Astronomical Calculations of Crescents
& Determination of The Beginning of Islamic Months
The Moon orbits Earth once every 29.53
days (average of synodic month). Because of this revolution, phases of
the Moon change as the Moon's position change relative to the Earth and
the Sun. So, during the Moon's orbit, if the Moon, Earth and the Sun lie
exactly at the same line and the Moon in the middle, the Sun will illuminate
half of the Moon that faces it, and the other half which faces us, will
be dark because it does not reflect rays of the Sun (However, due to the inclination of the Moon that might reach up to 5 degrees, it may reflect a very small percentage of Sun's rays, but according to my information no observer yet reported seeing such crescent). At this point, the Moon is called Wane or New Moon. After that, the Moon continues orbiting
the Earth and begins to reflect a small amount of Sun's rays and now we
see the Moon as a very small waxing crescent. Afterwards, it becomes first
quarter, full Moon, last quarter, waning crescent and then wane again.
Moon's age is measured from the moment of the wane (New Moon). We often
say this Full Moon is 14 days old, which means that the number of days
since the wane is 14. And we say this crescent is about 2-3 days old. But,
did any one ask himself what is the minimum age of crescent that we can
see ? Generally, through a telescope, it is not likely to see a crescent that is less than 12
hours, i.e. if we want to observe the thin waxing crescent to determine the beginning
of an Arabic month, the Moon should be in the wane phase (New Moon) 12 hours ago or
more. But why?!
The wane Moon (New Moon) is located exactly at the Sun's direction, so the Sun's
glare will prevent us from seeing it, in addition, the percentage of the
reflected rays out of the wane Moon (New Moon) is nearly equal to zero, and this percentage
increases as the Moon's age increases. Thus, GENERALLY human eye through
a telescope can't detect any reflected rays from the Moon if the Moon's
age is less than about 12 hours.
* When to Locate the Waxing Crescent?
The new waxing crescent is located near the Sun, so we
shall wait until Sunset, because it is obviously not possible to observe
the thin waxing crescent before Sunset. In addition,
we must wait a reasonable time until the twilight decreases, i.e. until
we can differentiate between Moon's light and twilight glare, a 10-minute
period could be enough sometimes to detect the thin waxing crescent.
* Where to Locate the Waxing Crescent?
As mentioned above, the wane Moon (New Moon) is located exactly near the Sun. If
we assume that the Moon will set when it is wane (New Moon), generally it will set
along with the Sun, but we are looking for a new crescent, which means that it is still near the Sun. So, we must look at the west,
a little bit over the Sunset point.
* When the Waxing Crescent Sets?
The Moon, like the Sun, rises from the East and sets after about 12
hours at the west (with exceptions at high-latitude areas), and since the waxing crescent lies near the Sun, it will set
after the Sunset, and in its best cases, the new waxing crescent sets about one
hour after the Sunset.
* Are the 12 hours only, enough as a factor to determine the crescent
visibility?
Of course not. There are several factors that must be met in order to
view the thin waxing crescent: Some of these factors are:-
- The crescent's altitude.
- The angular distance between the centers
of Sun and Moon.
- The Moon's staying (the interval between
the Sunset and the Moon set).
- The azimuth difference between the Sun and the Moon.
* What's the Meaning of Astronomical Calculations of the Crescent?
Most people think that the astronomical calculations mean absolute determination
of crescent visibility, but this is not true, the astronomical calculations
include the following:
-
The time of the wane Moon (New Moon) must be determined, and this time is accurately
calculated. For sure there is no chance for any error.
-
Some of the above factors are determined. Such as the Moon's altitude, the angular distance between the centers of the Sun and the Moon at the Sunset, Sunset time and the Moon set time, Moon's staying period, ...etc.
-
The results of the above calculations must be compared with crescent visibility
conditions in the previous years, and with the accurate practical and international
observations.
Note: It is absolutely impossible to see the thin waxing crescent after sunset
if the Moon didn't reach the Wane phase (New Moon) yet. How can we see
the new crescent if it is not wane yet?!. " Who claims that he viewed the thin waxing crescent
before the New Moon instant, is like the one who claims that he saw the
Sun before dawn, or he saw the baby before delivery", ancients said.
* Conclusion:
To locate the thin waxing crescent, we have to start looking for it after a
while of the sunset at the West, a little bit above the point at which
the Sun sets, in its best cases, crescent sets about one hour after Sunset.
"New MOONS" Not "New MOON" !!
The New Moon phase is defined as the instant at which the apparent celestial longitudes of the Moon and the Sun are the same. Considering the Sun, Moon, and the Earth to be points not disks. Adopting this definition, the New Moon phase is certainly a unique instant all over the world. But in reality the Sun, the Moon, and the Earth are viewed as disks not points, and so, observers on the Earth in different locations will not see the centers of the Sun and the Moon at the same longitude in the same instant. The difference may reach up to four hours. This would be obvious during a solar eclipse, which can be considered as a "visible" New Moon phase, since it is well-known that a solar eclipse does not begin at the same instant all over the world.
