Introduction
Measurement of time by the date, day, hour and minute is a fundamental part of human life. Thanks to modern technology, most of us do not need to make much of an effort to determine the exact time, and as a result, the calendar is something we tend to take for granted.
However, the methodology involved in calibrating any calendar with the astronomical cycles in our Universe is anything but simple. This is true of the secular calendar in respect to the seasons of the year – the 365.2425 days used by the Gregorian calendar for the average solar (tropical) year is not 100% accurate.[1] Similarly, the 24-hour period measured by atomic clocks, used in Coordinated Universal Time, does not correlate exactly to the average rotation time of the Earth.
In both cases, the discrepancies cannot be fully negated just by using a 'more accurate' system (e.g. by adjusting the length of the second or the number of leap years), as the speed of the Earth's rotation is getting gradually slower over time, and also fluctuates due to several unpredictable contributing factors. To mitigate for this, a decision is made every six months as to whether a second must be added on June 30 or December 31. A total of 27 'leap seconds' have been added since 1972.[2]
The halachic day and night are dependent only on the rotation of the Earth (not by any fixed length second or hour), which seemingly avoids any problems caused by changes in the speed of rotation. However, the Jewish calendar also uses lunar (synodic) months, introducing another factor that is extremely difficult to calculate exactly. Here we shall examine some problems that this may cause, and some potential solutions.
The Mean Synodic Month
The interval between new moons varies significantly due to various factors, from a minimum of about 29 days 6 1/2 hours to a maximum of about 29 days 20 hours. Our calendar is based on the average interval (mean synodic month), measured by Chazal as being 29 days, 12 hours and 793 chalakim (there are 1080 chalakim in an hour).[3] The molad (lit. birth) of each month is defined as this interval of time after the molad of the previous month,[4] and the date of Rosh Hashana each year is fixed using the molad of Tishrei of that year.[5]
This measurement of the average interval is extremely accurate. The small discrepancy that does exist today is primarily because the length of the mean synodic month gets gradually shorter over time. The cause of this change is the same factor that causes discrepancies in the secular calendar – the reducing speed of the Earth's rotation.
Even today, Chazal's measurement of the length of the mean synodic month is correct to the nearest chelek (i.e. it is as accurate as it could be using chalakim as the smallest unit of time). Cumulatively, this means that the molad times used today are only around 100 minutes later than they should be.[6] However, using a more accurate mean interval for the molad would affect the date of Rosh Hashana (and therefore of other Yamim Tovim as well) in about 7% of years.[7] This is not a significant problem, as the halachic calendar follows the decisions of the Jewish People and its leaders, even when mistaken.[8]
The Lunisolar Calendar
It is well known that a year consisting of twelve lunar months is roughly eleven days shorter than the solar year, and that the Jewish year sometimes contains a thirteenth month in order to address this imbalance. The Torah says that Pesach is in 'the month of the spring,' Shavuos is the 'harvest festival' and Sukkos is the 'festival of ingathering (of crops)', and this could not be maintained using a uniform year of twelve lunar months.
The extra month of Adar Sheni is therefore added in seven out of every nineteen years. The resulting 235 lunar months in nineteen years produce an average year length of 365.2468 days; the actual solar year is 365.2422 days long.[9] The average discrepancy is about seven minutes per year, or a day every 216 years. Cumulatively, this has caused a seasonal drift of around seven days from the time that the calendar was originally fixed.[10] The spring equinox is astronomically on March 20-21, but by halachic calculations is currently on March 27-28.[11]
This discrepancy is far larger than the 100-minute discrepancy that exists with measurement of the molad. The current effect of it is that three times in nineteen years, an extra month is added a year earlier than necessary in order to keep Pesach in the spring (the original halachic requirement is to ensure that the first day of Pesach falls on or after the spring equinox[12]).
If no intervention is made, this gradual shift will eventually push Pesach into the summer.[13] Although this is not likely to be for thousands of years, I would nevertheless like to discuss a possible mechanism for correcting the small discrepancies. While there is no pressing need to use this mechanism, it is certainly useful to get a better understanding of the halachic authority behind the fixing of the calendar.
