad moment could have been almost 14+
1/
2 hours late. Astronomically, in the era of the
Talmud
the absolute minimum elapsed time from the actual lunar conjunction
(New Moon) until the moment when the visible crescent for the month of
Tishrei could be visible at sunset in Jerusalem under
rare ideal conditions was about
3/
4 day. In other words, when the actual lunar conjunction of
Tishrei occurs shortly after midnight in Jerusalem, the new lunar crescent
might
be seen at sunset that same day. Such an early crescent would be truly
exceptional (<2 2="2" a="a" altitude="altitude" and="and" at="at" between="between" crescents="crescents" favorable="favorable" first="first" font="font" highly="highly" its="its" lunar="lunar" moon="moon" most="most" moving="moving" near="near" occur="occur" of="of" one="one" orbital="orbital" perigee="perigee" rapidly="rapidly" require="require" size="-1" sunset="sunset" the="the" visible="visible" whereas="whereas" would="would" years="years">
12>
/
2 days after the actual lunar conjunction, 50% occur more than 1+
3/
4
days after conjunction, and 30% more than 2 days after conjunction.
When the lunar altitude is exceptionally unfavorable and Moon is moving
most slowly near its orbital apogee, which occurs in about 7.5% of
years, the visible crescent of
Tishrei is first seen more than 2+
1/
2
days after conjunction — but the crescent is essentially never first
seen beyond 3 days after conjunction (unless weather conditions
interfered with its visibility).
The earliest new lunar crescent sightings from the records of the present era
Israeli New Moon Society at <
http://sites.google.com/site/moonsoc/> are always more than 24 hours after the actual lunar conjunction (at sea level, without optical aids). Relative to the
molad of
Tishrei,
which can be as much as 16 hours later than the actual conjunction in
the present era, the earliest visible new lunar crescent should be at
least 6 hours later than the
molad moment. Therefore the 6-hour cutoff cited from the
Talmud does fit the astronomy of the present era if the term
molad is understood to refer to the
molad
arithmetic of the Traditional Hebrew Calendar. On the other hand, it
would be very uncommon for the new crescent to be visible only 6 hours
after the
molad, and in the era of the
Talmud the minimum elapsed time would have had to be at least 7+
1/
2 hours.
The Earth-to-Moon distance at the lunar orbital perigee is quite
variable. Lesser perigee distances are associated with faster lunar
orbital motion and shorter elapsed times from conjunction to visible
crescent. Likewise the Earth-to-Moon distance at the lunar orbital
apogee is also quite variable. Greater apogee distances are associated
with slower lunar orbital motion and longer elapsed times from
conjunction to visible crescent.
It might seem that the lunar latitude is not very important in regard to the
molad of
Tishrei, because
Rosh HaShanah
is near the southward equinox, when Sun and Moon set close to due west.
If the lunar latitude is at its extreme 5° south of the ecliptic, Moon
will appear to set to the left of the sunset point, or if Moon is at its
extreme 5° north of the ecliptic it will appear to set to the right of
the sunset point. The greater the lunar latitude is at sunset, however,
either south or north of the ecliptic, the longer the arc-of-light from
Sun to Moon will be, enhancing the probability that the new lunar
crescent will be visible.
In the far distant future, around Hebrew year 12000 if the Hebrew
calendar solar drift is left uncorrected, when the Earth orbital
aphelion is close to
Rosh HaShanah (it is currently in
Tammuz), the lunations will tend to be shorter at that time of year. In that millennium the maximum limit will be reduced to 2+
1/
2 days (97.5th percentile) or absolute maximum of 2+
3/
4
days, but the minimum limit will increase closer to a full 24 hours (at
sea level, without optical aids). Only 5% of years in that millennium
will have less than 24 hours elapsed from actual conjunction to visible
crescent in Jerusalem.
