ISLAMIC MOON AND ECLIPSES
-----------------------
John Pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies@nyskies.org
2020 August 14
Introduction
----------
A spinoff of the interest in First Crescent observations is the
curiosity about calendars based on these events. There are called lunar
calendars. some are hybrid, like the Jewish calendar, where every so
often by rule and schedule the lunar dates are brought back into step
with the solar year. Others are pure lunar with no regard for the Sun.
Examples are the current islamic and ancient cultural Egyptian
calendar.
I knew already that the Islamic calendar is a fully Moon-based
system but I wanted to somehow demonstrate directly. In my stable of
astronomy software is a general purpose lunar observing program that
also gives data for First Crescent for each lunation. Yes, I long ago
set up the program for New York.
Basic scheme
---------
The Islamic calendar is a pure lunar calendar having 12 lunar
months to the year. There is no adjustment to keep pace with the solar
year. Possibly there were only weak seasons, driven by the solar
year, in the Arabian dessert to worry about?
Altho most Islamic regions work with the civil calendar the
cultural Islamic calendar is is wide use in parallel with it.
A lunar month ideally is the interval between successive passing
of the Moon thru a specified elongation from the Sun. Most lunar
calendars use New Moon to start each lunar month, elongation zero.
As reasonable as this practice is, for the rebirth of the Moon
from its last round of the sky, New Moon can not be casually observed.
It occurs only a couple degrees north or south of the Sun in the sky.
The only time a true New Moon is seen by eye is during a solar
eclipse. The Moon overlaps the Sun.
The best early skyeatchers could do is look for the first instance
of Moon soonest after New Moon. it is the thin sliver low over thwhere
the Sun just set. Originally this event of first Crescent was
witnessed by calendar officials, who then announced the start of the
new lunar month.
A round of twelve of these months constitutes the lunar year on
which the calendar is built.
Modern First Crescent
-------------------
Over the centuries of lunar calendars an assortment of methods was
developed to assure that First Crescent was captured on time. Along
with that was the spread of calendar followers into latitudes and
longitudes far from the home location. Today, except for traditional
ceremony, First Crescent is calculated by astronomy and cultural
procedures and the notice of new month is sent out by electronic
means.
The visibility of First Crescent is strongly modulated by the
observer's longitude. form the moment of new Moon, observers farther
west have a better chance of catching first Crescent because at local
sunset the Moon moved farther away from the SUn, into higher altitude
and darker twilight. to keep the calendar synchronized for all
followers most, the official start of each new month is announced by
the home station, like the town the calendar ws first put into effect.
This could be a day before when locally the First Crescent is seen due
to the longitude effect.
Because First Crescent is sen at irregular lags of many hours
after New Moon, the length of a lunar month is not precisely the
synodic month between New Moons. Some calendars recognize this
observation defect and adjust the number of days in the month.
Table of First Crescents
----------------------
Some lunar observing software can deliver fascinating information
about First Crescent for the observer's location. They give for
assorted lunar calendars the civil date when each new month is
anticipated.The date is not the same for all lunar calendars because
each system applies its own cultural procedures to the Moon's
behavior.
For the Islamic calendar, extra items are the day number and lunar
month number of the First Crescent date. Thee are counted from the
start of the Islamic era in civil year 662 AD.
From these data I demonstrate the working, od the calendar.
For civil year 2020 I picked the entry for First Crescent of Islamic
date 1 Muharram 1442. This occurred at sunset on 20 August 2020,
computed for New York City, This date started a new Islamic year,
rolling over from the previous month in year 1442.
-----------------------------------------------------
Islamic date | civil date | day # | month #
----------------+----------------+-------- +--------
. . . | . . . | . . . | . . .
1 Muharram 1442 | 20 August 2020 | 510643 | 17293
. . . | . . . | . . . | . . .
----------------------------------------------------
Count of days and months
---------------------
The figure for days and months is the number of the day or month
corresponding to 1 Muharram 1442. It is the 510,643rd day and is in the
17,293rd lunar month.
Like other calendar systems, the count of days and months starts
with number 'one', not 'zero'. The civil initial month of January is
month #1 and its first day is day #1. This screws up maths, which are
based on the initial unit of time as #0.