For most purposes, it is suitable to consider the New Moon phase as a unique instant all over the world, and so, nearly all the astronomical books and magazines publish times of New Moon phase as a unique instant, which is for the center of the Earth. But to observe the very thin crescent
shortly after the New Moon phase, and to know the exact interval between the New Moon phase and the observation time (Moon's age), we should adopt the instant of the New Moon phase that occurs from the location of observation. Consequently, times of the New Moon phase in this document are calculated for Amman, or for Iraq in the Iraqi report.
To calculate the Topocentric new Moon, prayer times, and Qiblah direction, kindly download the program "SalatTimes" by Ali Alhadad.
Comments from Scientists Concerning the above Paragraph
- Dr. Myles Standish, president of the Ephemerides Commission / IAU, "I found the explanation of the Moon's phases very well-written and easy to understand. The example using solar eclipses to illustrate why true "New Moon" occurs at different times on the Earth should be very helpful for people."
- Mr. Dennis McCarthy, United State Naval Observatory (USNO), "I've looked over the "New MOONS not New MOON" section and it looks good."
- Mr. Jean Meeus, A well-known astronomer and mathematician, and author of many astronomical books, which are devoted to astronomical calculations, "Counting the age of the Moon from the topocentric New Moon makes sense for
instants shortly (a few hours) after the conjunction.
- Dr. Richard Miles, British Astronomical Association (BAA), "My first thoughts are that the text is essentially correct. Many astronomical phenomena are expressed in terms of the geocentric condition, which can never actually be observed as it is impossible to reach that particular observing site (at the centre of the Earth !).
However the geocentric configuration is a useful one for distant objects but of course the Moon is near.
Of course the centres of the Earth, Moon and the Sun are rarely in line - this corresponds to a total solar eclipse. At other times, locations away from the line, there is a crescent Moon. Thus even at New Moon from any particular location the crescent will change in extent and position. Likewise when New Moon is defined for a particular observer on the Earth, as the Moon and Sun sharing the same celestial longitude (Right Ascension), the crescent will be positioned either north or south near to but not necessarily centered on the poles of the Moon (libration of the Moon defines the extent to which it appears to wobble). Of course there will be a line roughly in longitude where all observers on the Earth will see the Moon and Sun at the SAME Right Ascension."
- Mr. Ali Alhadad, holds Bsc and Msc in the fields of mathematics and Computer logic, "I find your article (Visibility of Crescents) interesting and I have the same opinion regarding the use of Topocentric New Moon instead of the Geocentric one. However, only two comments I have in mind: 1- The difference between Topocentric and Geocentric New Moons can reach up to +-2 hours, 2- The difference between Geocentric Elongation and Topocentric can reach up to 1 degree (These two statements are not in the current version of your paper but still worth to mention)
- Mr. Roy Bishop, the editor of the The Observer's HandBook, of the Royal Astronomical Society of Canada (RASC), revised the above paragraph in detail, and made a few corrections.
- Prof. Francois-Rene Querci, astrophysicist at Midi-Pyrenees Observatory in Toulouse, revised all this document and made a few corrections.
- Dr. Reinhold Bien, and Dr. Ulrich Bastian, Astronomisches Rechen-Institut in Germany, gave some comments. However, they tend to prefer the geocentric configuration than the topocentric.
Many thanks for those who assist JAS, their efforts are highly appreciated. Furthermore, JAS welcomes any other comments or suggestions.
Methods to Start the Islamic Months in Different Countries
There is not a unique method adopted by all the Islamic countries to start the Islamic months. There are many methods spread all over the Islamic World, some of them are:-
- If the Wane Phase (New Moon) occurs before midnight, then the next day is the first day of the Islamic Month. This method is adopted in astronomical books and magazines and some Islamic countries.
- If the Wane Phase (New Moon) occurs before Sunset, then the next day is the first day of the month. Since the Islamic day starts at Sunset not at midnight.
- Some countries adopt specific criteria, such as the Moon's age, altitude, the interval between Sunset and Moon set,...etc., and if the Moon fulfills these criteria at Sunset, then the following day is the first day of the Islamic Month.
- Some countries adopt the actual sighting of the crescent with the assistance of astronomical calculations. This is the most reliable and accepted method among people and scientists, as well as among most of scientists of Islamic Shari'a nowadays. JAS adopts this method, since the Prophet Mohammad "ASWS" ordered us not to start the month unless we sight the crescent, thus it must be seen, and we use astronomical calculations in order to know where and when to observe, as well as the probability of observing the crescent, since sometimes it would be useless to observe the crescent if the calculations show that there is no crescent in the sky after Sunset !
- Other countries adopt several different ways, some of them make the month 29 and 30 days alternately, others make Ramadan either 29 or 30 days always, and finally some countries don't adopt any specific thing !
JAS Observes the Crescents