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DanielBanner

In the fourth year of King Darius, the word of the LORD came to Zechariah
on the fourth day of the ninth month, which is Chislev… – Zechariah 7:1

So the king's scribes were called at that time in the third month
(that is, the month Sivan), on the twenty-third day… – Esther 8:9

 

Introduction

In my last article, “The Hebrew Calendar of the Second Temple Era,” I wrote near its conclusion:

In certain ways the ancient Babylonian calendar more closely approximates what the Jews followed up to the fall of the Temple in AD 70. But, lacking firm evidence the Jews of that period ever followed the 19-year intercalation pattern that undergirds the ancient Babylonian calendar, the Metonic Cycle of the Greeks, and the modern calculated Hebrew calendar, we cannot simplistically equate any of these with the Jewish calendar before the first century AD.

As I was wrapping it up, I was intrigued to receive an email from an online acquaintance, Charles Murphey. He invited me to take part in a discussion on Academia.com on a paper he wrote, “The Reconstructed Jewish Calendar of the Late Second Temple Period." This invitation held out the possibility of gaining fresh insights on the Hebrew calendar I had just spent several weeks investigating.

The result was two weeks of intensive online interactions with Murphey and a handful of other discussion participants. Murphey sought to answer this question: “Can the Calendar employed by the Jewish Leadership during the late Second Temple Period be reconstructed?” His aim was to delve into the Talmud for insights into the structure of the Jewish calendar around the time of Christ. This approach was different from mine, which paid no attention to rabbinical sources. Instead, I endeavored to figure out from Scripture, historical data in Parker and Dubberstein’s Babylonian Chronology 625 B.C.–A.D. 75 (henceforth “P&D,” accessible online HERE), astronomical data from NASA astronomer Fred Espenak on the Astropixels.com website (http://astropixels.com/ephemeris/phasescat/phases-0099.html and http://astropixels.com/ephemeris/phasescat/phases0001.html), and data previously posted on the United States Naval Observatory website, what the Jewish calendar probably looked like in Jesus' day. These investigations suggested a way to equate the Jewish calendar and that of the Babylonians.

Parker and Dubberstein cover

It turned out that, although Murphey and I took different approaches, we shared a dependence on objective astronomical data to anchor our conclusions, resulting in our different paths leading to remarkably similar results. In fact, the calendars we devised differed in only one year out of a regular cycle of 19! This may not seem like much of a difference, but it results in different patterns of leap years – intercalary years – which impacts how similar the Babylonian and Jewish calendars were. This in turn affects whether certain years can be considered candidates for the crucifixion.

In this article I will describe how I approached this search for the original Hebrew calendar, its findings, how they differed from Murphey’s results, and their implications.

Preliminary Understandings

I undertook this study with a number of preliminary understandings based on Scripture passages and certain articles I had read. Some essential background is covered in the “The Hebrew Calendar of the Second Temple Era,” so I would ask the reader to check it out if anything written below is hard to understand.

1 – The original Hebrew calendar, ordained by God during the exodus, predated by centuries the similar lunisolar Babylonian calendar. The latter carried over into the Persian/Achaemenid and Seleucid eras. The Hebrew calendar’s roots are given in Exodus 12:2: “This month [when the exodus began in 1446 BC] shall be the beginning of months for you; it is to be the first month of the year to you.” It follows that we cannot speak of the later Jews copying the Babylonian calendar, though many assume this. The Hebrew calendar predated that of the Babylonians by centuries. This original calendar of the Hebrews used no names for its months, simply numbering them from first through twelfth month, with a thirteenth month used as needed to keep the first month aligned with the arrival of spring.

2 – The Hebrew calendar was originally based on visual observation of the light-connected cycles of the sun and moon. God says in Genesis 1:14, “Let there be lights in the expanse of the heavens to separate the day from the night, and let them be for signs [Heb. 'owth; in this context, meaning regular tokens or indicators for time-keeping] and for seasons [Heb. moedim, “appointed times” the Hebrews were to observe] and for days and years…” The sun defined each day of 24 hours of alternating darkness and light. By cycling through a changing arc through the sky that progressed from south to north (the winter and summer solstices) and back again, it also defined the solar year. The light of the moon defined the start and end of each month, measured from one observed thin crescent moon to the next. We call this a lunation, which lasted 29 or 30 days. Although the modern Hebrew calendar uses calculations, from the beginning this was not so; the ancient Hebrews did not have the requisite astronomical knowledge, nor did they have a Temple to organize things around. So if we would follow Scripture, we cannot depend on rabbinical calculations. Actual observation of the behavior of the sun and moon was key.

3 – The primary significance of the Hebrew term abib in Scripture is to spring, not barley. Deuteronomy 16:1 says, “Observe the month of Abib and celebrate the Passover to the LORD your God, for in the month of Abib the LORD your God brought you out of Egypt by night” (NASB). In my previous article on the Hebrew calendar I wrote:

The term abib, as used in Scripture, refers to a descriptive characteristic of the lunation that marked the start of the year. That characteristic was the greenness of new vegetation generally, not of barley specifically; barley only comes into the picture in terms of the food crop spring was known for. The Jewish website Chabad.org recognizes this when it says that the Hebrew word abib translates as “spring.” … The oft-made association of “abib” with immature, still-green barley is a derived one, not the primary meaning of the word. It is not about barley per se, but about the season of spring in which the grain’s heads green up and fill out.

