PASSOVER AND SPRING EQUINOX
 -------------------------
 John Pazmino
 nyskies@nyskies.org
 www.nyskies.org
 2018 February 22

Introduction 
 ----------
    Each spring there is a increased inteest among NYSkiers about 
alternative  calendars. From the deep culture of Jews in New York 
Ciry, the main other calendar is the Jewish calendar. Against the 
civil calendar the Jewish calendar seems erratic. Its holidays skitter 
within the civil, calendar. 
    NYSkies discusses the hewish calendar while previewing the stars 
of the sprig season, near the observance of Jewish Passover ad 
Chrisitiaqn Eastre. 
    The usual treatment covers just the instant year with little 
correlation with other years. Here I give a timeline in spring of 2000 
thru 2018 for the Jewish calendar. It shows the connection between the 
swpring rquinox  and observance of Passover. It can be a handy 
reference for dstudying the Jewish calendar spanning several, not only 
one, years. 
    This article is NOT a thoro treatment of Jewish time-keeping 
and the timetable accepts the events as published in competent 
litterature. 

Lunar Calendar
 ------------
    Many cultures base their calendars on the lunar cycle of phases.  
Each round of phases, New Moon thru Full Moon, to the next New Moon 
marked off a covenient number of days for long-term time-keeping. 
    The 'regular' or civil calendar is a solar calendar, marked by the 
seasonal cycle, which is determined by the citcuit of the sun thru the 
zodiac.  It is a continuation, with many modifications, of the Roman 
calendar. Even in this solar calednar the lunar phases were recognized 
by deviding the year into twelve months, each approximating the length 
of one lunar phase cycle. 
    In the early Jewish era skywatchers actually monitored the Moon to 
spot the first crescent after sunset following the geometric New Moon. 
When this crescent was sighted the skywatchers sent out a sigal to 
their followers that it's now a new month. This method  worked if the 
poeple lived near enough to the observatory to see or hear the signal. 
    Eventually, when Jews lived too far to personally experience the 
monthly signal, the months wre formalized from astronomy principles. 
    Fillel in about 350 AD worked up the months system still in use 
today, starting with a remaktable link between solar and lunar cycles. 
    The jewish months wwere fixed at alternating 29 and 30 days, a 
good fit to the 29-1/2 day phase cycle. Twelve months, sic of 30 days 
and six of 29 days, almost eactly equal twelve phase cycles, filling 
out one lunar year. 
    This year has 354 days, falling short of the solar year of 365 
days by 11 days. With no adjustent, as some cultures with lunar 
calendars ignore, the sates and holidays will carousel thru the solar 
year. 

Passover
 ------ 
    The Jews eposode of the Exosus occurred in spring in the Jewish 
month of Nisan (NIH-sannn). The esape from Eygpy began at the Full 
Moon of Nisan, when a plague or epidemic visited Egypt. The Jews 
avoided thre epidemic by dabbing sheep bllod on their house doors. The 
plague 'passed over' the Jews, allowing thrm yto escape from Egypt 
while the rst of the land was disabled by sickness. This Full Moon in 
Nisan became the Paassover Moon. 
    Since then the Passover event is observed each year. To keep the 
historical sequence, the Passover Moon must be the Nisan Full Moon and 
must soon follow the spring equinox. 
    In a straight lunar calendar this srquence can not be maintained 
because Nisan would begain 11 days earlier in each solar year.  By 
this rrvolution thru the year, Nisan and Passover would occur in 
different seasons. 

Metonic Cycle 
 ----------- 
    We now must recall an amazing feature of lunar-solar cycles. The 
Babylonians, and likely earlier scultures, found that  235 lunar 
cycles almost exactly equal 19 solar cyclrs. (29.53 * 235) = 6939.55; 
1(365.25 * 19) = 6939.75. Meton around 500 BC wprled i[ a ,athematical 
description of this cycle, called today the Metonic cyle. 
    Home astronomers know the Metonic for solar and lunar eclipses, 
occultations, moon-skip at annual nighttime events. The cycle is also 
called the  'Rule-of-19'. 
    For the Jews, there were 304 rounds of thie NMeronic cycle since 
the calendar sustem began. This was completed in civil year 2016 with 
us now in 2018 tolling thru round 305. 