Back in the millennium beginning with Hebrew year 4000, when the Earth orbital aphelion was in
Sivan, the lunations near
Rosh HaShanah
tended to be slightly longer than they are at present, so an actual
lunar conjunction after midnight was essentially never associated with a
visible crescent at the next sunset in Jerusalem. This leads to
another possible explanation. The classical Hebrew word used to specify
the cutoff time is
chatzot. The context of the cutoff time
discussion is that if witnesses come to testify that they saw the new
lunar crescent, but the moment of the (actual) lunar conjunction is
calculated to have occurred after
chatzot, then their testimony can be confidently refuted because it is still too early for the new crescent to be visible. The word
chatzot,
unqualified, has two possible meanings: either midnight or noon, so it
can refer either to the middle of the day or the middle of the night. To
unambiguously qualify the intended meaning, the qualifier
haLeilah (of the night) or
haYom (of the day) could have been used. Thus
chatzot haLeilah would have unambiguously referred to midnight, and
chatzot haYom would have unambiguously referred to noon. The
Talmud, in its typically terse style, only used the unqualified
chatzot. All commentators and translators that I have seen have understood the word
chatzot
as referring to noon, but astronomically it could only be sensible to
understand it as referring to midnight, unless the intention was to err
on the side of very liberally accepting doubtful testimonies.
2. Lo ADU Rosh: If the molad of Tishrei falls on Sunday, Wednesday or Friday then postpone Rosh HaShanah to the next day.
This is the most commonly invoked postponement rule, but logically
should be checked after the first rule given above, because the first
rule can postpone the
Rosh HaShanah weekday from an allowable
weekday to a disallowed weekday, in which case this second rule would
cause a further one day postponement to the next allowable weekday.
For example, Hebrew years 5746, 5749, 5753, 5780 have Sunday to
Monday postponements; years 5741, 5748, 5768 have Wednesday to Thursday
postponements; and years 5757, 5764, 5784 have Friday to Saturday
postponements.
This postponement rule is for
ritual convenience: The
Talmud Bavli tractate
Rosh HaShanah page 20a states that excluding Wednesday and Friday is to prevent
Yom Kippur from occurring on either side of
Shabbat, which would be ritually inconvenient with regard to the burial of a corpse, and the
Talmud Bavli tractate
Sukkah 43a as well as
Talmud Yerushalmi tractate
Sukkah 4:5 says that excluding Sunday is to prevent
Hoshannah Rabbah from occurring on
Shabbat, which would render the willow branches
muktze (not to be touched on
Shabbat) so they couldn't be beaten to symbolize the final elimination of sins. Note that
Succot always starts on the same weekday as
Rosh HaShanah.
Remy Landau <
http://hebrewcalendar.tripod.com/#10> points out that this rule reduces the number of
Qeviyyot (Hebrew year types) from 28 to 16, and it also prevents the first day of
Rosh HaShanah from falling adjacent to
Shabbat (although
Rosh HaShanah can and does fall on
Shabbat itself).
Implementation tip: If the
molad date is converted to a weekday as an integer from Sunday=0 through Saturday=6 then the
molad is on a disallowed weekday if (
MoladWeekday × 3 )
MOD 7 < 3.
3. If the molad of Tishrei for a non-leap year (12 months) falls on Tuesday on or after 9 hours and 204 parts then postpone Rosh Hashanah to Thursday.
There is no need to check this rule if the
molad moment was already found to fall
on or past noon or on a
disallowed weekday.
As explained by Remy Landau, see <
http://hebrewcalendar.tripod.com/#12>, this rule eliminates all of the 356-day years that would otherwise be caused by the disallowed weekday rule.
If the
molad of
Tishrei falls on Tuesday on or after 9h 204p and the year is not a leap year, then the
next molad of
Tishrei will be 12 × the
molad interval later, which will place it on or after noon on
Shabbat
(Saturday), which will be postponed to Sunday, but that day is not
allowed, so it will be postponed again to Monday. This double-day
postponement would cause
this year length to be 356 days, but the longest possible length of a non-leap year is 355 days (where
Cheshvan and
Kislev both are full 30-day months). Therefore
Rosh HaShanah this
year is postponed from Tuesday to Wednesday, and because Wednesday is
not allowed it is postponed again to Thursday, making this year an
acceptable 354 days.