I also commented there,

Deuteronomy 16:1 ties in with this way of looking at the relationship between spring and the first month/lunation of the Jewish year. It says the Hebrews were to “observe” (Heb. šāmar, שָׁמַר) the “month” (Heb. chodesh, חֹדֶשׁ, the lunation) of abib (spring). Although chodesh is often equivalent to our word “month,” it also can refer specifically to the crescent new moon that starts a month. The verse can thus be read, “take note of the new moon at the time of spring greening.” The lunar crescent that marked the start of the Jewish year had to be that which fell in the spring.

During the forty years of wandering in the wilderness, there was no organized agriculture; the wandering Jews ate manna. Leviticus 23:10 states, “When you enter the land which I am going to give to you and reap its harvest, then you shall bring in the sheaf of the first fruits of your harvest to the priest.” Without agriculture or first fruits wave-sheaf offerings until after the entry into the Promised Land, there was no cause during those years to watch for barley to reach the abib state of green ears. The suggestion that messengers could have gone from Egypt to Canaan to search for barley as the marker of spring (cf. https://www.karaite-korner.org/abib_faq.shtml#abib_in_the_desert) makes little practical sense, and more so in the historical situation the Jews found themselves in during the exodus. They were to stay together and follow the LORD’s pillar of cloud and fire wheresoever it led (Num. 14:14, Neh. 9:12), so they would not have sent out messengers to go barley-hunting in Canaan. The arrival of spring in the Sinai wilderness would logically have been tied not to barley maturity but to other plants that greened up at the same time after spring rains, including wildflowers and the leafing-out of deciduous trees. The significance of the abib green-ear stage of barley lay in that it was an Egyptian crop (destroyed by the plague of hail, Ex. 9:31) which the ancient Hebrews would have connected with the start of spring. There would surely have been other similar indicators in non-crop plants which would have indicated the arrival of spring during the wilderness wanderings. In short, the “month of Abib” meant “the month of spring.” (It is unfortunate that the NASB translators chose to capitalize abib, for it was not a month-name in either the Egyptian or Hebrew languages.)

4 – The early Hebrew calendar paid no attention to the vernal equinox. This matter was covered in some detail in the previous article, especially under “Defining ‘Spring’.” After 500 BC the Babylonians settled on a pattern of intercalations that invariably placed their Nisanu 1 on or after the vernal equinox, usually the Julian date March 23. But the Jews did not do likewise; their choice of which lunation to call Nisan had always been tied to the greening-up of spring, without reference to the equinox. The Jews’ determination of Nisan apparently remained largely independent of Babylonian and Greek influence until the second century AD, when the Talmud reflects that the Jewish leadership, apparently influenced by Hellenistic Greek astronomy, began to redefine the Hebrew term tekufah from its Old Testament meaning “circuit” to a more technical meaning “equinox” (discussed in the previous article under “Significance of the Tekufah”; see also https://karaite-korner.org/abib_and_tekufah.shtml). For this reason we cannot assume the Jews before that time used the vernal equinox to define spring. Instead, they used practical observation of growing vegetation – principally the barley crop after entering Canaan – to decide when spring had come, then assigned Nisan to the first lunation after that. (There is Talmudic evidence that the Jewish leadership during the first century AD allowed pragmatic considerations of facilitating Temple worship to influence when Nisan was started, but this seems not to have been related to the vernal equinox.) By starting with the apparent greening-up of plants, they guaranteed that the Passover and wave sheaf of first fruits would always take place when the spring harvest was ready.

Nor does it mean that closeness of a first sighted lunar crescent to the vernal equinox originally had any bearing on defining Nisan. First the external signs that spring had arrived were observed, then the date of the next lunation – the next observed crescent moon – was defined as Nisan 1. It therefore made no difference how close this lunation was to the vernal equinox. The Jews used the observed heavenly Lights of God to arrange their months and years, subject to Nisan beginning in the spring when things began greening up, including – but not limited to – the barley crop. Hence, for centuries the vernal equinox was a non-factor; what mattered was whether the greening-up of spring had arrived, regardless of whether the date of the first lunation of spring was closer to the vernal equinox than the subsequent lunation.

5 – The original Hebrew calendar introduced in Exodus 12 did not depend on the fall “appointed times” to define that calendar. If the beginning of the year was properly set with Nisan starting in observable spring, then just as this resulted in the first fruits being ready by Passover, it also followed that the fall harvest would be gathered in and properly celebrated in Tishri. Derek Davies wrote on his Century72.com Bible Calendar website (https://century72.com/the-bible-calendar-part-ii under “What the Jewish captives in Babylon remembered”):

The day that starts the seventh month is now called “Rosh Hashanah.” This phrase means “the head of the year” or “the beginning of the year.” But when that calendar was first used, some time after the destruction of the temple in the year 70, and before the calculation was disclosed in the year 358, the first month was still seen as the start of the year.

