Some Aspects of the Judaic Calendar *glossary contents
|Author:||Dr. Julian Schamroth|
|Date:||6 July, 2006|
The luni-solar Judaic calendar is based on both the lunar and the solar cycle. This article is an overview of some aspects of the solar year.
The tropical year is the time taken by the Sun to complete one circuit of the celestial sphere from its position at one vernal (spring) equinox to the next. The current value is:
365 days 5 hours 48 minutes 45 seconds = 365.24219 days
The Judaic calendar, however, uses two different measurements for the tropical year. These are the "Mar Shmuel" year and the "Rav Adda" year.
The Mar Shmuel Year
According to Mar Shmuel, each season lasts 91 days 7 1/2 hours.  The duration of a tropical year is thus:
4 x (91d 7h 30m) = 365.25000 days
Mar Shmuel, also known as Shmuel Yarchinai, was a prominent Talmudic scholar, physician and astronomer who lived in the third century (165 - 250 c.e.). Although he was no doubt aware of the more accurate duration of a tropical year, he used the less accurate figure of 365 1/4 days since:
The figure of 365 1/4 days is much easier to work with, especially for the general populace who were not proficient in mathematics. The astronomer Ptolemy acknowledged that he too used multiples of 60 in order to avoid dealing with fractions.  Similarly, we find that the Talmud gives a value of 3 instead of pi (3.141592...) for the relation between the diameter and the circumference of a circle. 
As an aside, the value of pi (π) is hinted at in the Bible's description of King Solomon's copper tank: 
And he made the tank of copper ten cubits from brim to brim ...and a line of thirty cubits was its circumference. 
Superficially, it appears that by using the figures 10 and 30, this verse is indicating a value of 3 for pi. However, the Hebrew word for "line" is written קוה, but is read as קו. Now, the numerical value of קוה is 111, and that of קו is 106. Assuming the ratio of 111 to 106 to be the same as the ratio of π to 3, then:
111/106 = π/3
therefore π = 3 x 111/106 = 3.141509
It is thus clear that Mar Shmuel's duration of the year, the value of pi, and other values in the Talmud such as the relation of the area of a circle to its circumscribed square,  were accurately known, but were rounded off to enable easier computations for the performance of the necessary religious precept.
The figure of 365 1/4 days was already being used at that time by the Romans.
The Mar Shmuel year is currently only used for determining when to say the Blessing on the Sun (Birkat Ha'chamah) and the Prayer for Dew and Rain (Tal U'matar).
The Rav Adda Year
According to Rav Adda bar Ahava, the tropical year is defined as one-nineteenth of a 19-year solar cycle. Its duration is given as:
365d 5h 55m 25.4s = 365.24682 days.
The Rav Adda year is about 5 minutes less than the Mar Shmuel year, and is the more accurate of the two systems. It is used for all civil and religious calculations apart from the two prayers mentioned above.
At this point, it is appropriate to compare some aspects of the Christian calendar with the Judaic calendar.
The Julian calendar
The Julian calendar was introduced by Julius Caesar in 46 b.c.e. and, like that of Mar Shmuel, was based on a year of 365 1/4 days. Its structure was as follows:
To correct previous inaccuracies, the year 46 b.c.e. was made to last 445 days... the so-called annus confusionis. That year ran from the 13th of October 47 b.c.e. to the 31st of December 46 b.c.e..
The vernal equinox was set as occurring on the 25th of March at 6:00 p.m. (Since the Hebrew day begins at 6:00 p.m., this date corresponded to the beginning of the 26th of March.)
All future years were to consist of 365 days in a normal year, and 366 days in a leap year.
A leap year would occur every 4th year.
The Julian calendar compares with the tropical year as follows:
In each 1,000 year period, there are:
250 leap years = 250 x 366 = 91,500 days
750 normal years = 750 x 365 = 273,750 days
There are thus a total of 365,250 days every 1,000 Julian years compared with 365,242.19 days every 1,000 tropical years. The Julian year (as does the year of Mar Shmuel) thus gains on the tropical year by:
365,250 - 365,242.19 = 7.81 days every 1,000 years.
The Gregorian calendar
By the year 1582, the Julian calendar was about 10 days ahead of the tropical year, and an adjustment was again necessary. With the help of the astronomer Christopher Clavius, Pope Gregory XIII consequently introduced two adjustments, and the Gregorian calendar, which is still in use today, was established. (The calendar adjustments were promulgated by the Council of Nicaea so that the date of Easter would not coincide with the Jewish Passover.)
