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Young Crescent (Hilal) Visibility

All ancient (Chinese, Egyptian, Hindu, Jewish, Christian and Muslim) calendars were lunar. Man has always been using the crescent moon to count the beginning of a month. This was done in all civilizations from time immemorial. In recorded history, the issue of moon sighting and the problem of predicting the visibility of the new crescent moon has been of interest for centuries from the time of the Babylonians and may be before that. The earliest methods depended upon parameters such as the age of the moon and the time from sunset to moonset (Lag). Hindus (Indians) used the old Babylonian criterion, but with a more elaborate system of calculation that was developed in the time of early Hindu texts, Siddhantas (AD 500).

Muslims followed the guidelines given in Qur’an and Hadith. The Qur’an says:
يَسْأَلُونَكَ عَنِ الأَهِلَّةِ قُلْ هِيَ مَوَاقِيتُ لِلنَّاسِ وَ الحَجِّ {البقرة 189}

They ask thee concerning the New Moons. Say: They are but signs to mark fixed periods of time in (the affairs of) men, and for Pilgrimage.(Al-Baqarah 2:189)

In a well-known and authentic Hadith the Prophet of Allah, upon him be peace, said, "Begin fasting at the sighting of it (crescent), and break your fast at the sighting of it. But if you are clouded over, then estimate it". Another version of the same Hadith ends in the words, "But if you are clouded over, then complete the period of Sha'ban as thirty".

Scholars of Fiqh (Islamic Law), say that the Hadith both indicates an objective and specifies a means for achieving it. The objective in the Hadith is clear, to ascertain the beginning and ending of Ramadan by any means possible, so long as such means are available to the general populace and will not cause them hardship or difficulty in their religion. The means for achieving it was physical sighting, that was the simplest and most feasible means available to people in that age; and that is why the Hadith specified it. Had the Hadith ordered them to use some other means, like astronomical calculations, at a time when the Ummah was un-lettered and un-learned in higher mathematics, it would have been an unbearable burden for them. If a surer means of achieving the objective in the Hadith were to be found, which is less susceptible to mistakes, and that means became feasible for one and all and not a hardship to the Ummah, then that means should be used. We are now living in a time when Muslims have learnt astronomy, mathematics, physics, and computer programming, then why should we insist on the same old means and ignore the objective sought by the Hadith ?

Certainly today, the adoption of mathematical calculations as a means for ascertaining the months should be accepted in accordance with the principle of qiyas al awla or accepting the better analogy. We now have at hand a means that will bring us closer to the unity sought for us by the Qur’an. That is where the calculations for predicting the visibility of the new crescent moon come into the picture. This visibility depends on many factors. These factors are the geometry of the positions of the sun, the moon, and the horizon; the width of the crescent; the moon's surface illumination, the absorption of the moon's light and the scattering of the sun's light in the earth's atmosphere (temperature, pressure and humidity) and the human optical facility or ability.

To explain the visibility of the new crescent moon in simple terms, we shall try not using technical terms, so any ordinary Muslim can understand what is involved in the visibility. The moon revolves around the earth and completes its cycle in 29 to 30 days. That is why the crescent moon appears after 29 or 30 days. What makes this thin crescent luminous is the light from the sun falling on the moon’s surface reflected to the earth. Just consider that the moon comes exactly between the earth and the sun in its cycle and at that moment the sunlight falling on the moon cannot come to the earth as it is reflected back to the sun. This instant of time is called the “Birth of New Moon” and it occurs roughly every 29 or 30 days. This instant of time can occur at any time in the 24 hour period of the clock, not just at sunset, which means that the cycle of the moon is 29 days and some hours, but always less than 30 days. As the time passes, the moon continues to revolve around the earth, and when it moves away from the position of “Birth of New Moon” there comes a time when the sun light coming to the moon is now reflected towards the earth, and we see the crescent. So, the most important factor for the visibility is that the moon has moved enough from the position of “Birth of New Moon”. The second most important factor is whether the moon is above the horizon or not. Due to the curvature of the earth, the moon may be above horizon in some countries and below the horizon in other countries. There are additional important factors for visibility like the distance of the moon from earth, and distance of earth from the sun. The moon revolves around the earth in an elliptical orbit, and that places the moon at different distances from the earth at different times in its orbit. Similar is the situation of the earth around the sun. The earth too revolves around the sun in an elliptical orbit, and that places the earth at different distances from the sun at different times in its orbit.

These important factors for visibility can be calculated with great precision and accuracy, thanks to modern science and to computers. We have collected observations of sighting or non-sighting for more than 160 years from different locations on earth in different months and calculated all the factors that affect visibility and have derived an algorithm (relationship of different factors) that match the visibility or non-visibility.

Further, there are other less important factors for visibility like the pressure, temperature, and humidity of the atmosphere, which bring about different angles of refraction in different locations on the earth and in different months. These factors cannot be put in the calculations for visibility as they are not known when the calculations are made. However, we must understand that these factors are less important and we will explain later how we accommodate them in visibility calculations anyway. Now, we will explain how we make the visibility calculations and plot the map below, which is for July 31, 2011:

We calculate all the important factors for every location on earth (every latitude and longitude) at the local sunset time. Then using the visibility algorithm (relationship of all important factors calculated at local sunset time), we determine whether the crescent moon will be visible to the normal human eye or not. We plot all the visibility points on the map of the world in green color. The less important factors (pressure, temperature, and humidity of the atmosphere) are accommodated in blue (or cyan) color, where we have noticed by previous recorded observations that the same factors make it visible in some locations and not in other locations. This is due to different atmospheric conditions (pressure, temperature, and humidity) prevailing at previous observations.

We also plot the visibility points on the map of the world in gray and red color. The gray color areas are where binoculars are necessary to spot the moon. The red color areas are where the naked eye cannot see the moon, but it can be seen with a more powerful optical aid : a telescope. The black areas are where the moon is either below their horizon, or the factors calculated are not sufficient to make the thin crescent moon visible even with high powered telescopes. Remember, this is a composite map meaning it is it not for any specific time; the map represents visibility after local sunset at every latitude and longitude, based on the position of the moon.

Using this method we will talk about the above shown visibility map for the month of Ramadan 1432. The green areas include the Southern areas of Africa, whole South America, and half of Central America, where the moon can be easily seen by naked eye. Remember, we are not talking about cloudy/rainy conditions at all. The blue areas are where the moon can be or can’t be seen by naked eye, because of prevailing slightly different than normal pressure, temperature, or humidity conditions. These areas include Central Africa, parts of Caribbean Islands, parts of Central America, and the very southern parts of North America. Other areas in gray or red color are where it is very unlikely that the moon can be seen by naked eye. The areas in black are those where it is almost impossible to see the moon.

We can plot such maps for any month desired. This serves as a tool to make an Islamic calendar by calculations, based on statistical observations recorded in 160 years in different areas in different months.

In conclusion, we say that all knowledge is due to Allah (Subhanahu wa Ta’ala), and whatever He taught us, we use that knowledge for making an Islamic calendar, so that we know ahead of time, when the months begin and in doing so bring the Ummah towards unity following the commandments by Allah (Subhanahu wa Ta’ala),

“And hold fast, altogether, to the rope of Allah, and not be divided” (Aal-e-Imran 3:103).

If any thing good comes out of this, it is from Allah (Subhanahu wa Ta’ala), and if there are any mistakes, they are all mine. May Allah (Subhanahu wa Ta’ala) open the hearts of all Muslims to this subject, make us united in the way He pleases, and forgive our mistakes. Aameen!

Khalid Shaukat