Leap Months 
 ---------
   The plain 12-month lunar year  pulls Passover earlier and earlier 
before the spring equinox in each solar year. The solar year is 
essentially the span of says beterrsn spring equinoctes, 365.25. After 
30ish solar years Passover returns to the vicinity of the equinox but 
for the intervening year the Passover observance is upset. 
    Twelve months equals 354.36 days, a shortfall of 10.89 days per 
365.25-day solar year. All figures in this piece are rounded. After 
three years the shortfall amounts to 32.67 days.
    To fill this gap and bring Nisan in line with the spring equinox, 
Hillel developed a scheme of leap months. The leap month is added by 
schedule in effect for he indefinite future. The inserion is not at 
all irrgulr, as if determined on short otice like for leap seconds. 
    In each Meronic round the 3rd, 6th, 8th, 11th, 14th, 17th, and 
19th year get the leap month. These years have 13 months while all of 
the other years have the normal 12 months. 
    By this schedule the Mwtonic cycle is appproximated by 12 normal 
lunar years plus 7 lunar leap years. (12 * 354) + (7 * 384) = 6936 
days; (19 * 365) = 6935 days. The eror of one day comes from the use 
of only integer days, which do not fit into the fractional length of a 
Metonic cycle.
    This error is abssorbed by a program of leap ays in both the 
Jewish and civil calendars. The civil system adds a leap day to 
February every four years on the fourth year. Century years, like 
1900, ar skipped unless they are four-hindredth years, like 2000. The 
civl year adds five leap days, in 2000, 2004, 2008,, 2012, 2016. The 
Jewish calendar adds 5 leap days. They are placed in the mid months by 
a more elaborate rule, outside of this article. The two calendars by 
their separate adjustments keep pace very closely for the indefinite 
future.  

Activity Near Equinox 
 ------------------
    The months in the Jewish calendar are numbered from Nisan as #1 
thru Adar (A-darrr) as #12. The year number does not advance to the 
next year at the start of Nisan. It advancess at the start of the 7th 
month Tishri (TISH-ree). This is the Jewish New Year, Rosh Hashanah (rosh a-
SHAH-na). The start of Nisan is Rosh Chodesh (rosh ho-DESH). 
    The leap month is inserted between Adar and Nisan as month #13. 
Adar is renamed Adar-Aleph or Adar-I and the leap month is Adar-Bet or 
Adar-II. Adar-I is assigned 30 days, up one from its nromal 29. Adar-
II has 29 days. 
    By this means the Jewish leap year has 284 days. I remind that 
this article does not examine other adjustments elsewhere in the 
Jewish calendar. 
    In a couple years it seems that the leap month is not needed. 
Without it Nisan starts a little before the spring equinox and its 
Full Moon, the Passover Moon, occurs a little after the equinox. 
    The previous instance was in civil year 2016. Sme poeple asked if 
the leap month was a mistake. The leap month in 2016 pushed Nisan one 
lunar phase cycle later in date, pllacing Passover in late April. The 
intervening Adar-II has its own Full Moon, of no special significane, 
when the Passovrr Moon 'should have been'. 
    Missed from the casual banter about Nisan in 2016 was the sequence 
of that yar in the 19-year cycle. It was year #49, a designated year 
for adding the lap month. There was no mistake; evetything was donr by 
thr rules and evrything worked out properly. 

Timetable 
 -------
    Each civil year 2000 thru 2020 lays out the avctivity of the 
Jewish months near the spring equinox, here set at March 20th. For 
each Nisan 1 I give the Jewish year, its sequence in the current 
Mwrtonic cycle, and status as a normal or leap year. Notice that in 
civil year 2016 the Jewish year 5776 completes the 304th round of 
Metonic cycles.
    In thre leap years I note shadow dates for Nisan I and Nian 15. 