The published count of days and lunar months must be reduced by 1
to get the number of elapsed days and months before continuing with
this example
Synodic period
------------
The length of the lunar month is the elapsed days divided by the
elapsed lunar months
(days in a lunar month) = (510642 days) / (17292 months)
= 29.5305 days/month
This is very nearly the lunar synodic period of 29.5306 days.
Strictly, we should use the elapsed number of New Moons, not
First Crescent. While the true synodic period is stable, the interval
from observed or predicted First Crescent wanders by many hours, up to
a full day, from this smpdic period.
It turns out that the long timespan smoothed out this irregular
spacing of first Crescent to an average number of hours after real New
Moon. This makes the First Crescent interval essentially equal the
synodic month .
Lunar years
---------
The number of completed lunar years is the number of lunar months
divided by 12
(lunar years) = (17292 months) / (12 month/year)
= 1441.0000 years
This is the years elapsed because Mubarran is the first month of the
next year 1442.
The 12 lunar months in an Islamic year span 354.37 days
(days in Islamic year) = (29.5305 day/month) * (12 month/year)
= 354.37 day
This is, shorter than a solar year by 10.88 days. Islamic dates, like
1 Mubarran, occur 11 days earlier on the civil calendar year-to-year.
This slippage is continuous because there is no compensation for the
asynchronism of the islamic against the solar year. A complete round
of the civil calendar for a given islamic date is about 33 years.
Islamic civil calendar
--------------------
The Islamic civil calendar is mostly a tool of historians but is
also in general circulation in many parts of the Islamic world. Some
calendar works put this as THE 'Islamic calendar', probably from its
elegance, typical of Islamic maths and science in the Dark and early
Middle Ages. In fact, it was developed in the 700s AD as a normalized
lunar calendar for civil functions, leaving the raw lunar calendar for
strict cultural use.
The Islamic civil calendar is built on a cycle of 30 years. The 12
months of each year alternate 30 and 29 days. A prescribed set of 11
years in the cycle are leapyears, with the leapday added to the 12th
month. That month has 30 days in the stead of its normal 29.
The 30 years plus 11 leapdays are 10.964 days. This calendar at
first seems too simple for Islam followers, but is amazingly accurate.
The 10.631 days are 359.9995 lunations!
Over the 1441 years, as at civil year 2020, of the Islamic era, it
is off by, yikes!, only a couple minutes from the strict lunar
calendar. The advantage is that it is easy to calculate dates in the
past without stepping back thru the individual formally called new
months. For future dates there is no loose forecasting of First
Crescent occurrences. The worse error is a single day within a
particular year, which is dissolved in the adjacent years.
Eclipses
------
Can a lunar calendar keep track of eclipses? Solar eclipses occur
at New Moon; lunar, Full Moon. Since a lunar month begins at First
Crescent, New Moon is a day or to before then. on the last day or two
of the preceding month. Solar eclipses always come in the final days
of the month while lunar eclipses come in the middle of the month.
In the civil calendar we play with two rules for eclipses, the
rule-of-19 and the Saros. The rule-of-19 says that every 19 solar
years on the same calendar date a solar. or lunar, eclipse occurs. The
Saros says that an eclipse comes every 18 years and 10-1/3 days. Both
series last for many decades before the slight ineactitudes of solar
and lunar motion loosen them up and produce no more eclipses. New
series form when the motion start coinciding. Mind well that these
rules do not foretell the very next eclipse in time. During the Saros
or RO19 span there many other eclipse, all part of their own Saros and
RO19 series.
Islamic series
------------
I tabulate here one series of RO19 and Saros lunar eclipses from
1950 to 2040and compare their dates in the islamic and civil
calendars. I use numbers for the Islamic months to emphasize their
sequence within the lunar year. Lunar eclipses in a lunar calendar
take place on the 14 or 15 pf the month, coinciding with Full Moon.
---------------------------------------------
Saros civil | Islamic || RO19 civil | Islamic
-------------+--------++--------------+--------
1950 Apr 2 | 1369 06 || 1951 Aug 17 | 1370 14
1968 Apr 13 | 1388 01 || 1970 Aug 17 | 1390 06
1986 Apr 24 | 1406 08 || 1989 Aug 17 | 1410 01
2004 May 4 | 1425 03 || 2008 Aug 18 | 1429 08
2022 May 16 | 1443 10 || 2027 Aug 18 | 1449 03
2040 May 26 | 1462 05 || --- ---
-------------------------------------------------
At first the Islamic months seem irregular. They are actually
spaced 18y, 7 moths apart for Saros eclipses and 19y, 7 month for RO19
eclipses.