Rather than explicitly checking the
molad time against the fixed cutoff of 9h 204p, which is incompatible with any variable interval
molad such as the
progressive molad or the actual lunar conjunction, a generic alternative is simply to postpone
Rosh HaShanah if the
next molad of
Tishrei will be on or after noon on
Shabbat. The
Gauss shortcut (adding
1/
4 day) can also be used on that
molad moment, triggering the 2-day postponement for this year if the
next molad of
Tishrei plus
1/
4 day will land on Sunday. Alternatively, postpone this
Rosh HaShanah by two days if the following expression is true:
floor(
NextTishreiMolad +
1/
4 day ) –
floor(
ThisTishreiMolad +
1/
4 day ) = 355
This rule is invoked in only about 3.31% of years (for example,
Hebrew years 5620, 5640, 5647, 5667, 5718, 5745, 5789, 5796, 5816, 5867,
5887, 5894), and such years are always non-leap years having 354 days.
Although the intervals between these uncommon postponements average to
about once per 30 years, only 8 intervals are actually possible within
the Traditional Hebrew Calendar:
Interval (years): |
7 |
20 |
27 |
31 |
44 |
51 |
64 |
71 |
% Occurrence: |
18.7% |
35.2% |
10.1% |
2.6% |
1.9% |
24.1% |
1.1% |
6.3% |
4. If the molad of Tishrei after a leap year (13 months) falls on Monday on or after 15 hours and 589 parts then postpone Rosh Hashanah to Tuesday.
There is no need to check this rule if the
molad moment was already found to fall
on or past noon or on a
disallowed weekday.
As explained by Remy Landau, see <
http://hebrewcalendar.tripod.com/#13>, this rule eliminates all of the 382-day years that would otherwise be caused by the disallowed weekday postponement rule.
If the
molad of
Tishrei is Monday on or after 15h 589p and the prior year was a leap year, then the
previous molad of
Tishrei would have been 13 × the
molad
interval earlier, which would have placed it on or after noon on
Tuesday, which would have been postponed to Wednesday, but that day is
not allowed, so it would have been again postponed to Thursday. This
would have caused that prior year length to be only 382 days, but the
shortest possible length of a leap year is 383 days (where
Cheshvan and
Kislev both are deficient 29-day months). Therefore
Rosh HaShanah this year is postponed from Monday to Tuesday, making the prior year an acceptable 383 days.
Rather than explicitly checking the
molad time against the fixed cutoff of 15h 589p, which is incompatible with any variable interval
molad such as the
progressive molad or the actual lunar conjunction, a generic alternative is simply to postpone
Rosh HaShanah if the prior
molad of
Tishrei was on or after noon on Tuesday. Again, the
Gauss shortcut (adding
1/
4 day) can be used on that
molad moment, triggering a postponement for this year if the
prior molad of
Tishrei plus
1/
4 day landed on Wednesday. Alternatively, postpone this
Rosh HaShanah by one day if the following expression is true:
floor(
ThisTishreiMolad +
1/
4 day ) –
floor(
PriorTishreiMolad +
1/
4 day ) = 383
This rule is invoked in only about 0.54% of years (for example,
Hebrew years 5096, 5194, 5441, 5519, 5688, 5766, 6013, 6111), and again
such years are always non-leap years having 354 days. Although the
intervals between these rare postponements average to about once per 186
years, only 5 intervals are actually possible within the Traditional
Hebrew Calendar:
Interval (years): | 78 | 98 | 169 | 247 | 345 |
% Occurrence: | 22.1% | 15.5% | 12.3% | 41.2% | 8.9% |
Frequencies of Rosh HaShanah Postponements and Weekdays
The overall frequencies of applicability of the
Rosh HaShanah postponement rules are shown below, and are similar to those given by Remy Landau at <
http://hebrewcalendar.tripod.com/#24.3>. Note that it is least common for
Rosh HaShanah to start on Tuesday, and most common for it to start on Thursday.
When
Rosh HaShanah does start on Thursday there are two days of
Yom Tov (High Holy Days) followed by
Shabbat for
Rosh HaShanah, plus, outside Israel, the same for the first two and last two days of
Sukkot.