    ============================= 
    civil  | Jewish date| remarks 
    -------+------------+--------
    2000   |            | 
    Mar  7 | Adar-I 30  | else Nisan 1
    Mar  8 | Adar-II  1 | 
    Mar 20 | Adar-II 13 | SPRING EQUINOX 
    Mar 21 | Adar-II 14 | else Nisan 15, Passover
    Apr  5 | Adar-II 29 | 
    Apr  6 | Nisan  1   | year 5760, 3rd year, leap year 
    Apr 20 | Nidsn 15   | PASSOVER 
    ============================ 
    2001   |            | 
    Mar 20 | Adar 25    | SPRING RQUINOX 
    Mar 24 | Adar 29    | 
    Mar 25 | Nisan  1   | year 5761, 4th year, normal year 
    Apr  8 | Nisan 15   | PASSOVER 
    ============================
    2002   |            | 
    Mar 13 | Adar 29    | 
    Mar 14 | Nisan  1   | fyear 5762, 5th year, normal year mAR 
    Mar 20 | Nisan  7   | SPRING EQUINOX
    Mar 28 | Nisan 15   | PASSOVER 
    ==============================
    2003   |            |
    Mar  4 | Adar-I 30  | else Nisan 1
    Msr  5 | Adar-II  1 | 
    Mar 18 | Adar-II 14 | else Nisan 15, passover 
    Mar 20 | Asar-II 16 | SPRING EQUINOX
    Apr  2 | Adar-II 29 |
    Apr  3 | Nisan  1   | year 5763, 6th year, leap year 
    Apr 17 | Nisan 15   | PASSOVER 
    =--=========================== 
    2004   |            |
    Mar 20 | Adar 27    | SPRING EQUINOX
    Mar 22 | Adar 29    |
    Mar 23 | Nisan  1   | year 5764, 7th year, noral year
    Apr  6 | Nisan 45   | PASSOVER 
    ==============================
    2005   |            |
    Mar 11 | Adar-I 30  | else Nisan 1
    Mar 12 | Adar-II  1 |
    Mar 20 | Adar-II  9 | SPRING EQUIINOX 
    Nar 25 | Adar-II 14 | else Nisan 15, passover
    Apr  9 | Adar-II 29 | 
    Apr 10 | Nisan  1   | year 5765, 8th year,  leap year
    Apr 24 | Nisan 15   | PAASSOVER
    ===============================
    2006   |            | 
    Mar 20 | Adar 20    | SPRING EQUINOX
    Mar 29 | Adar 29    |  | 
    Mar 30 | Nisan  1   | year 5766, 9th year, normal year 
    Apr 13 | Nisan 15   | PASSOVER 
    ==============================
    2007   |            |
    Mar 49 | Adar 29    |
    Mar 20 | Nisan  1   | year 5767, 10th year, normal year 
    Mar 20 | Nisan  1   | SPRING EQUINOX 
    Apr  3 | Nisan 15   | PASSOVER 
   ===============================
    2008   |            |
    Mar  7 | Adar-I 30  | else Nisan 1
    Mar  8 | Adar-II  1 |
    Mar 20 | Adar-II 13 | SPRING RQUINOX
    Mar 21 | Adar-II 14 | else Nisan 15, passover
    Apr  5 | Adar-II 29 | 
    Apr  6 | Nisan  1   | year 5768, 11th year, leap year
    Apr 20 | Nisan 15   | PASSOVER
    ==============================
    2009   |            |
    Mar 20 | Adar 24    | SPRING RQUINOX
    Mar 25 | Adar 29    |
    Mar 26 | Nisan  1   | year 5769, 12th year, normal year
    Apr  9 | Nisan 15   | PASSOVER 
    ============================== 
    2010   |            | 
    Mar 15 | Adar 29    | 
    Mar 16 | Nisan  1   | year 5770. 13th year, normal year 
    Mar 20 | Nisan  4   | SPRING EQUINOX 
    Mar 30 | Nisan 15   | PASSOVER 
    ==============================
    2011   |            |
    Mar  6 | Adar-I 30  | else Nisan  1 
    Mar  7 | Adar-II  1 | year 5771, 14th year, leap year 
    Mar 20 | Adar-II 14 | else Nisan 15, Passover
