Lunar Crescent Visibility and Islamic Calendar [Archives:1998/22/Last Page]

Introduction
Muslims do not have a definite calendar at this time and some of them feel that it is impossible to make one because there is something unpredictable about the motion of the moon. This causes a great deal of argument and confusion in the community and is most embarrassing for all of us.
In reality, the calendar based on the holy Quran that was established during the days of prophet Mohammed (pbuh) is quite definite and can be used internationally if we get organized and agree upon certain conventions.
Because this has not been done, we often have conflicting interpretations on what the Islamic date is. Europeans went through a similar phase in the last century. As they started traveling over great distances quickly, there was confusion over dates. Soon a date was agreed upon among the leaders and the common man was merely informed after the decision.
With advancements in technology, Muslims have been debating on a possible lunar calendar. The lunar cycle is not as obvious as the solar cycle of day and night. Many people do not realize that just as we can not ascertain whether it is day or night at our locations by calling relatives in distant countries, we cannot be certain about a lunar date confirmed by someone half a world away. One has to look at the local sky. Not every Muslim is an astronomer, he can not rationally decide about such matters. His decisions are often based on emotional and devotional reasons and are often scientifically wrong. It is essential that the community pay urgent attention to solve this problem.
The Motion of Heavenly Bodies
The relative motion of all heavenly bodies is governed by a few simple laws commonly known as Newton’s laws of motion and the law of gravity. The curved path of a body through the heavens is such that gravitational force is always balanced against (i.e. equal and opposite to) the centrifugal force due to the acceleration of the body. As a result, planets generally move in an elliptic orbit around the sun such that the sun remains at one of the foci of the ellipse. A circular orbit is just a special case of an ellipse when the foci are congruent. The two equations that have to be solved simultaneously for computing the orbit of a planet are as follows :
Gravitational force =
                        G*M1*M2/R2… (1)
Acceleration of a body =
                        G*M2/R3 … (2)
Where: G is the gravitational constant, M1 is the mass of the planet, M2 is the mass of the sun and R is the instantaneous distance between them.
For a two-body system, the method is quite simple. As the numbers increase, it becomes increasingly difficult to solve these equations. But, all this has been done by modern computers and tables giving relative positions of bodies in our solar system which are available in most libraries. To construct a calendar, all one has to do is to learn to use and read them.
The Earth, Moon and Sun Systems
The holy Quran states that the sun and the moon move according to ‘Hisab’ i.e. governed by laws. We have known these laws for some time in enough detail to be confident about their location in the heavens at any time. This is all that is needed for constructing prayer time tables and calendars. A calendar can be considered merely as a special time table that tells us when to say Subeh or Eid prayers, etc.
Motion of the Earth
The earth basically moves in three different ways.
1. It spins on its axis to produce day and night. This takes 24 hours. Its spin axis is tilted about 23.5 degrees in relation to its orbital plane.
2. It revolves around the sun in a near circular orbit. Because of the tilt of its rotational axis, the sun appears to move north and south throughout the year. This change in the angle of incidence of light from the sun is responsible for the change in seasons. Its rotational period is about 365.25 days or roughly a year.
3. A third less known motion of the earth is called precession. The axis of rotation describes a cone in space over a period of about 25,800 years. This necessitates frequent correction in the length of the solar year to prevent the seasons from sliding through the year. This is done by means of a system of having or not having a leap year (366 days a year) every four, one hundred, four hundred and four thousand years. This also corrects for fractional number of days in a solar year.
Motion of the Moon
The moon moves under the influence of gravity, mainly of the sun and the earth. It is also slightly disturbed by other planets. Its orbit around the earth is only approximately elliptic because the sun disturbs it. Its orbital plane is tilted in relation to the earth’s orbital plane (ecliptic) by about 5 degrees. The moon’s orbital plane is not fixed in space in relation to the stars. Even though it maintains a constant tilt in relation to the earth’s orbital plane, the line of intersection of these two planes (nodes) rotates slowly in space. Because of the tilt of its orbit, the moon appears to move to the north and south of the sun and the new crescent is sometimes seen to the left and at other times to the right of the setting sun. Viewed from space, the path of the moon is like a sine wave imposed over the near circular path of the earth.
The moon produces no light of its own, but shines due to the sun’s light. Like earth, only half the surface of the moon’s sphere is illuminated by the Sun at any time. Depending on the relative position of the three bodies we can see varying portions of the illuminated side of the moon from the earth. When the moon is between the earth and the sun, only the far side of the moon is illuminated and we can not see it. This position is called astronomical new moon. When the earth is between the moon and the sun, we see full moon. Viewed from the moon, the earth appears to change phases much like the moon.
From figure-1 it can be seen that the width of the crescent W that can be seen from earth is r* (1 Cos M). Where: r is the radius of the moon’s disk and M is the angle between the lines of sight from the earth to the sun and the moon. Since the moon appears to move about 360 degrees around the earth in relation to the sun in one month (29.5 days) its apparent daily motion is about 12.2 degrees on the average. Because of the elipticity of the moon’s orbit, this varies from 11.5 to 13.1 degrees a day. Earliest visibility is possible when the moon is closest to the earth and the angle from the sun is changing fastest. Therefore, the greatest angle M = 13.1* A/24 degrees.
