Definition of New Moon

In astronomical terminology, the phrase new moon is the lunar phase that occurs when the Moon, in its monthly orbital motion around Earth, lies between Earth and the Sun, and is therefore in conjunction with the Sun as seen from Earth. At this time, the dark (unilluminated) portion of the Moon faces almost directly toward Earth, so that the Moon is not visible to the naked eye.

The original meaning of the phrase new moon, by man, (or Jewish reasoning) was the first visible crescent of the Moon, after conjunction with the Sun. This takes place over the western horizon in a brief period between sunset and moonset, and therefore the precise time and even the date of the appearance of the new moon by this definition will be influenced by the geographical location of the observer. The astronomical new moon, sometimes known as the dark moon to avoid confusion, occurs by definition at the moment of conjunction in ecliptic longitude with the Sun, when the Moon is invisible from the Earth. This moment is unique and does not depend on location, and under certain circumstances it is coincident with a solar eclipse.

## Determining new moons: an approximate formula

The time interval between new moons—a lunation—is variable. The mean time between new moons, the synodic month, is about 29.53... days. An approximate formula to compute the mean moments of new moon (conjunction between Sun and Moon) for successive months is:

$d = 5.597661 + 29.5305888610 \times N + (102.026 \times 10^{-12})\times N^2$

where N is an integer, starting with 0 for the first new moon in the year 2000, and that is incremented by 1 for each successive synodic month; and the result d is the number of days (and fractions) since 2000-01-01 00:00:00 reckoned in the time scale known as Terrestrial Time (TT) used in ephemerides.

To obtain this moment expressed in Universal Time (UT, world clock time), add the result of following approximate correction to the result d obtained above:

$-0.000739 - (235 \times 10^{-12})\times N^2$ days

Periodic perturbations change the time of true conjunction from these mean values. For all new moons between 1601 and 2401, the maximum difference is 0.592 days = 14h13m in either direction. The duration of a lunation (i.e. the time from new moon to the next new moon) varies in this period between 29.272 and 29.833 days, i.e. −0.259d = 6h12m shorter, or +0.302d = 7h15m longer than average.[4][5] This range is smaller than the difference between mean and true conjunction, because during one lunation the periodic terms cannot all change to their maximum opposite value.

See the article on the full moon cycle for a fairly simple method to compute the moment of new moon more accurately.

The long-term error of the formula is approximately: 1 cy2 seconds in TT, and 11 cy2 seconds in UT (cy is centuries since 2000; see section

What are Postponements:

The Jewish Calendar's Postponements

Before we proceed naively to assume that any given month of the common calculated Jewish calendar actually begins on the day of its molad, it is imperative to introduce the matter of the four dehiyyot, commonly referred to as “rules of postponement.”

Acknowledging that “Tishri 1…is rarely the day of the molad,”  the Encyclopaedia Judaica mentions that “there are four obstacles or considerations, called dehiyyot, in fixing the first day of the month (rosh chodesh) [of Tishri].  Each dehiyyah defers Rosh Ha-Shanah by a day, and combined dehiyyot may cause a postponement of two days…”[21]

U.S. Naval Observatory astronomer Doggett summarizes the four dehiyyot [postponements] as follows:

• (a)  If the Tishri molad falls on day 1 [Sunday], 4 [Wednesday], or 6 [Friday], then Tishri 1 is postponed one day.
• (b)  If the Tishri molad occurs at or after 18 hours (i.e., noon), then Tishri 1 is postponed one day.  If this causes Tishri 1 to fall on day 1, 4, or 6, then Tishri 1 is postponed an additional day to satisfy dehiyyah (a).
• (c)  If the Tishri molad of an ordinary year (i.e., of twelve months) falls on day 3 [Tuesday] at or after 9 hours, 204 halakim [at or after about 3:11 a.m.], then Tishri 1 is postponed two days to day 5, thereby satisfying dehiyyah (a).
• (d)  If the first molad [the Tishri molad] following a leap year falls on day 2 [Monday] at or after 15 hours, 589 halakim  [at or after about 9:32 a.m.], then Tishri 1 is postponed one day to day 3 [Tuesday].[22]

Since the calculated Jewish calendar is fixed according to a pre-established pattern, the dates during the remainder of each year are dependent upon whatever dates have been established for Tishri 1 of the current and immediately subsequent year.

