Article by Samad Husain Rizvi, Pakistan

Sighting of the new Shawwal Moon crescent, or ‘Chand Raat’, used to be an exciting and romantic event that heralded the even more joyful Eid day. All that has changed in recent years, and bitter arguments over the sighting of the new Moon crescent have spoiled the bliss. In an age when people are calculating what happened in the far away galaxies millions of years ago and billions of miles away, there should be no harm if we get the help of scientific knowledge of the celestial events in predicting the new Moon crescent.

We are familiar with the predictions of solar and lunar eclipses that are made years ahead and with the precision of seconds. Although the calculations are more complicated, the sighting of the new Moon crescent can also be predicted similarly. This is because all these phenomena depend upon the relative positions of the Sun, the Earth, and the Moon. Methods to predict the new Moon crescent was used since ancient times, perhaps even before the Babylonians. The Hindus have been calculating it in a rather crude way since remote antiquity because they base many of their religious ceremonies on sighting of the new Moon crescent. Until the twentieth century the western astronomers did not work substantially on the subject because they had little interest in the phenomenon. However, few people are aware that Abu Rehan Al-Biruni developed an extremely precise method of predicting the sightability of the new Moon crescent, more than a thousand years ago. Unfortunately it was forgotten by the decadent culture, and his works remained in oblivion for a thousand years. We will discuss more of it later.

In order to understand how it is possible to predict the visibility of the new Moon crescent, let us consider some basic concepts in a simple manner, avoiding scientific terms as much as possible. Unlike the full Moon that travels across the middle of the sky all through the night, the new Moon crescent appears in the western sky near sunset, its path makes a small arc, and it disappears below the western horizon after a few minutes. Seeing from the Earth, the Sun lies towards the opposite side of the Moon during this period, such that the un-illuminated hemisphere of the Moon faces the Earth, and hence the Moon largely remains invisible to us. However, after a brief period of complete invisibility (the conjunction of the Sun and the Moon), a little crescent of illuminated portion encroaches towards the Earth, upon the margin of the Moon, and this is visible to us as the thin crescent or ‘Hilal’. This is because the Sun shifts a little off the Earth-Moon axis (fig-1). When the entire hemisphere of the Moon facing the Earth becomes totally dark, the event is termed as ‘the Conjunction of Sun & Moon’ or ‘Birth of the New Moon’, or the ‘Astronomical New Moon’ which is different from sighting of the new Moon crescent and occurs 18 to 24 hours before the crescent becomes visible to us. This event has got nothing to do with the Islamic sighting of the new crescent Moon.

When we look towards the western horizon near the sunset after the end of the lunar month, the Sun and the Moon can be in any of the following three positions relative to each other and the Earth’s horizon. These positions are usually different when viewed from different geographical locations of the Earth on the same date.

Position A:

The sunset has occurred while the Moon is still in the visible horizon (Fig-2). This is the situation when the new Moon crescent can be seen, provided the weather is clear. (Heavy clouds can hide even the Sun in midday!). However, sighting of the Moon crescent becomes difficult if it sets very soon after the Sun.

Position B:

The Moon has disappeared below the horizon while the Sun is still above the horizon (Fig-3). It is impossible to sight the Moon crescent in this situation.

Position C:

The Sun and the Moon are both above the horizon at the same time (Fig 4). The naked eye cannot see the Moon crescent because the brightness of the Sun makes it invisible. (We cannot see the stars in daylight although they are there in the sky). With some modern powerful telescopes, available in advanced observatories, the Moon crescent can some times be sighted in the presence of the Sun, but this is not the usual case.

The position of the celestial bodies is determined by their altitude and azimuth, just as a location on Earth’s surface can be determined by its latitude and longitude. These positions of the heavenly bodies can be, and have been calculated for several hundred years to come. Celestial events such as the solar and lunar eclipse are predicted using these calculations. One can easily understand that if the azimuth and altitude of the Sun and the Moon are known for a certain location on Earth at a certain date at sunset, the arrangement of the Sun and the Moon relative to the horizon i.e. position A, B, or C can be calculated and hence the visibility of the new Moon crescent can be predicted. However, apart from the simple mathematics, several other factors, such as the refraction and diffraction of light and different states of atmospheric pollution contribute to the visibility of the Moon crescent. Furthermore, the limitations of the human eye in seeing small objects at a certain distance (the visual acuity), and the necessity of a certain minimal difference in the brightness of an object and its surroundings (contrast sensitivity) can interfere with the visibility. All these phenomena create a small area of doubtful predictability that stretches across the globe as a strip or zone only a few miles wide. For the rest of the globe (i.e. more than ninety five percent) the visibility (provided the weather is clear) or non-visibility can be precisely calculated. Even for the zone of doubt, predictions can be made more accurate empirically, based on the statistical data of a large number of actual sightings.