Traditional Rosh HaShanah Postponements and Weekdays
(number of years per 1000 years, disallowed weekdays are Sunday, Wednesday, Friday)
Year Range |
No Shift |
Delayed 1 |
Delayed 2 |
Monday |
Tuesday |
Thursday |
Saturday |
4001-5000 |
394 |
469 |
137 |
277 |
116 |
318 |
289 |
5001-6000 |
388 |
469 |
143 |
282 |
114 |
319 |
285 |
6001-7000 |
390 |
468 |
142 |
280 |
117 |
316 |
287 |
7001-8000 |
390 |
470 |
140 |
280 |
114 |
323 |
283 |
8001-9000 |
387 |
471 |
142 |
280 |
115 |
318 |
287 |
9001-10000 |
390 |
469 |
141 |
278 |
116 |
318 |
288 |
The Visibility of the New Lunar Crescent on Rosh HaShanah
Rambam, in
Hilchot Kiddush HaChodesh (literally
translates as "The Laws of Sanctification of the New Month") wrote that
the reason for the postponements has to do with the underlying nature of
the mean astronomical calculations that are employed for the
molad, in point 7 of chapter 7, vaguely suggesting that the postponements bring the date of
Rosh HaShanah
closer to the actual lunar conjunction. In the next statement, however,
he contradicted himself by hinting that the postponements increase the
likelihood that the lunar crescent will be visible at sunset at the
beginning of
Rosh HaShanah (point 8 of chapter 7). These
attributes are mutually exclusive. The actual lunar conjunctions precede
the visible new lunar crescent by 1 to 3 days. If the postponements
were to bring
Rosh HaShanah closer to the actual lunar
conjunction then they would have to decrease the probability of
observing the new crescent on the holiday. On the other hand, if they
were to increase the likelihood of observing the new lunar crescent on
Rosh HaShanah
then that could only be accomplished by delays relative to the actual
lunar conjunctions. Astronomical analysis of the visible crescent
frequencies on
Rosh HaShanah will reveal which of these alternatives is correct, as follows:
I used the computer algorithms for the lunar cycle, solar longitude, and visible crescent criteria from "
Calendrical Calculations"
by Nachum Dershowitz and Edward M. Reingold, third edition published in
2008 by Cambridge University Press, hereinafter referred to by the
mnemonic
CC3, plus some algorithms from "
Astronomical Algorithms" by Jean Meeus, second edition, published in 1998 by
Willmann-Bell, Richmond, Virginia, USA.
Lunar crescent visibility varies with weather conditions, clouds,
atmospheric dust and clarity (especially in the westerly direction),
temperature, humidity, nearby and westerly light pollution, and local
elevation with unobstructed view of the horizon. Astronomically it
depends on the apparent lunar size and brightness,
elongation
from Sun, and altitude above the horizon at sunset. Human factors
include observer maturity, truthfulness, sanity, visual acuity and
stereoscopic perception, iris pigmentation and pupil diameter,
experience and preparation, and the use of optical aids such as
telescopes or binoculars.
It also helps a lot to know exactly when and where to look, and then
to actually look at the correct position in the sky! When the new lunar
crescent is very dim, it may be visible only to more light-sensitive
peripheral vision, rather than the sharpest central color vision. In
such cases, it might be seen only when one looks slightly askance of its
position, then away, then back again.
The probability of false sighting for a typical observer has been
estimated at 15%, hence observational calendars that depend on a few
positive sightings from a large number of observers will almost
invariably start early by mistake. False sightings can, however, be
refuted if the Moon was actually below the horizon or ahead of the
actual lunar conjunction at the moment when it is claimed the new lunar
crescent was seen. If the moment of the actual lunar conjunction is
known to good accuracy (better than ±1 minute is easy to calculate),
then testimony claiming a sighting less than 18 hours later is highly
doubtful.