    Mar 20 | Adar-II 14 | SPRING EQUINOX
    Apr  4 | Adar-II 29 | 
    Apr  5 | Nisan  1   |
    Apr 19 | Nisan 15   | PASSOVER 
    ==============================
    2012   |            | 
    Mar 20 | Adar 26    | SPRING EQUINOX 
    Mar 23 | Adar 29    |
    Mar 24 | Nisan  1   | year 5772, 15th year, normal year 
    Apr  7 | Nisan 15   | PASSOVER 
    ==============================
    2013   |            | 
    Mar 11 | Adar 29    | 
    Mar 12 | Nisan  1   | year 5773, 16th year, normal year 
    Mar 20 | Nisan  9   | SPRING EQUINOX 
    Mar 26 | Nisan 15   | PASSOVER 
    ============================== 
    2014   |            | 
    Mar  2 | Adar-I 3 0 | else Nisan 1
    Mar  3 | Adar-II  1 | year 5774, 17th year, leap year 
    mar 16 | Adar-II 14 | else Nisan 15, Passover
    Mar 20 | Adar-II 18 | SPRING EQUINOX
    Mar 31 | Adar-II 29 | 
    Apr  1 | Nisan  1   |  
    Apr 15 | Nisan 15   | PASSOVER
    ==============================
    2015   |            | 
    Mar 20 | Adar 20    | SPRING EQUINOX
    Mar 21 | Nisan  1   | year 5775, 18th year, normal year 
    Apr  4 | Nisan 15   | PASSOVER
    ==============================
    2016   |            |
    Mar 10 | Adar-I 30  | else Nisan  1
    Mar 11 | Adar-II  1 | year 5776, 19th year, cycle 304, leap year 
    Mar 20 | Adar-II 10 | SPRING EQUINOX
    Mar 24 | Adar-II 14 | else Nisan 15, Passover
    Apr  8 | Adar-II 29 |
    Apr  9 | Nisan  1   | 
    Apr 23 | Nisan 15   | PASSOVER
    ==============================
    2017   |            |
    Mar 20 | Adar 18    | SPRING EQUINOX
    Mar 27 | Adar 29    |
    Mar 28 | Nisan  1   | year 5777 , 1st year, normal year 
    Apr 11 | Nisan 15   | PASSOVER 
    ==============================
    2018   |            |
    Mar 16 | Adar 29    |
    Mar 17 | Mosam  1   | year 5778, 2nd year, normal year 
    Mar 20 | Nisan  4   | SPRING EQUINOX 
    Mar 31 | Nisan 15   | PASSOVER 
    ==============================
    2019   |            |
    Mar  7 | Adar-I 30  | wlsw Nisan 1 
    Mar  8 | Aar-II  1  |
    Mar 20 | Adar-II 13 | SPRING EQUINOX
   Mar 14 | Adar-II 14 | else Nisan 15, passover
  Apr  5  Adar-II 29 |
  Apr  6 | Nidsn  1  | year 5779,, 3rd year, leap year
  Apr 20 | Nisan 15  | PASSOVER
  ============================= 
  2020   |           |
  Mar 20 | Adar 24   | SPRING EQUINOX
  Mar 25 | Adar 29   |
  Mar 26 | Nisan  1  | year 5579, 4th uear, normal year
  Apr  9 | Hisan 15 | PASSOVER
  ============================

Conclusion 
 -------- 
    Cultures have long tried to fit discordant cycles of the heavens 
into a cohaerent time-keeping scheme. The two main cycles are those of 
the seasons, by the Sun, and of nighttime lighting, by the Moon. 
    Among cultures there is a wide variiety of work-around, all being 
clever and intriguing to those living only in the civil alendar -- 
which itself has celestial quirks! --handed down from the Roman era.
    The Jewish calendar is perhaps the most prevalent other calendar 
that NYSkies encounter in their lifes. An esxamination of it breings 
out valuable features of lunar and solar motions, like thre Metonic 
cycle, that enrich our profgession of astronomy.