Various explanations for the postponements have been offered by Jewish leaders at various times.   Writing in the 12th century CE, Maimonides, the renowned medieval Jewish Rabbanite authority also known as the Rambam, proclaimed “if the [molad] occurs in one of these four instances [Rosh HaShana] is not established on the day of the [molad], but rather on the day that follows, or on the day following that, as explained.”[23]

However, in contrast to the erudite quality of much of his work, aspects of Maimonides’ explanation for the four postponements were both fanciful and contrived.  Maimonides posed:  “Why is [Rosh HaShana] not established [on the day of the molad] when it falls on Sunday, Wednesday, or Friday?  Because these calculations determine the conjunction of the sun and moon only according to their mean [rate of] progress, and do not [necessarily] reflect the true position [of the sun and moon in the celestial sphere], as explained.  Therefore, they instituted that [on] one day [Rosh HaShana] would be established and on the following day it would be postponed, so that they would ascertain the day when the true conjunction takes place…. This same principle, that the calculations are based on the mean rate of progress, is also the motivating factor for the other [of the] four reasons for the postponement.”[24]

Of course, Maimonides’ suggestion as to the “motivating factor” for the postponements is nonsensical.  As students of astronomy are well aware, the true lunar conjunction is not confined to any particular days of the week.[25]

Nonetheless, we find Eliyahu Touger, a modern Jewish scholar of some repute, suggesting: “In defense of the Rambam’s position, it must be noted that both earlier (Rabbenu Chanan’el) and subsequent (the P’nei Yehoshua) Talmudic commentaries understood the reasons given by the Talmud as being merely the external dimension for the calendar’s adjustment, while the inner meaning is associated with the actual position of the sun and the moon in the heavenly sphere.”[26]

Yet the facts force Touger to the admission that “even according to this perspective, there is, however, a difficulty with the Rambam’s statements.  Although it is correct that the true positions of the sun and the moon often differ from the position determined by calculating their mean movement, the concept of postponing the celebration of Rosh HaShanah on these three days appears arbitrary and without any obvious connection to the movement of these bodies in the celestial sphere.”[27]

Touger also points out that, differing from Maimonides’ rationale for the postponements, “the Talmud states that if Rosh Hashanah falls on either Wednesday or Friday, Yom Kippur will fall on either Friday or Sunday, and thus there would be two consecutive days, Yom Kippur and the Sabbath, when it would be forbidden to bury the dead.  In the Talmudic era, this could have caused a corpse to deteriorate, detracting from its honor and respect.”[28]

“Alternatively, the Sages [sic] state that if Rosh Hashanah fell on any of these three days, there would be two successive days when it would be forbidden to pick fresh vegetables, and the people would be unable to celebrate the festivals or the Sabbath properly.”[29]

Here again, we find inconsistent excuses for calendaric postponement.  Although the Talmudic "Sages" (at Rosh HaShana 20a) were purporting to prevent the perceived  “emergency” of  “the case of a festival which comes just before or just after Sabbath,” the reality is that the common Jewish calendar continues to allow  such cases with regard to two of the annual festivals – Shavuot (Pentecost) and the Days of Unleavened Bread (its 7th day)!

For example, according to the common Jewish calendar:

·        Shavuot (Pentecost) is routinely allowed to adjoin the Saturday Sabbath.

For those who observe a Sunday Pentecost, yet retain the common calculated Jewish calendar, this irony is profound – because every observance of Pentecost adjoins the weekly Sabbath!

However, even  for the majority of Jews who observe Shavuot on the 6th of Sivan, the observance of Pentecost adjoining the Sabbath, on either Friday or Sunday, is quite common.  A sequence of a few years  to illustrate this incidence shows that in 1998, the 6th of Sivan observance was on Sunday, May 31; in 1999, the observance was on Friday, May 21; in 2000, the observance was on Friday, June 9; in 2002, the observance was on Friday, May 17.

·        The Last Holy Day of Unleavened Bread is routinely allowed to fall on Friday, adjoining the Saturday Sabbath.  As recently as 1998, Nisan 21 (the Last Day of Unleavened Bread) was observed on Friday, April 17th, immediately adjoining the Saturday Sabbath.