These two calendar adjustments were as follows:
Ten days were removed from the calendar in 1582.
This was immediately accepted in Spain, Portugal and Italy. The 5th of October of that year was thus followed by the 15th of October. Riots actually broke out in several European cities since people believed their lives were being shortened by ten days! Germany, Sweden and Denmark accepted the changes in 1700, whereas the Gregorian calendar system was only accepted in England in 1752. By that time, the Julian calendar was 12 days ahead of the tropical year, and the 2nd of September of that year was thus followed by the 14th of September. In Russia, the Gregorian calendar was finally accepted on the 14th of February 1918, by which time 13 days had to be dropped. The Russian Orthodox Church still keeps its ecclesiastical calendar according to the Julian calendar. These points should be borne in mind when consulting very old calendars or dated documents.
A centenary year not divisible by 400 is not a leap year.
The years 1700, 1800 and 1900 are therefore not leap years, whereas the years 1600 and 2000 are.
It follows that the Gregorian calendar is currently 13 days ahead of the Julian calendar (10 days for the initial correction, plus 1 day each for the three "skipped" leap years in 1700, 1800, and 1900). Thus 1st January in the Julian (or Mar Shmuel) calendar corresponds to 14th January in the current Gregorian calendar.
Just how accurate is the Gregorian calendar? In each 1,000 year period there are:
242 leap years = 242 x 366 = 88,572 days
758 normal years = 758 x 365 = 276,670 days
There are thus a total of 365,242 days every 1,000 Gregorian years compared with 365,242.19 days every 1,000 tropical years. The Gregorian year thus differs from the true tropical year by only:
365,242 - 365,242.19 = .19 days every 1,000 years.
Comparison of the Mar Shmuel and Gregorian calendar
According to the Judaic calendar, the vernal equinox currently falls on the 8th of April (or the 7th of April in a leap year), whereas according to the Gregorian calendar it falls on the 21st of March... some 18 days earlier. The 18 day difference arises from:
The current 13 day difference between the Gregorian and the Julian (or Mar Shmuel) calendar. (This comprises 10 days for the initial correction, plus 1 day each for the three "skipped" leap years in 1700, 1800, and 1900.)
The 5 day difference due to Caesar having established the vernal equinox as occurring on March 26th instead of March 21st.
A second way of looking at this 18-day difference is to consider that the Mar Shmuel year gains on the Rav Adda year by:
365.25000 - 365.24682 = 0.00318 days per year
According to Mar Shmuel, the Hebrew year 5760 is thus ahead of the Rav Adda year by:
0.00318 x 5,760 = 18.32 days.
(In the year 2100, this difference will increase by 1 day to 19.63 days: 0.00318 x 5,860 = 18.63, plus 1 = 19.63 days.)
At this point, it is appropriate to briefly consider the Blessing on the Sun and the Prayer for Dew and Rain, both of which are based on the Mar Shmuel year.
Blessing on the Sun (Birkat Ha'chamah)
This prayer is said every 28th year:
The Rabbis taught: Anyone seeing the Sun at its turning point... should say "Blessed is He who made the Creation." And when is this? Abaya said: every 28th year. 
On what is this 28 year cycle based? According to Hebrew tradition, the Sun was placed at the vernal equinox at the beginning of the fourth day of creation (Tuesday at 6:00 p.m.) as derived from the following passage:
And God made the two great luminaries, the great luminary to rule the day... 
Since the Mar Shmuel year lasts 365 1/4 days, or 52 weeks plus a remainder of 1 1/4 days, it follows that after one tropical year, the Sun will return to the vernal equinox, but will fall 1 1/4 days later in the week... or Wednesday at midnight. After a second year, the Sun will return to the vernal equinox, but it will be 2 x 1 1/4 days later in the week... or Thursday at 6:00 a.m. Only after 28 years, will the Sun return to the vernal equinox again at the beginning of the fourth day of the week. The Sages thus used this opportunity to institute a special prayer acknowledging God's might and His creation of the world. This 28-year cycle is called the Great Cycle (Machzor gadol).