This works out, where ly is lunar year, lm, is lunar month, sy is
,solar year.
(Islamic RO19) = (19 sy * 12.3686 lm/sy)
= 235.003
= 19 ly + 7 lm
The Saros period is just one lunar year less than the 19-period,
or 18 ly + 7 lm.
(Islamic saros) = (Islamic RO19) - 12 lm
= 235 lm - 12 lm
= 223 lm
= 18 ly + 7 lm
In the islamic calendar eclipses of the one or other series come
at intervals of 18 or 19 lunar years plus 7 lunar months.
Eclipses in Ramadan
-----------------
The table here gives lunar eclipses occurring during the month of
Ramadan for 2001-2100. It's based on the table in the Muslim
Apocalyptic web. Eclipses, both lunar and solar, in Ramadan have extra
cultural importance in Islam over eclipses in other months.
I cleaned up the text and removed paenumbral eclipses. In the
bare-eye era, when Islam developed, paenumbral eclipses were not
noticeable and probably were treated as somehow duds.
The civil dates of Ramadan start with the predicted occurrence of
First Crescent at sunset.The month ends at sunset on or just after the
next New Moon.
I work with lunar eclipses because they occur in the middle of the
lunar month, at Full Moon. Longitude offset can not shift them into an
other month. Solar eclipse occur at the end of the month, at New Moon,
where longitude dispersion could put the eclipse on thee first day in
the next month. Several entries in the original table note this
possibility, wh would distort the data.
The year is the civil year with Islamic in parens. With the
Islamic year shorter than the civil year, a couple years span two
Islamic years. Each has its own entry.
The eclipse date is civil with islamic, within Ramadan, in
parens. Total ecipses are flagged with 'T'; partial, 'P'.
----------------------------------------------
Year Ramadan Lunar Eclipse
----- ----- ----------------- ----------
2001 (1422) Nov. 16 - Dec. 15
2002 (1423) Nov. 06 - Dec. 04
2003 (1424) Oct. 26 - Nov. 23 Nov. 09 (15th) P
2004 (1425) Oct. 15 - Nov. 12 Oct. 28 (14th)T
2005 (1426) Oct. 04 - Nov. 02 Oct. 17 (14th) P
2006 (1427) Sep. 23 - Oct. 22
2007 (1428) Sep. 12 - Oct. 11
2008 (1429) Aug. 31 - Sep. 29
2009 (1430) Aug. 21 - Sep. 18
2010 (1431) Aug. 11 - Sep. 08
2011 (1432) July 31 - Aug. 29
2012 (1433) July 20 - Aug. 17
2013 (1434) July 09 - Aug. 06
2014 (1435) Jun. 28 - July 26
2015 (1436) Jun. 17 - July 16
2016 (1437) Jun. 06 - July 04
2017 (1438) May 26 - Jun. 24
2018 (1439) May 16 - Jun. 13
2019 (1440) May 05 - Jun. 03
2020 (1441) Apr. 24 - May 22
2021 (1442) Apr. 13 - May 11
2022 (1443) Apr. 02 - Apr. 30
2023 (1444) Mar. 22 - Apr. 20
2024 (1445) Mar. 11 - Apr. 08 Mar. 25 (15th) P
2025 (1446) Feb. 28 - Mar. 29 Mar. 14 (15th) T
2026 (1447) Feb. 18 - Mar. 19 Mar. 03 (14th) T
2027 (1448) Feb. 07 - Mar. 08
2028 (1449) Jan. 27 - Feb. 25