For the prediction of the visibility of the new lunar crescent I use the following mathematical criteria as recommended by
Dershowitz & Reingold in CC3, as implemented in their
visible-crescent function:
- for the locale of Jerusalem, Israel, compute the moment when the
mid-point of Sun is 4.5° below the western horizon, so that the western
sky is dark enough for possible observation of the new lunar crescent;
- at that moment, if Moon hasn't passed its solar conjunction, then it will be impossible to see a new lunar crescent;
- for that moment, compute the arc-of-light from the geocentric mid-point of Sun to the geocentric mid-point of Moon (the "elongation"
of Moon from Sun as if viewed from the center of Earth) — if the
arc-of-light is less than 10.6° then the crescent probably won't be
visible;
- for the same moment, compute the lunar altitude (above
the western horizon) — if Moon will be less than or equal to 4.1° above
the horizon, then the crescent probably won't be visible, even if the
arc-of-light is sufficient.
Using the above criteria, the absolute minimum elapsed time between
actual lunar conjunction and first visibility of the new lunar crescent
at sunset in Jerusalem is about
3/
4 day. Published crescent visibility reports, such the records of the
Israeli New Moon Society available at <
http://sites.google.com/site/moonsoc/sightings>,
rarely document reliable sightings any earlier than 24 hours after
conjunction, even with optical aids. Therefore the above criteria are
probably optimistic and applicable to ideal observing conditions.
The above criteria ignore the apparent lunar diameter (Moon can appear up to 25% larger at closest
perigee than at furthest
apogee), and the
CC3
algorithms ignore atmospheric refraction and lunar parallax when
calculating the lunar altitude. When Moon is near the horizon,
atmospheric refraction makes the apparent lunar position as seen from
the surface of Earth (
topocentric position) about
1/
2 degree higher than its position as calculated for the center of Earth (
geocentric
position), and lunar parallax makes Moon appear about 1 degree lower,
so the net effect of atmospheric refraction and lunar parallax will make
Moon appear about
1/
2 degree lower than I calculate. This partially accounts for "optimistic" crescent predictions.
Using the above methods and criteria I computed when the lunar
crescent ought to be visible from Jerusalem at sunset at the beginning
of the first and second days of
Rosh HaShanah (
click here or on the graphs below to view a high-quality PDF 91KB):
For the present era, the crescent ought to be visible from Jerusalem at sunset on the first day of
Rosh HaShanah in only about
1/
6
of years, but this proportion will more-or-less steadily increase in
coming years, reaching 50% of years a few centuries after the year
10000.
Of the visible crescents, most occur in years where Rosh HaShanah is delayed by two days, and the new lunar crescent will never be visible when Rosh HaShanah is not postponed — at least not until beyond the year 9000.
Naturally, the crescent is much more likely to be visible at sunset on the second day of
Rosh HaShanah: in almost
2/
3
of all years at present (increasing to almost 90% of years by year
10000), including almost all two-day postponement years, almost
2/
3 of the one-day postponement years (increasing to almost all such years by year 10000), and more than
1/
4 of the non-postponed years (increasing to almost
3/
4 of such years by year 10000).
Even though the postponements of
Rosh HaShanah do make it more
likely that the new lunar crescent will be visible, it would be hard to
defend any claim that that was an original consideration in the
development of the postponement rules, because in the era of Hillel ben
Yehudah the crescent ought to have been visible on the first day of
Rosh HaShanah
in only about 16% of years (although they should have seen the crescent
in more than 60% of years on the second day of the holiday).
Furthermore, they would not have known that the crescent would more
often be visible in distant future years.
In comparing actual lunar conjunctions to the moments of the traditional molad, where the molad
is expressed in the traditional manner as the number of hours since
sunset, which I call "Talmudic Temporal Time", it is necessary to
subtract 6 hours from the molad moment so that it is in terms of the civil time used for the actual lunar conjunctions.