Kidush HaChodesh
A clear assumption of Chazal in many places is that beis din declares Rosh Chodesh based on testimony of sighting of the new moon.[14] At some point in history, this practice was discontinued and a fixed calendar was implemented, but there is surprisingly no explicit mention of this in the gemara. The obvious question is who had the authority to make this change, and in general who has the authority to fix the calendar.
There is a broad halachic consensus that once no beis din existed whose members had semicha (rabbinical ordination passed down in an unbroken chain from Moshe Rabbeinu), it was no longer possible to continue declaring Rosh Chodesh based on sightings of the new moon.[15] Thus towards the end of the amoraic period (in the 4th century CE), it was necessary to move to a calendar based on calculations.
The Rambam writes that it is part of the Oral Tradition taught to Moshe at Sinai that when there is a Sanhedrin, Rosh Chodesh is declared based on sighting of the new moon; when there is no Sanhedrin, we must use the calculations in place today.[16] However, even today, only the calculation of the inhabitants of Eretz Yisrael is authoritative. Jews outside Eretz Yisrael may only rely on the knowledge of the methodology used by the community in Eretz Yisrael, and replicate the same calculations.[17]
The perhaps surprising, but clear implication of the words of the Rambam, is that to this day, the Jewish calendar and the yamim tovim are fixed by the word of the Jewish community in Eretz Yisrael. Were we to decide that the algorithm used until today requires updating, we would have the halachic authority to do so, even without the Sanhedrin.[18]
Ramban disagrees with all of this, arguing that it is not possible for those without semicha to have any authority in regards to the calendar.[19] Rather, as semicha was ending, the sage Hillel II (who did have semicha) instituted the fixed calendar and declared all the Roshei Chodashim and leap years until the end of time, in advance.[20]
Thus according to the Ramban, nothing can be done to re-calibrate our calendar until the Sanhedrin is re-established. However, the Ramban's account of the original fixing of the calendar is not accepted by historians. Aside from the gaping omission in the gemara of the fixing of the calendar, a letter of R' Sherira Ga'on attests to a date in the year CE 506 that is impossible according to the fixed calendar of today.[21] This can only mean that our fixed calendar was finalised at a later date, when there was no-one alive with the authority to do so according to the Ramban.[22]
Our conclusion is therefore that it would indeed be possible to re-calibrate our calendar today, even without the Sanhedrin. However, as practically speaking, there is no great need, and establishing a consensus on doing so would be challenging to say the least, it may be better to concentrate our efforts in more pressing need of change.
[1] This
discrepancy is small enough to have been largely ignored. Although a suggestion
has been made to make the system of secular leap years more accurate, this will
only be relevant from the year 4000 CE. See https://en.wikipedia.org/wiki/Gregorian_calendar#Accuracy
[3] Rosh
Hashana 25a. This measurement also appears in non-Jewish ancient sources and it
is unclear who should be credited with its determination, but this is not
important for our purposes.
[4] As
the time used for the molad is based on the average interval, the molad is
sometimes known as מולד האמצעי (the average molad), in contrast to the מולד
האמיתי (the true molad), which
has no halachic significance.
[5] Rosh
Hashana is either on the day of the molad or on one of the two subsequent days,
following an algorithm codified by the Rambam in Hilchos Kidush HaChodesh,
chapter 7 (the definition and calculation of the molad are explained in chapter
6).
[6] This
discrepancy is increasing at around three hours in 2,000 years. Due to the
reducing Earth rotation speed, the rate of increase in the discrepancy is
itself increasing.
[7] By my
calculations, the last time this would have happened would have been in the
year 5766 / CE 2005 (Rosh Hashana would have been on a Monday instead of a
Tuesday). It would happen again in 5789 / CE 2028 (Rosh Hashana would be on a
Tuesday instead of a Thursday) and the following year (Rosh Hashana would be on
a Shabbos instead of a Monday).
[8] See
Rosh Hashana 25a. Who exactly has the power to decide, and how this applies in
our times, will be discussed below.
[9] The
average year length produced by the Jewish calendar is thus more accurate than
that produced by the Julian calendar (365.25 days), used by the secular world
until 1582, but less accurate than the average year length produced by the
Gregorian calendar (365.2425 days). It is interesting to note that were we to
update the mean molad interval to a more accurate measure, correcting the
inaccuracy in measuring the lunar months, the Jewish calendar would produce a
mean year length of 365.2426 days and the inaccuracy of the current lunisolar
calendar would also be virtually eliminated.