2030 (1451) Jan. 05 - Feb. 02
2031 (1452) Dec. 25 - Jan. 23
2032 (1453) Dec. 15 - Jan. 12
2033 (1454) Dec. 03 - Jan. 01
do (1455) Nov. 23 - Dec. 21
0234 (1456) Nov. 12 - Dec. 10
2035 (1457) Nov. 01 - Nov. 29
2036 (1458) Oct. 20 - Nov. 18
2037 (1459) Oct. 10 - Nov. 07
2038 (1460) Sep. 29 - Oct. 28
2039 (1461) Sep. 19 - Oct. 17
2040 (1462) Sep. 07 - Oct. 07
2041 (1463) Aug. 27 - Sep. 25
2042 (1464) Aug. 16 - Sep. 14
2043 (1465) Aug. 06 - Sep. 03
2044 (1466) Jul. 25 - Aug. 23
2045 (1467) Jul. 15 - Aug. 12
2046 (1468) Jul. 05 - Aug. 02 : Jul. 18 (15th) P
2047 (1469) Jun. 24 - Jul. 22 Jul. 07 (14th) T
2048 (1470) Jun. 12 - Jul. 11 Jun. 26 (15th) P
2049 (1471) Jun. 01 - Jun. 30
2050 (1472) May 21 - Jun. 19
2051 (1473) May 11 - Jun. 08
2052 (1474) Apr. 30 - May 28
2053 (1475) Apr. 19 - May 18
2054 (1476) Apr. 09 - May 07
2055 (1477) Mar. 29 - Apr. 26
2056 (1478) Mar. 17 - Apr. 14
2057 (1479) Mar. 06 - Apr. 04
2058 (1480) Feb. 23 - Mar. 24
2059 (1481) Feb. 13 - Mar. 14
2060 (1482) Feb. 03 - Mar. 02
2061 (1483) Jan. 22 - Feb. 20
2062 (1484) Jan. 11 - Feb. 09
2063 (1485) Dec. 31 - Jan. 29
do (1486) D*ec. 20 - Jan. 18
2064 (1487) Dec. 09 - Jan. 06
2065 (1488) Nov. 28 - Dec. 27
2066 (1489) Nov. 18 - Dec. 17
2067 (1490) Nov. 08 - Dec. 06
2068 (1491) Oct. 27 - Nov. 24 Nov. 09 (14th) P
2069 (1492) Oct. 16 - Nov. 13 Oct. 30 (15th) T
2070 (1493) Oct. 05 - Nov. 02 Oct. 19 (14th) P
2071 (1494) Sep. 24 - Oct. 23
2072 (1495) Sep. 13 - Oct. 11
2073 (1496) Sep. 03 - Oct. 01
2074 (1497) Aug. 23 - Sep. 21
2075 (1498) Aug. 12 - Sep. 10
2076 (1499) Jul. 31 - Aug. 29
2077 (1500) Jul. 21 - Aug. 18
2078 (1501) Jul. 10 - Aug. 07
2079 (1502) Jun. 30 - Jul. 28
2080 (1503) Jun. 18 - Jul. 17
2081 (1504) Jun. 08 - Jul. 06
2082 (1505) May 28 - Jun. 26
2083 (1506) May 17 - Jun. 15
2084 (1507) May 05 - Jun. 03
2085 (1508) Apr. 25 - May 23
2086 (1509) Apr. 14 - May 13
2087 (1510) Apr. 04 - May 02
2088 (1511) Mar. 24 - Apr. 21
2089 (1512) Mar. 13 - Apr. 10
2090 (1513) Mar. 02 - Mar. 31 Mar. 15 (14th) T
2091 (1514) Feb. 19 - Mar. 20 Mar. 05 (15th) T
2092 (1515) Feb. 08 - Mar. 08
2093 (1516) Jan. 28 - Feb. 25
2094 (1517) Jan. 17 - Feb. 15
2095 (1518) Jan. 07 - Feb. 04
2096 (1519) Dec. 27 - Jan. 25
do (1560) Dec. 15 - Jan. 13
2097 (1521) Dec. 04 - Jan. 02
2098 (1522) Nov. 23 - Dec. 22
2099 (1523) Nov. 13 - Dec. 11
2100 (1524) Nov. 03 - Dec. 01
---------------------------------
Two features of this table are immediately apparent. First is the
drift of Ramadan against the civil calendar A complete round takes
about 33 years, or three per civil century.
The other is that Ramadan lunar eclipses take place in only three
bands of civil dates, These are Oct-Nov, Mar, Jun-Jul. I thought this
may be a short term effect that in other centuries unravels.