Just as Scripture indicates the Jews originally ignored the vernal equinox, they likewise paid no attention to the autumnal equinox. This is why the approach discussed in this article takes no thought for the date of Tishri, for Scripture itself does not, regardless of the later practices of Jewish leaders. It was not until long after the exodus that they – not God! – decided to make the seventh month the first month of the secular year. In short, since the seventh month followed directly from the first month’s placement, if the first month was properly set for the spring harvest, then the seventh would fit into its proper place automatically for the fall harvest.

6 – The Jewish calendar, by defining spring as the season of greening-up, sometimes assigned Nisan to the lunation before that of the Babylonian calendar, which defined spring by the vernal equinox. The Babylonians did not observe defined “appointed times” related to the maturity of crops like the Jews did, so they had no problem arbitrarily defining “spring” in reference to the astronomical equinox rather than the readiness of crops for harvest. This meant the Jewish calendar sometimes applied Nisan to the lunation prior to the Babylonians’ Nisanu. This difference in when the first month was observed impacted which years had 13 months, and must be taken into account when determining how to correlate the two calendars.

7 – The Jewish calendar did not follow the Babylonian calendar in intercalating a second Ululu-II once every 19 years. It only intercalated a year – added an extra month to it – by inserting an Adar-II as Month 13 as needed to stay in sync with spring, and did so not only in the years when the Babylonians included an Addaru-II, but also when they added an Ululu-II in Metonic cycle (MC) Year 17. That this was how the Jews would have dealt with Ululu-II years is seen in the Babylonian calendar in 446 and 427 BC. Whereas the settled intercalation pattern of the Babylonians would normally have inserted an Ululu-II at mid-year in MC 17, under the Achaemenid Persian ruler Artaxerxes I an Addaru-II at the end of those years was used instead. The next table, adapted from P&D, shows that after 465 BC there were two 19-year cycles where MC 17 skipped using an Ululu-II, instead pushing the September lunation into Tashritu (Jewish Tishri) and intercalating those years with a year-ending Addaru-II. After this two-cycle hiatus under Artaxerxes I, Ululu-II intercalations resumed in 408 BC. (The red numbers in the far right column of the table show the Babylonians' repeating 2-2-1-2-2-2-1 pattern of non-intercalated years starting with their MC 1, to be discussed in the next section.)

DANIEL9 PD 466 402 BC

8 – The Jews during the exile used Babylonian month-names alongside their original numbered months, indicating the two calendars were closely related. This can be seen in the books of Zechariah (1:7, 7:1) and Esther (2:16, 3:7, 3:13, 8:9, 8:12, 9:1), where months are given with both the original Jewish numbered-month designation and the corresponding Babylonian name. This indicates the two calendars could be equated at that time in history, with both using the same intercalation pattern (not the same as the intercalated year sequence, as discussed below). Due to Jerusalem’s more westerly location, the first observed crescent moon was theoretically visible there thirty-seven minutes before it could have been seen at Babylon (P&D p. 25), so the Jews may occasionally have spotted the earliest crescent a day sooner than the Babylonians. Thus, we cannot presume on perfect synchronicity; but on the whole, Scripture indicates the two calendars were basically the same. The different bases of intercalation – crop readiness for the Jews, equinox proximity for the Babylonians – also led to some variability.

From the reign of Xerxes I (485–465 BC) onward, the P&D tables indicate the Babylonians observed a repeating 19-year cycle of intercalations, with a 13th month added every two or three years to keep the lunar cycles in sync with the growing seasons. Though popularly known as the Metonic cycle from its use in the calculated system devised by the Greek astronomer Meton beginning in 432 BC, this 19-year cycle was recognized by the Babylonians before his work, so calling the early Babylonian 19-year cycle “Metonic” is not exactly correct.

The Wikipedia article on the Metonic cycle states, “In the Babylonian and Hebrew lunisolar calendars, the years 3, 6, 8, 11, 14, 17, and 19 are the long (13-month) years of the Metonic cycle. This cycle forms the basis of the Greek and Hebrew calendars.” But Wikipedia is mistaken here: those particular long years of each cycle would only be correct for the Hebrews if their cycles began in a year which correlated with the Babylonian sequence, which supposedly began in 747 BC (P&D Plate I, p. 6, reproduced below). Change the start year from which the Hebrews counted their 19-year cycles, and you change which years were their long years.

DANIEL9 PD Plate I

However, even if the particular sequence of long years changed, the pattern of intercalations every 19 years could still have been the same. The P&D tables demonstrate a regular 2-2-1-2-2-2-1 pattern of non-intercalated years every 19 years, apparent in Plate I. This pattern starts with two consecutive non-intercalated years (years I and II, henceforth MC 1 and MC 2), then an Addaru-II intercalation in MC 3, then two more non-intercalated years followed by an intercalation in MC 6, and so on to create the pattern. If the Hebrew start year for counting cycles was one year earlier than that of the Babylonians – aligning its MC 1 year with the Babylonian MC 19, as I will later show was the case – then the intercalation sequence 1, 4, 7, 9, 12, 15, 18 would have had the same pattern of non-intercalated years as the Babylonian sequence 3, 6, 8, 11, 14, 17, 19. The only difference was the start point of counting. A Rolling Intercalation Chart will be presented later that presents all possible variants of this pattern (such as 1-2-2-1-2-2-2) over 19 years, then compares those options to P&D’s Babylonian data. This comparison will show that the 1, 4, 7, 9, 12, 15, 18 sequence, when offset one year earlier than the Babylonian 3, 6, 8, 11, 14, 17, 19 sequence, duplicates the Babylonian 2-2-1-2-2-2-1 non-intercalated year pattern. This common pattern connects the month-names and month-numbers of the two calendars, making the 1, 4, 7, 9, 12, 15, 18 intercalation sequence that of the presumptive Exodus Hebrew Calendar.