The reason for the distant future increases in crescent visibility is that the
molad interval is now
2/
3 second longer than the actual mean duration of lunations (
mean synodic month). The mean synodic month is continuing to get shorter at a steady rate of about
1/
3 mean solar second per thousand years, due to
tidal slowing of the Earth rotation rate, which was not recognized until the beginning of the 20th century and then was accurately measured only after the advent of
Atomic Time (1955) and
Laser Lunar Ranging (1969). This progressive shortening of the mean synodic month is causing an accelerating lateward drift of the
molad, such that future
moladot will occur at progressively later moments with respect to the actual mean
lunar conjunctions. In the era of
Hillel ben Yehudah (Hebrew year 4119 = Julian 358 AD), the
molad of
Tishrei was about 4+
1/
5 hours later than the actual mean lunar conjunctions. In the present era that
molad is about 6 hours late. By year 8000 it will be 11+
3/
4 hours late, and by year 10000 it will be about 21+
1/
3 hours late. The probability of the crescent being visible on
Rosh HaShanah (or on any
Rosh Chodesh, especially for months that follow a postponed
Rosh HaShanah) progressively increases as the
molad gets later and later with respect to the actual lunar conjunctions. Please see my analysis of the
molad drift, what is causing it, how it varies between months and over the years, and what can be done to adjust the
molad arithmetic, presented on my
Hebrew Calendar Studies web page at <
http://www.sym454.org/hebrew/>.
The Net Effect of the Rosh HaShanah Postponements
During the development of the
Rectified Hebrew Calendar, I experimented with allowing
any month to have 29 or 30 days, whichever yielded the best alignment relative to the
molad.
I then compared the date agreement against the Traditional Hebrew
Calendar, and found that the best agreement was obtained by adding 24
hours to the
molad moments used for the
Rectified Hebrew Calendar, and this offset was optimal for both the traditional
molad and the
progressive molad. This observation suggests that the
net effect of the
Rosh HaShanah postponements, on average, is the equivalent of delaying month starts by 24 hours relative to the
molad moment. This is an interesting observation, because in the present era,
as mentioned above,
the earliest time that the new lunar crescent can be seen is 24 hours
after the actual lunar conjunction. I therefore conclude that the net
effect of the
Rosh HaShanah postponements is to prevent the old
lunar crescent from still being visible when a month starts, and to
enhance the likelihood that the new lunar crescent will be visible when
months start (but not before it starts).
Obviously there are exceptions to this average net effect, because
the nominally alternating 29- or 30- day fixed month lengths of the
Hebrew Calendar can get "out of phase" with respect to the actual lunar
conjunctions, especially when there are 3 deficient or full months in a
row (when
Cheshvan and
Kislev are either both deficient 29-day or both full 30-day months), and there is the superimposed ±14 hours of
periodic variability of the actual lunar conjunctions relative to the secular mean lunar conjunction moments. (The word
secular, derived from the Latin
saeculum, in this context refers to a variation that spans centuries, that is the progressively shorter
mean synodic month).
When people first study the traditional Hebrew calendar, they are always surprised to learn that the traditional
molad moments that are announced during the Sabbath morning synagogue services prior to the start of each new month (except
Tishrei) actually have nothing to do with the Hebrew calendar itself, for it is only the
molad of
Tishrei that has any relevance to the calendar. Most people mistakenly belief that months start on the day of the
molad, or on the day after the
molad, but that would have required allowing any month to have 29 or 30 days.
The establishment of fixed lengths for most Hebrew calendar months was a major side-effect of adopting the Rosh HaShanah postponement rules, because allowing 2-day postponements of
Rosh HaShanah created a constraint precluding variable month lengths, for otherwise such a postponement could have extended the month of
Elul to 30 or 31 days with truncation of the following
Tishrei to 29 or only 28 days!
http://individual.utoronto.ca/kalendis/hebrew/postpone.htm
BIBLICAL NEW MOON CALENDAER
http://www.everlastingkingdom.info/article/115/
Summary
The molad zakein rule prevents any molad
moment from landing after the first day of any calendar month, the
disallowed weekday postponement rule serves ritual convenience, and the
3rd and 4th rules prevent impossible year lengths that would otherwise
be caused by the effect of the molad zakein rule on Rosh HaShanah of the prior or coming year, respectively. The net effect of the Rosh HaShanah postponement rules is to cause months to start on average one day after the molad moment. The establishment of fixed lengths for most Hebrew calendar months was a major side-effect of adopting the Rosh HaShanah postponement rules. |