I found a more careful analysis that shows Ramadan lunar eclipse
occur only, in Gregorian, within 22 February to 13 March, 20 June to
11 July, and 16 October to 7 November.
Civil versus Islamic
------------------
Because an islamic month can have only one New Moon, near its
final day, and one Full Moon near the middle, only two eclipses are
possible in the month. A lunar eclipse can take place on/near the 15th
and the solar eclipse on/near the 29th. Islam give heightened
importance to Ramadan when two eclipses occur within it, as they did
in 2003 ( Nov 9 lunar, Nov 23 solar).
The civil moth is 30-31 days long, to span two New Moons or two
Full Moons. the opposite phase occupies the middle of the month. It is
possible to have three eclipses in a civil month, which last happened
in 2000 (Jul 1 solar, Jul 16 lunar, Jul 31 solar). The solar eclipses
are at the ends of the month; lunar, middle. or vice versa.
Schematicly the moons and months are
Nf F Nf N F N
--+---------------+--- ---+------------------+---
| Islamic month | | civil month |
F N F
---+------------------+---
| civil month |
N F N
---+------------------+---
| civil month |
The timelines represent the length of the month, from the first to
last day, with some overlap into adjacent months. N is new Moon; F ,
full Moon; f, first Crescent;
The islamic month, as in a pure lunar calendar, has only one
arrangement of moons. The month begins with First Crescent and ends
with the next New Moon. the Full Moon is near the middle of the month.
The civil month can have any arrangement of moons because it is
not tied to the phases. The month here shows three phases fitting into
it. In the upper timeline the first New Moon is on the first, maybe
second, of the month. Full Moon is near the middle and the next new
Moon is near the last day.
In the middle timeline the Full Moons are at the ends and the New
Moon is in the middle. The Full Moon near the last day is, in the
common meaning, a Blue Moon as the second Full Moon in the month.
Usually, like in the lower timeline, there is one Full Moon and
one New Moon in the month, about 15 days apart but not centered within
the month. The next or previous New.Full Moon is in an adjacent month,
The occurrence of Full and New Moons in a month, either Islamic
or civil, can be affected by longitude. The phase at the one end of
the month in a given longitude could fall into the adjacent month in
an other longitude. This is why a Blue Moon is announced by an
astronomer working in, say, Europe but is passed over y Canadian ones,
five and more hours earlier on the clock.
A lunar eclipse occurs not only when the Full Moon is on its orbit
node. That produces a central pass of the Moon thru the umbra for a
longer totality.
The Moon may be some angular distance away from the node and still
produce an eclipse. it may be a shorter total with the Moon passing
of-center thru the umbra, or a partial eclipse. The cycle of nodes
allows the Moon to fall within the distance limit for a couple years,
to generate eclipses in the same month, either calendar, for a couple
years. Beyond that the nodal distance causes the Moon to miss the
umbra and presents a normal Full Moon.
All of this applies to one node, say the descending node. The
opposite node goes thru the same process, doubling the number of
possible eclipses. The alternation of eclipses at each node, with
spans of no eclipses in between, causes eclipses to come in 'seasons'.
There are two or three eclipses together, then a gap of 5-1/3 civil
months, and then the next season of eclipses. In the islamic calendar
the spacing of seasons is either 5 or 6 lunar months. This pattern
says nothing about the actual witnessing of an eclipse at a given
location. The eclipse is seen from some where in the world.
This discussion of eclipses in a lunar calendar is loose. I'm in
the search for an astronomy text written for the Islamic calendar for
a better explanation, along the lines of that offered in works for the
civil calendar. Those for a lunisolar calendar, like the Chinese or
Hebrew ones, are interrupted by the abrupt adjustments to mesh the
lunar and solar cycles.
Conclusion
--------
Lunar calendars are continuously set to the first Crescent every
month, keeping them in step with the Moon's synodic cycle. The common
lunar calendar in the United States is the Islamic calendar. It all
works out in the long term even tho it uses a potentially difficult
observation of the Moon soonest after new Moon.
For eclipses there are cycles comparable to the civil Saros and
rule-of-19 methods. I could not find, like an astronomy text written
for the Islamic calendar, a discussion of how these are employed for
figuring our eclipses. At least the date is fixed at the end of the
month for solar eclipses and in the middle for lunars.