The Analysis

With those basic understandings set forth, we can use them to analyze the historical and astronomical data. Since we cannot assume that the lunar observation conditions at Jerusalem were the same as at Babylon, we cannot use the Babylonian data found in P&D to definitively determine the dates of first observed crescent moons at Jerusalem; we can only approximate them, even if relatively accurately. It is beside the point of this particular study to wrestle with the complex issue of determining precisely when first visible crescents were seen at Jerusalem; others have attempted this, including Karl Schoch (“The Earliest Visible Phase of the Moon,” The Classical Quarterly, Vol. 15, Issue 3-4 [July 1921], 194, online at https://www.jstor.org/stable/635876); NASA astronomer Bradley E. Schaefer (“Lunar Visibility  and the Crucifixion,” Quarterly Journal of the Royal Astronomical Society 31 [1990], 53–67, online at https://articles.adsabs.harvard.edu/pdf/1990QJRAS..31...53S); and Roy E. Hoffman (“Observing the New Moon,” Monthly Notices of the Royal Astronomical Society, Volume 340, Issue 3 (April 2003), 1039–1051, online at https://academic.oup.com/mnras/article-pdf/340/3/1039/4863482/340-3-1039.pdf). I will note here just one thing: though Hoffman’s Israeli New Moon Society survey found every lunar crescent at least 27 hours after conjunction was visible, yet some sightings were made as early as 19.5 hours after the conjunction. This illustrates the inherent uncertainty in using observed earliest lunar crescents to establish the start of a month. The United States Naval Observatory presents a very helpful overview that discusses crescent moon visibility generally at https://aa.usno.navy.mil/faq/crescent.

Granted, then, that there is some uncertainty in determining the precise date a historical crescent moon was first observed at Jerusalem, it is still possible to determine three things objectively: the observed first crescent moon dates at Babylon, subject to the accuracy of Schoch’s tables used by P&D (cf. p. 25); the corresponding astronomical New Moons preceding those dates by one to three days, which also applied to the Jewish calendar; and the intercalation pattern used at Babylon. Understanding that the Jews were able to equate their calendar with that of the Babylonians from the Achaemenid era on, we can then use the Babylonian intercalation pattern as a proxy for that of the Jews. This should allow us to equate the Babylonian and Jewish calendars during the exile as Scripture indicates.

Adjusting the Babylonian Data for Adar-II

Step 1 in analyzing the Babylonian calendar tables of P&D is to slightly modify them to match Jewish norms, eliminating the Ululu-II intercalations in MC 17 and replacing them with Adar-II months at the end of the year. For the period 19 BC–AD 37, this yields the following table:

DANIEL9 Babylonian 19 yr cycle Ululu II removed

The red arrows designate where Babylonian Ululu-II months were shifted over to Babylonian Tashritu/Jewish Tishri. (The asterisked dates of Babylonian observed first crescent moons correspond to astronomical New Moons at the end of the previous year – the observed first crescent was typically seen two or three days after the New Moon conjunction.) Since according to the P&D cycle start date of 747 BC the Ululu-II intercalations took place in MC 17, this chart tells us that MC 1 aligns with Julian years 6/5 BC, AD 14/15, and AD 33/34 (the last also noted on P&D Plate I). The numbers with blue backgrounds signify non-intercalated years; the darker blue sets apart the repeating pattern of three consecutive pairs of non-intercalated years separated by Babylonian MC years 11, 14 and 17. The intercalated years 3, 6, 8, 11, 14, 17 and 19 are given in red text on a yellow background. These three background colors will later be used when discussing the rolling options for non-intercalated year patterns.

Adjusting the Babylonian Data to place the Nisan Lunation in Spring

Step 2 is to make allowance for the Jews, who were not obliged to keep Nisan 1 on or after the vernal equinox, assigning an earlier lunation to Nisan than the Babylonians. A great distinctive of today’s Karaite sect is their focus on finding barley in Israel at the abib stage of green heads of grain. A website cited by Murphey, https://www.scribd.com/doc/118459479/KARAITE-AVIV-BARLEY-REPORTS-1999-2014#, shows that abib barley was found on dates which place Nisan 1 in the range March 12 to April 8:

DANIEL9 Karaite Nisans

In my previous article I similarly noted that another website, Yahweh’s Restoration Ministry, had an article titled “Abib Confirmed!” at https://yrm.org/abib-confirmed/. This stated that green-head barley was observed six days before the lunation that began on March 14, 2021, making that date – by Karaite standards – Nisan 1. These two references constitute objective evidence that it is incorrect to limit Nisan 1 to dates on or after the vernal equinox, as the Babylonians did.