[10] The
length of the solar year, measured in solar days (the rotation time of the
Earth), has not changed significantly over this time (the length measured in
fixed length seconds has changed by a similar degree to the change in the
length of time taken for the Earth to rotate).
[11] These
halachic calculations are codified by the Rambam in Hilchos Kidush HaChodesh,
chapter 9.
[12] Rosh
Hashana 21a. It should be noted that our fixed calendar does appear to allow
for a small breach of this rule on rare occasions. In the year 5773 (CE 2013),
the first day of Pesach was on March 26, the day before the halachic equinox
(the next recurrence is in 5849 / CE 2089). The Meiri explains that ensuring
Pesach falls in the spring is only a strict requirement when Sanhedrin are
ruling on each month in its time, based on testimony of sighting of the New
Moon. Now that we have a fixed calendar, it is only necessary to ensure that
the calendar stays approximately in sync with the seasons of the year
(Sanhedrin 13a). However, see also Yad Rama there (13b), who reinterprets the
gemara to mean that only the first day of Chol Hamoed need be on or after the
equinox.
[13]
Chazal did not define when the 'spring' ends, but there clearly is significant
leeway. Before the calendar was fixed, the extra month could be added for a
variety of reasons, even when there was no danger of Pesach being before the
spring.
[14] See Rosh
Hashana 22a-26a.
[15] The
Rambam writes that the power to declare Rosh Chodesh in this manner lies solely
with the Sanhedrin, or with another beis din in Eretz Yisrael delegated by the
Sanhedrin (Kidush HaChodesh 5:1). Ramban agrees that this was true while the
Sanhedrin existed, but argues that in times when there is no Sanhedrin, any
beis din comprising of three people with semicha may declare Rosh Chodesh. If
no such beis din exists in Eretz Yisrael, a beis din with semicha outside Eretz
Yisrael may declare Rosh Chodesh based on testimony (Sefer Hamitzvos, Asei
153).
[16] Kidush
Hachodesh 5:2
[17]
Ibid. 5:13. See also Sefer Hamitzvos (Asei 153), where the Rambam adds that
were it possible for Eretz Yisrael to become empty of Jews, the calculations
would be of no use and we would not be able to fix months and years outside
Eretz Yisrael.
[18] One
could argue that the traditional method of calculation in its entirety is part
of the Oral Tradition, and that we therefore must not deviate from it. To me it
seems improbable that Hashem would have taught Moshe an imperfect system, and
it is far more likely that the Oral Tradition was more generic, teaching us
that human calculation is to be used when there is no Sanhedrin. Even if I am
wrong and we are commanded to stick to the old system, it does seem clear that
if we did decide to make a change, ipso facto this change would be halachically
binding.
[19] He
also has a historic objection to the Rambam's view, based on midrashim that
state that for a period after the destruction of the first Beis HaMikdash,
there was no community in Eretz Yisrael. However, it would appear that this
difficulty can be reconciled easily. The Rambam also agrees that if a great man
was exiled, leaving no-one of his stature in Eretz Yisrael, he can make a beis
din in his place and declare Roshei Chodashim (based on testimony of sightings
of the new moon) and leap years (Kidush HaChodesh 1:8).
[20]
Sefer Hamitzvos, Asei 153. The attribution of the fixing of the calendar to
Hillel is first found in a responsa of Rav Hai Gaon quoted in Sefer Ha'Ibur
(Ma'amar 3, Sha'ar 7); Rambam writes that this change was made in the days of
Abaye and Rava (Kidush HaChodesh 5:3), contemporaries of Hillel II.
[21] At
the end of the section about the savoraim, he writes that Rav Achai bar Rav
Huna died on Sunday, Adar 4 of year 506 (he records this as the year 816, based
on the Seleucid calendar in use at the time). According to the system in place
now, this date would have been a Monday. If it were a Sunday then Pesach of
that year would be on a Friday and the following Rosh Hashana would be on a
Sunday, in violation of a basic rule of our calendar.
[22]
Although the Rambam also writes that the switch to a fixed calendar happened
earlier, it is quite possible that the original fixed calendar did not have the
same rules as today's calendar, and these were added or edited over time.