Where: A is the age of the moon or the time of the astronomical new moon in hours. In radians, M = 13.1* 3.14/24*180 or about 0.00952*A. Since the Cos M = 1-M2/2 when M is small, the width of the crescent of age A hours as seen from the earth can be approximated as follows:
Width = r* (0.00952*A) 2/….. (3)
Since the minimum distance of the moon from the earth is about 357,000 km and r = 1738 km and the angle subtended by the widest part of the crescent on the eye of an observer on earth is its width divided by distance.
Therefore:
Angle = 1738* (0.00952*A)2/2*357,000 radians…………(4)
= 0.045*A2 seconds of arc……(5)
Hence, it is seen that the width of the young crescent is proportional to the square of its age. The constant 0.045 is just an estimate, it depends on the distance of the moon from the earth. Since the resolving power of the human eye is about 20 seconds of arc (1 second of arc is 1/2600 of a degree) the approximate age of the crescent for visibility can be estimated from equation (5) as follows:
20 = 0.045*A2……….(6)
or A = 21 hours.
This is the basis for the much talked about 20 or 22 hour rule for the earliest visibility of the crescent.
Criterion to determine crescent visibility
It is apparent that Muslims have to use astronomical facts and data for fixing the beginning of Islamic new month and in particular at the Ramadhan date.
Astronomers have been trying to find a simple criterion to determine when a crescent will always be visible. But their efforts did not succeed until the mid 1980s when a renewed interest in the visible moon forced some prominent western astronomers like L.E. Doggett, B.E. Schaeffer and others from the most respected observatories such as the US Naval Observatory and the Royal Greenwich Observatory to start collecting and evaluating ‘verifiable’ observation reports from around the world.
Mr. D.B. Yallop of the Royal Greenwich uses the moon’s 10 degree altitude at sunset for the moon to be visible to naked eye observers. Muslim experts who have gathered sighting reports for the last 16 years in North America have found that a 12 degree angle of the moon’s separation from the sun along with an altitude of 10 degrees at sunset is a more reliable criteria. The experts also take into consideration the following:
* moon’s distance from the earth
* crescents width and light intensity
* the brightness of the sky near western horizon at sunset
* lunar mountain’s shadowing effect
* atmospheric refraction effect
* human eye’s role as detector of contrast etc.
First sighting of the crescent in 1998
The table outlines the calculated date, time and place of the first sighting of the crescent in the year 1998. The calculations are based on the criteria that the best place and time for making the first crescent sighting is where the crescent is vertically above the sun at sunset, i.e. their relative azimuth is zero and where the apparent altitude of the moon is 10 degrees. In addition, the table provides the civil date and local time at sunset for the first sighting, time difference from universal time (UT), the time between sunset and moon set in minutes, the longitude and latitude of the best place and age of the moon since its birth or what is commonly referred to as astronomical new moon.
It should be noted that age is shortest when the moon is nearest to the earth and longest when the moon is furthest from it. The last column of the table provides an approximate geographical description of the place. The holy Quran clearly says that the sun and moon move according to laws and are for the reckoning of time. There has always been a tendency among common people of all faiths to ascribe some mystical meaning or significance to their appearance and motion. The holy Quran does not support such a view. To us, they are nature’s clocks to determine time.
Islamic conventions about time keeping are different from those in common use in the western world today. For example, to a Muslim a day (like Thursday or Friday, etc.) begins at sunset, not at midnight. A week, month and year are similarly affected.
The 12 Islamic months are not fixed duration. Muharram can sometimes be 29 days and sometimes 30 days, etc. The month starts with the visibility phase of the moon and not with the birth of the moon or astronomical new moon as stated in some other calendars.
Calendars can be based on either the motion of the moon or the sun or both. Most lunar calendars are unisolar, that is although they count a month based on lunar cycle, they introduce some corrections to keep their calendar synchronized with the seasons that depend on the solar cycle. This is usually done by adding a 13th month every few years. This is known as intercalation.
The holy Quran forbids intercalation and clearly states that a year has 12 months. Since a lunar month on the average has 29.5 days, the Islamic year has only 354+1 days. This injunction leaves the Islamic year 11.25 days shorter than the average solar year. For this reason, our observances move through the seasons and come about 11 days earlier in each succeeding year.
International Lunar Date Line
Just as there is a solar date line (180 degrees longitude) to mark the start of a date on a solar calendar, a lunar date line can be constructed to indicate the start of a lunar date. Because an Islamic date begins in the evening with the first visibility of the crescent, these points of first visibility can be considered to constitute the lunar date line.
For a given solar dip angle and angular separation between the sun and moon, the moon appears to be higher above the horizon at sunset near the equator than at high latitudes. For this reason, higher contrast is achieved in the tropical regions. As we move to higher latitudes, because of reduced contrast, a bigger crescent is required for visibility and visibility is delayed. For this reason, the line of first visibility appears like a parabola enlarging towards the west.
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