A page that used to be on the United States Naval Observatory website, but can still be accessed via the Internet Archive “Wayback Machine,” is at https://web.archive.org/web/20190614042628/https://aa.usno.navy.mil/faq/docs/SpringPhenom.php. It presents New Moon dates from 25 BC through AD 38, listing for each year both the conjunction New Moon date on or preceding the vernal equinox, and that following the equinox. This information allows us to give alternative, earlier lunation dates for Nisan to the vernal equinox-determined dates given in P&D’s tables.

Redefining the First Year of the 19-Year Intercalation Cycles

Step 3 is to make a minimal adjustment – a redefinition of the cycle start dates – to the P&D tables modified in the first two steps, consistent with a simple strategy by which the Jews could equate the Babylonian calendar with theirs during the Achaemenid era.

To place the first fruits wave offering in spring, the Jews had to use lunations for Nisan close to the Karaite range of March 12–April 8, the adjustment made in Step 2; but at the same time, their calendar had to conform with the Babylonian 2-2-1-2-2-2-1 pattern of non-intercalated years. Examining the P&D tables, one can see that the years with late dates for Nisanu 1 – those in the range of April 12–22 – are all in years which follow an Addaru-II intercalation on or after March 13. If all of the Addaru-II dates on or after March 13 are shifted down to become Nisanu 1 dates in the following year, it changes all of the years that now have earlier dates for Nisanu into 13-month intercalated years. This is seen in the next adjusted P&D table:

DANIEL9 Jewish 19 yr cycle with Adar II shifted to Nisan

To facilitate direct comparison, here are the Babylonian and presumptive Exodus Hebrew Calendar tables side-by-side:

DANIEL9 Babylonian to Hebrew Conversion

The foregoing changes to the P&D tables cause 19 BC, which originally was a non-intercalated year with Nisan starting on 4/14, to become a 13-month intercalated year with Nisan starting on 3/16. (To have Nisan start with the lunation of abib/spring in 19 BC, the 3/16 lunation had shifted forward from the previous Adar-II.) This shifting of Adar-II to the following Nisan changed neither the Julian year from 19 BC nor the Hebrew year from 3742. What it did do was redefine the starting point of the 19-year intercalation cycle to one year earlier, so that the intercalation pattern that would have applied to 20 BC of the original Babylonian table was applied to 19 BC instead. It all boils down to a change in the year the cycles began to be counted from, shifting the entire pattern of intercalations by one year.

Precedent for shifting the cycle start year is seen in 311 BC, the first year of the Seleucid Era. The P&D tables (pp. 36–37) show 311 BC (Seleucid Year 1) was an intercalated year that followed two years after an Ululu-II intercalation in 313 BC. Since, from the Achaemenid era on, every Ululu-II intercalation was in an MC 17 year, this means 311 BC corresponded with MC 19 of the original Babylonian pattern. But at the transition to the Seleucid Era, the original intercalated MC 19 of the Babylonians was redefined as the intercalated MC 1 of the Seleucids, in effect shifting the intercalation pattern up one year. (This shift of Seleucid MC 1 up to Babylonian MC 19 is reflected in the later Rolling Intercalations Chart at 6 BC, AD 14 and AD 33.) This shift made the Jewish pattern of intercalated years exactly match the intercalation pattern of the Babylonians. By redefining the cycle count starting point to a year earlier than the Babylonians, even though the MC years changed from the original 3, 6, 8, 11, 14, 17, 19 sequence to 1, 4, 7, 9, 12, 15, 18, they shared the same 2-2-1-2-2-2-1 pattern in both calendars. This makes this strategy the primary candidate for the proposed Exodus Hebrew Calendar, subject to closer examination of the astronomical data.

Applying Astronomical New Moon Dates to the Data

Step 4 is to convert the observed first crescent dates from the adjusted P&D tables to corresponding astronomical New Moon dates. This is done by using Espenak’s data at Astropixels.com. This results in the following table:

DANIEL9 Astronomical New Moon Dates with PD Data using Babylonian Intercalations

The astronomical start date of each lunation given in that table allows constructing the following Exodus Hebrew Calendar (which can be downloaded HERE), where the Julian date of each lunation’s start is tied in with the astronomical New Moon. Except for yellow, used to highlight the astronomical first day of each lunation, the background colors used in the MC# column of the earlier tables are also applied to this calendar to facilitate tracking the MC patterns.

DANIEL9 Exodus Hebrew Calendar 19 BC-AD 37 rev 7/17/23This calendar demonstrates how the 2-2-1-2-2-2-1 pattern and the conjunction New Moons of every month fit together with the first visible crescents of the Babylonians from 19 BC through AD 38. The first visible crescents reported by the Babylonians unfailingly begin not more than three days after every conjunction. This indicates the reliability of the adapted Babylonian data (with the Adar-II > Nisan shift) as an indicator of the Jewish observed first crescents, showing that we need not assume dependence on the vernal equinox by the early Hebrews. This approach to creating a calendar avoids the subjectivity involved in deciding if any particular first crescent observation at Babylon matched up with that at Jerusalem.