The Blessing of the Sun was last said on the 8th of Nissan 5741 (corresponding to the 8th of April 1981). This was the 205th 28-year cycle of the Sun. It will be said again on the 8th of April in the years 2009, 2037, 2065 and 2093. In the 22nd century, the date will advance to the 9th of April for the years 2121, 2149 and 2177. (A detailed analysis, in English, of the Blessing of the Sun may be found in the book Bircas Hachammah. )
Prayer for dew and rain (Tal U'matar)
The prayer for dew and rain is said from the 60th day of the autumnal equinox:
Chanania says: in the Diaspora the prayer for rain is said after sixty days in the season .
According to the Gregorian calendar, the autumnal equinox falls on 23rd September. As explained, the corresponding Mar Shmuel date falls 18 days later on 11th October, and the Prayer for Dew and Rain should thus commence 60 days later on 9th December. The prayer, however, is recited some 4 days earlier... from 5th December (or 6th December in leap years). Why then, the 4 day discrepancy?
According to Mar Shmuel, each season lasts an average of 91 days and 7 1/2 hours (or 91.31 days). However, the elliptical orbit of the Earth results in seasons of differing lengths: summer being about 3 1/2 days longer than winter... a point noted by early Talmudic scholars.  (The Persian calendar takes these seasonal variations into account so that the first day of the 1st, 4th, 7th, and 10th months coincide with the day of the equinoxes and solstices.)
|Season Length: Actual vs. Mar Shmuel|
|Season||Actual Duration (days)||Cumulated Duration (days)||Cumulated Duration (Mar Shmuel)|
|Spring (Mar 21 - Jun 20)||92.84||92.84||91.31|
|Summer (Jun 21 - Sep 22)||93.60||186.44||182.62|
|Autumn (Sep 23 - Dec 21)||89.80||276.24||273.93|
|Winter (Dec 22 - Mar 20)||89.02||365.26||365.25|
From the above Table, it is evident that by the time of the autumnal equinox, on the 23rd of September, the true season is almost 4 days ahead of the Mar Shmuel season (186.44 days - 182.62 days). The Prayer for Dew and Rain is thus not recited on the 9th of December, but 4 days earlier on the 5th of December.
Blessings for other astronomical events
In addition to the Blessing on the Sun and the Prayer for Dew and Rain, a Blessing may be said on sighting comets (cochva d'shavit ) or shooting stars. Comets and their periodicity (i.e., their cyclical re-appearance) were known in Talmudic times. The Talmud relates how Rabbi Ye'hoshua took extra provisions on a sea voyage because:
...once every seventy years a star appears that leads ships astray. 
(Historically, this event does not appear to relate to Halley's comet which has a periodicity of 76.03 years, and could not have appeared at the time when Rabbi Ye'hoshua undertook his voyage. )
I am as familiar with the paths of heaven as with the streets of Nehardea, except for the comet, about which I am ignorant. 
The Talmud says that a blessing should be said whenever zikin are seen.  These could be meteors, or "shooting stars," since zikin are defined as a "kind of star that shoots across the sky like an arrow, from one point to another, and whose light is drawn out in a rod-like line."  An alternative definition of zikin could be comets, or "a star with a tail and a rod of light." 
- Based on Dr. J Schamroth, A Glimpse of Light - A discussion on the Hebrew Calendar and Judaic Astronomy, Targum/Feldheim Press 1998. Submitted by the author.
- B.T. Eruvin 56a
- Ptolemy. Almagest 1:10
- B.T. Eruvin 13b
- Rabbi M Munk. Sinai, Tammuz 5722, p218; also in HaDarom 27 Nissan 5728
- Kings I, 7:23
- Talmud, Tractate Succah 8a
- Hirsch Mendel Piniles, Darkoh Shel Torah (Vienna 1861), p147-150
- J.T. Avodah Zarah 1:2
- B.T. Berachot 59b
- Genesis 1:16
- Rabbi J D Bleich. Bircas Hachammah, Mesorah Publications Inc. (New York), 1980
- B.T. Tractate Ta'anit 10a
- R Isaac Israeli, Yesod Olam VI:11
- B.T. Berachot 58b
- B.T. Horayot 10a
- Brodetsky, Astronomy in the Babylonian Talmud. Jewish Review, May 1911, p72
- B.T. Berachot 58b
- B.T. Berachot 54a
- Shulchan Aruch, Orach Chaim 227
- Mishna Berurah 227