Going on, Touger enlarges, “Sukkah 43a gives another reason why Rosh Hashanah is not held on Sunday: were this to be the case, Hoshana Rabbah, the seventh day of Sukkot, would fall on the Sabbath.  In such an instance, restrictions were placed on the willow ritual in the Temple.  (See Hilchot Shofar, Sukkah V’Lulav 7:21-22)  To avoid such an instance, the Sages [sic] structured the calendar so that Rosh Hashanah never falls on Sunday.”[31]

Here we should take note of the fact that the very existence of formulated restrictions for the willow ritual on the Sabbath speaks of a time without postponements.  (If the postponements had always been in place, Hoshana Rabbah, the seventh day of Sukkot, would never have fallen on the Sabbath, so restrictions for this occurrence would never have been needed or implemented.)  Although we find the concept of “forbidden days” mentioned in the Talmud, segments of the Mishnah definitively establish the absence of that rule of postponement during the Second Temple period, which includes the time of Christ.

Another of the several Mishnaic examples establishing the absence of the “forbidden days” rule of postponement, pertains to the offering of the wave omer (or sheaf):  During the Second Temple period, the Jews reaped and processed the wave omer on the 16th of Abib, the day immediately following the first day of Unleavened Bread.   However, an effect of the postponement rules of the common calculated Jewish calendar is to prevent the 15th of Abib – the first day of Unleavened Bread – from occurring on any Friday.  Thus, using the common calculated Jewish calendar of today, the 16th of Abib can never fall on the weekly Sabbath.  Yet in Menachoth 63b, the Mishnah documents discussion of procedures for processing the wave omer on the weekly Sabbath.[32]

The Jewish Calendar's Year

The year, according to the common Jewish calendar, more often than not, consists of 12 months. The ordinary year contains 353, 354, or 355 days and the leap (intercalary) year contains 383, 384, or 385 days.  The months are ordered as follows:[33]

Tishri (Tishri currently begins in September or October. It is the month which contains Rosh Hashannah [New Year’s Day], Yom Kippur [Day of Atonement] , Sukkot [Tabernacles], and Shmini Atzeret [Eighth Day.
Heshvan
Kislev
Tevet
Shevat
(only in intercalary years)
Nisan (Nisan currently begins in March or April. It is the month which contains Passover [including the Days of Unleavened Bread].)
Iyyar
Sivan
(Sivan currently begins in May or June.  It is the month which contains Shavuot [Pentecost].)
Tammuz
Av
Elul
Attempting to maintain correlation with the seasons, a 13th (intercalary) month is regularly added to the common Jewish calendar in a set pattern of intercalation in the years 3, 6, 8, 11, 14, 17, and 19, out of every 19 years.[34]

That pattern of intercalation has its own imperfection, which a Jewish expert has termed “The Rosh Hashannah Drift.”  Thus, we find the Jewish calendar dates for the annual festivals are very slowly shifting later, relative to the seasons.

For example:  In the year 987 AD, the calculated Jewish calendar date for the 1st of Tishri [Rosh Hashannah ] was September 1st.  Yet by 1987 AD– 1000 years later – the 1st of Tishri could fall no earlier than September 5th.[35]

Summary

Through examining the history and the various components of the common calculated Jewish calendar, we have seen that this Jewish calendar represents a significant level of human achievement.  Yet at the same time, this humanly-devised calendar seems unnecessarily complex.  Moreover, in several respects, it is significantly flawed in the execution of what it purports to achieve.  In other words, this calendar reflects both the strengths and the weaknesses of its human creators.

On the other hand, God tells us that He is consistent.  He is perfect, even in the most complex of situations. God is not limited by the lack of man’s mathematical development.  Any calendaric system revealed divinely by God will bear His signature of perfection.  God’s authorship will never produce less perfection than what man has the ability to independently produce!

God’s invisible attributes, His eternal power and His divine nature are clearly seen, being understood through what He has made.  For example: just look at a flower – any flower – and consider its intricate perfection and its glory.  Then look at the deficiencies of the common Jewish calendar.  We can know at once that this calendar is crafted by imperfect human beings; it simply does not reflect the awesome perfection of the Creator of the universe.

For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse.  (Romans 1:20)

Most importantly, however, we must not accept any system which rejects  any boundaries which God has set in Scripture.  Therefore, with this background, let’s now briefly evaluate the common Jewish calendar in comparison to God’s Scriptural requirements for the calendar.

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