It should be pointed out that this Exodus Hebrew Calendar, being primarily based on conjunction New Moons rather than observed first crescents, makes no attempt to follow Jewish calendar rules that fix the length for certain months at either 29 or 30 days, while allowing Heshvan and Kislev to vary from year to year (cf. https://www.chabad.org/library/article_cdo/aid/3921740/jewish/The-Jewish-Month.htm). The month-lengths in this calendar depend only on the first observed lunar crescent data from Babylon. It was decided to use this data – which was to some degree calculated, as P&D notes (p. 25, which refers to the use of some “unattested” dates in the tables, represented by the small letter “a” in Plate I) – without arbitrarily defining which months had 29 or 30 days. Since there exists one to three days of leeway between the conjunction and the first visible crescent, arbitrary month-lengths could be assigned if desired, but the subjectivity of this approach dissuaded me from doing so.

Closest to the Vernal Equinox?

The next chart, integrated into the Rolling Intercalations Chart, is based on the USNO data. It highlights in light blue, in columns 3 and 4 from the left, the lunation dates from 19 BC through AD 38 consistent with the Nisan 1 date range seen in the Karaite data (March 12–April 8). These astronomical New Moon dates, also found in Espenak’s data on the Astropixels website and reflected in the Exodus Hebrew Calendar, were then copied over to the first column at left as candidate Exodus Hebrew Calendar New Moon dates. Finally, since an objective is to maintain the 2-2-1-2-2-2-1 pattern of non-intercalated years which is integral to the Babylonian data, the light blue/darker blue/yellow color code applied to the MC# columns of the earlier adjusted P&D tables was added to the chart to indicate the years which conform to that pattern.

DANIEL9 Lunations consistent with Karaite and Murphey dataIt will be noted in the chart that I did not use the USNO’s earlier lunations in 16 BC, AD 4 and AD 23 (tinted in red – March 10, 9 and 10 respectively) for the Exodus Hebrew Calendar, instead assigning Nisan to the corresponding subsequent lunations on April 9, 8 and 8 (the last at 10 pm Greenwich time, therefore on Jewish date April 9). The earliest acceptable astronomical New Moon in the Exodus Hebrew Calendar is on March 11, seen in AD 12 and 31, because it fits the 2-2-1-2-2-2-1 pattern of the Babylonian data in P&D and the Karaite data. The latest acceptable Nisan 14 date is April 22.

Recall that the 15 years of Karaite data gave a range of possible observed first crescents from March 12 to April 8. With a difference of one to three days between the conjunction and the first visible crescent, this hypothetically would allow the earlier lunations reported by the USNO (on or before the date of the equinox) to be used for Nisan, which was Murphey’s approach (Column 2, incorporating the dates in the red-tinted cells of Column 3 as intercalated months). That I did not accept these three earlier dates – which, incidentally, follow a 19-year sequence – in my strategy reflects a key difference between Murphey’s results and mine. One can adhere to a Talmud-derived “rule” that the Nisan lunation had to be that closest to the vernal equinox. Or, one can maintain the Babylonian 2-2-1-2-2-2-1 pattern of non-intercalated years in every 19-year cycle starting in 747 BC. But one cannot do both. The two approaches are incompatible, for using the earlier lunations in those three years makes them 13-month intercalated years. That disrupts, with an intercalated year, the start of the 2-2-2 block of consecutive pairs of non-intercalated years in the Babylonian pattern. Using the three earlier lunations leads to Murphey’s 2-1-2-2-1-2-2 pattern seen in the forthcoming Rolling Intercalations Chart. But no direct way is evident to go from this pattern to the 2-2-1-2-2-2-1 Babylonian pattern, which is apparently required for the Babylonian and Jewish calendars to coincide during the exile. This difficulty led me to allow the Babylonian pattern of non-intercalated years to take priority, requiring the later lunations to be used for Nisan in 16 BC, AD 4 and AD 23. Using the earlier lunations for Nisan in those years destroys the 2-2-1-2-2-2-1 pattern.

Since the Hebrews during the exodus were simple pastoralists who were unlikely to have had the astronomical sophistication to observe the vernal equinox, and since Scripture describes the coming of spring in terms of plant growth (abib), the objective existence of an equinox-dependent “rule” at that early point in their history appears doubtful. It may indeed have been a “rule” adhered to by Jewish leaders during Talmudic times, but that does not make it a rule of the biblical period. There is no evidence it was adopted until after Greek astronomical knowledge had become pervasive in the Roman world and the need was seen, after the destruction of the Temple in AD 70, to use a calculated calendar. The late redefinition of tekufah from “circuit” to “equinox” indicates this delayed change from biblical practice.

Summarizing the Data

With this background we can now bring things together visually. The following Rolling Intercalations Chart presents, to its left, a rolling sequence of all possible options of the non-intercalated year pattern 2-2-1-2-2-2-1. The red numbers in the cells indicate the MC years when 747 BC is assumed as the first year of cycle counting, which coordinates with 19-year cycles starting in 6 BC, AD 14 and AD 33 (the last indicated in P&D’s Table I). This pattern contains three pairs of non-intercalated years (in darker blue) that always follow consecutively as 2-2-2, together with a lighter 1-2-2-1 pattern. Color-coding these two sequences allows us to see more easily not only the close relationship between the proposed Exodus Hebrew Calendar and the Babylonian calendar, but also allows one to judge how similar other calendar strategies are to the Babylonian pattern.

Rolling Intercalations Chart

(Larger downloadable copy HERE)

When Nisan lunations are determined by being closest to the vernal equinox, making 16 BC, AD 4 and AD 23 (MC 10 years) intercalated, they replace the Exodus Hebrew Calendar intercalations in 17 BC, AD 3 and AD 22 (MC 9 years). This results in the 2-2-2 pattern being offset by 8 years from the 2-2-2 in the Babylonian sequence. This greatly complicates the effort of coordinating the Babylonian and Jewish calendars during the exile. One year in every 19 in the Babylonian calendar would not have matched with the Jewish calendar, being a lunation ahead of it.

But if we reckon that the Jews began counting their cycles in a year coordinated with the Seleucid Year 1 offset in 311 BC, the intercalated years match exactly. The observed first crescent dates from P&D and the Exodus Hebrew Calendar have been added on the right side of the rolling options. When the start of the 19-year cycle of the Exodus Hebrew Calendar is shifted up by one year, as shown in the last column on the right, then the intercalation pattern and resulting dates of the Exodus Hebrew Calendar precisely match the P&D Babylonian data. In effect, this shift up reverses the intercalation pattern change caused by shifting down the Addaru lunations to Nisanu lunations. Starting the cycle counts a year earlier returned the pattern back to its original Babylonian 2-2-1-2-2-2-1 pattern.

Other Intercalation Strategies

Besides Murphey’s intercalation pattern, the Rolling Intercalations Chart also indicates the patterns yielded by two other strategies – that of D. Beattie on the CGSF.org website in the third column of the Rolling Intercalations Chart, and the Modern Calculated Hebrew Calendar (MCHC) followed by most Jews today in the fifth column.

The CGSF website states (http://www.cgsf.org/dbeattie/calendar/about):

The “Hebrew” years illustrated here prior to the time of Maimonides are hypothetical, superimposing the Rabbinic computations backward in time through 142 AD. Prior to 142 AD the same Rabbinic methods of computation are used here, except that a change in the arrangement of leap years was made to “correct” a presumed calendar drift, thus allowing for the calculated calendar to support a Wednesday, 31 AD crucifixion of Jesus Christ. (Whether Jesus actually died in 31 AD is another story. But while astronomical evidence would allow for a Wednesday Passover that year, the current Rabbinic computations, without any adjustment, would not.)

The CGSF tables follow a 1, 4, 6, 9, 12, 14, 17 MC sequence when 6 BC is taken as a start year coordinated with the P&D Babylonian 19-year cycles. This yields a 2-1-2-2-1-2-2 pattern. It results in AD 30 being an MC 17 intercalated year, resulting in Nisan 1 of AD 31 being pushed forward to April 12, two days after the New Moon of April 10. This allows the CGSF to claim Nisan 14 was Wednesday, April 25. But the foregoing examination has shown that in AD 31 the Nisan lunation actually began the previous month, so that Nisan 14 was on Tuesday, March 27 in AD 31 (in the Full Moon column). There is no way to reconcile a Tuesday crucifixion with the New Testament records. Nor is there an apparent way to tie the Babylonian non-intercalated year pattern to this one, which is separated from it by six years. We are justified in regarding a proposed AD 31 crucifixion as an ad hoc determination made for theological reasons.

Similarly, the MCHC derived from Talmudic/rabbinical rules, which serves as the basis for many online Hebrew calendar calculators (e.g., the Fourmilab Calendar Convertor at https://www.fourmilab.ch/documents/calendar/), also gives no clear route for coordinating its Hebrew years with the Babylonian calendar. Again starting from AD 6, its MC sequence is 3, 6, 8, 11, 14, 16, 19, yielding a non-intercalated pattern of 2-2-1-2-2-1-2. This conforms with neither the CGSF nor the P&D Babylonian calendar. It cannot be the basis by which the Jews equated their calendar with that of the Babylonians during and after the exile.

Conclusions

This analysis has demonstrated a way by which an equivalence between the Babylonian and Jewish calendars consistent with the passages in Esther and Zechariah can be seen, while avoiding the assumption that the early Hebrews knew anything about the vernal equinox. The evidence that equinoxes were not dealt with astronomically until Meton, plus the redefinition of tekufah by the Sanhedrin apparently not until the first century AD, indicates the Jews did not take the equinox into consideration until centuries after the exile. It also avoids making the unrealistic assumption that the Hebrews during the exodus tied their calendar determinations into the state of barley in Canaan. They were only concerned that the lunation which started their year fell in spring, which could be determined from the growth of other vegetation besides barley.

What implications does this study have regarding proposed dates for the crucifixion? These are always given in terms of observed first lunar crescents, not astronomical conjunctions. They are noted in the Exodus Hebrew Calendar as the Nisan 14 dates shaded in light red in the years AD 27–34, which were derived by reckoning the observed Nisan first crescents in the Babylonian data as Nisan 1. For example, the calendar shows that in AD 30, March 25 corresponded with the observed Nisan 1, three days after the conjunction New Moon on March 22. (This observed March 25 date also matches that independently arrived at by Murphey.) As a result, Nisan 14 corresponds with the Julian date Friday, April 7 as the Passover in AD 30. By the definition of the Jewish day, Nisan 14 began the previous Thursday evening at 6 pm, and ended at 6 pm Friday evening, when the Sabbath began at sunset. As the Full Moon column on the Rolling Intercalations Chart notes, the full moon began on Thursday night, April 6, at 8 pm; this means Nisan 14 was the night of the Passover full moon that year, and also the date of the crucifixion.

The Exodus Hebrew Calendar gives the following dates for Nisan 14 in the candidate years for the crucifixion:

  Year     Nisan 14     

    27    Thur, Apr 10
    28    Tues, Mar 30
    29    Mon, Apr 18
    30    Fri, Apr 7
    31    Tues, Mar 27
    32    Mon, Apr 14
    33    Fri, Apr 3
    34    Thur, Apr 22

Of these dates, those placing the crucifixion on any day of the week except Friday should be ruled out on the basis of the plain sense of the gospel accounts. The last 24 hours of Jesus’ mortal life began on Nisan 14, when He ate the Last Supper seder meal in the Upper Room with His disciples on Thursday evening after sunset. They then proceeded to Gethsemane under a Passover full moon; then came the betrayal by Judas and the Sanhedrin trial in the wee hours of Friday morning. The crucifixion began at mid-morning on Friday; He gave up His spirit around 3 pm that afternoon; and finally He was hurriedly laid in Joseph’s tomb (still on Friday) just before Nisan 14 ended at sunset. Then the Sabbath began as Nisan 15 got underway; He rested in the grave that Saturday; and then near dawn on Sunday, Nisan 16, He was resurrected. It all fits smoothly together.

Justin Martyr, in chapter 67 of his First Apology (ca. AD 155–157), affirmed this three-day sequence when he wrote: “For He was crucified on the day before that of Saturn; and on the day after that of Saturn, which is the day of the Sun, having appeared to His apostles and disciples...” (emphasis added). This is confirmation that at a very early date, the Church recognized the Roman “day of Saturn,” i.e. Saturday, as the day that immediately followed the day of the crucifixion. It also confirms that Sunday was the “third day” when the risen Lord appeared to His disciples. This is solid historical evidence against any claims the crucifixion took place on a Wednesday or Thursday. Only a Friday crucifixion fits with what Justin Martyr wrote.

In his book Paul’s Early Period, Rainer Riesner reviews briefly the cases for several proposed crucifixion dates. He quickly dismisses some as having no significant scholarly support, leaving him to focus on 30 and 33 (pp. 54–58). He first notes (p. 54) that 33 is “astronomically possible.” The Exodus Hebrew Calendar confirms this, placing Nisan 14 in both years on Fridays. But as discussed in earlier articles in The Daniel 9:24–27 Project, AD 33 is incompatible with the probable date of the conversion of Paul, which Riesner places in 31/32 (p. 71). This independently testifies to the soundness of the case presented in my 2019 article, "How Acts and Galatians Indicate the Date of the Crucifixion,” which concluded, on the basis of historical and grammatical considerations, that Paul was probably converted in AD 31. There are additional difficulties with AD 33 connected with the timeline of Daniel 9:24–27, discussed in "Daniel 9:24-27: The Sixty-Ninth and Seventieth Weeks,” not the least of which is its dependence on the supposed 360-day “prophetic year” of Sir Robert Anderson. We have no biblical basis for assuming the first 483 years of Daniel’s “70 Weeks” followed anything but ordinary 365-day solar cycles. An AD 33 crucifixion also depends on the unsupported assumption that the public ministry of Jesus lasted for 3-1/2 years, though John’s Gospel only mentions three Passovers covering two full years.

Finally, in his Handbook of Biblical Chronology Table 179 (p. 363), Jack Finegan presents dates for Nisan 14 and 15 in AD 27–34. The dates as calculated by Fotheringham (“The Evidence of Astronomy and Technical Chronology for the Date of the Crucifixion,” Journal of Theological Studies 35 [1934], pp. 146–62, online at https://www.biblicalstudies.org.uk/pdf/astronomy_fotheringham.pdf) are based on his (and Schoch’s) determination of earliest visibilities of crescent moons, while those following P&D’s tables accommodate intercalated months in AD 27, 30 and 32 which cause the first day of Nisan to be postponed by one month:

                      Fotheringham Data

Year             Nisan 1                Nisan 14

AD 27          Friday, 3/28          Thursday, 4/10
AD 28          Wednesday, 3/17 Tuesday, 3/30
AD 29          Tuesday, 4/5         Monday, 4/18
AD 30          Saturday, 3/25      Friday, 4/7
AD 31          Wednesday, 3/14 Tuesday, 3/27
AD 32          Tuesday, 4/1         Monday, 4/14
AD 33          Saturday, 3/21      Friday, 4/3
AD 34          Thursday, 3/11     Wednesday, 3/24

Except for AD 34, where Fotheringham chose a very early observed first crescent date for Nisan outside of the Karaite date range, these dates match those in the independently-derived Exodus Hebrew Calendar. This should give us confidence in the reliability of this study.

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