Now let us go back to the Al-Biruni’s method of predicting the new Moon crescent. As a child growing up in Aligarh, India, in 1930s, I became interested in stargazing and the local Hindu pundits were happy to explain to me the heavenly objects and events. I learned Sanskrit language to read their books, and soon mastered their astronomy. Both the Hindus and the Muslims particularly appreciated my predictions of the new Moon crescent. That created in me a passion for predicting the sighting of the new Moon crescent. Later, while doing my B.Sc. in the Engineering College of the Aligarh Muslim University in 1940s, I had the chance of learning the western astronomy. E. W. Maunder had done some work in this regard in those days. During this time I came across a reference to a Moon crescent sighting method in a hard to find Arabic book ‘Ghuratuz –Zijaat’ by Al-Biruni. Determined to find it, I finally got a copy after a great effort, and went through it; Arabic been taught to me as a family tradition. To my dismay, Al-Biruni had used enigmatic ancient Arabic terminology that didn’t mean anything to me. I was about to ignore the book, like so many must have done before me during the centuries before, when I decided to give it one last try in the light of the ancient Hindu, and the modern western astronomy, since Al-Biruni must have taken help from both the Indian and Greek astronomy. Suddenly, like a virtual Rosetta Stone, some terms started to make sense. I went on and soon the entire work was clear to me. Al-Biruni was amazingly modern in his concepts! People marvel at his calculating the Earth’s diameter, but here was some thing much more sophisticated.

I meticulously studied the method and translated the Arabic terms in the equivalent modern terminology and even translated the whole book into English. I used numerous actual sightings, made by myself in the past several years, to further refine the formula empirically. I was studying electrical engineering, and it remained my carrier throughout life, but I still managed to take some time out and tried to introduce Al-Biruni’s method to the scientific community through scientific conferences and research articles as much as my circumstances allowed. Unfortunately nobody was interested in it in those days. The Muslims were not educated enough, the European and American astronomers did not have anything to do with it. That was a long time back. My presentations at scientific conferences have been forgotten, and most of the scientific journals containing my articles are now extinct. Since about the past quarter of a century I had confined the activity to the monthly prediction for the date of the new Moon crescent visibility published in a local daily newspaper, which I have been doing since 1950s. However, feeling that the issue is becoming more and more controversial and politically dangerous in the past few years, I decided to educate the general public by every possible means, although I am nearing ninety years of age. At the same time I am glad that now some scholars, like Dr. M. Ilyas and Dr. S K. Shaukat, besides B.D. Yallop and others from the western countries have done commendable work on the subject. Several criteria have been set to make the prediction more accurate. However, I have found that Al-Biruni’s criterion is still the most accurate yet. Unfortunately I am not in a position to participate in academic activity now because of my health, age and other circumstances.

I am describing here a rather over-simplified method for calculating the first sighting of the new crescent Moon, at a given location on the required date, by means of a graph, (Fig 5), that I have devised with the help of Al-Biruni’s method, and have further refined it. Following are the steps to calculate the prediction.

Step 1

Find out the exact latitude and longitude of the place from where the Moon crescent is to be sighted. Any atlas or some websites can provide the information. Some of the websites are:

https://geography.about.com/cs/latitudelongitude/

https://www.realestate3d.com/gps/world-latlong.htm

Step 2

Get the time of sunset of that location at the required date. There are many websites that can provide the information (one of these is https://www.timeanddate.com/worldclock/sunrise.html)

Step 3

Determine the azimuths of the Sun and the Moon at sunset. Altitude of the Moon at this time is also needed. Getting this information from H M Nautical Almanac Office in London used to be a difficult process, but now anyone can get this information easily from the Astronomical Applications Department of the United States Naval Observatory, Washington D.C.) (Website: https://www.aa.usno.navy.mil/data/docs/AltAz.html)

Or the Australian Government’s astronomical information website: https://www.ga.gov.au/geodesy/astro/smpos.jsp

Step 4

Find the algebraic azimuth difference between the Sun and the Moon (Sun azimuth minus the Moon azimuth), and plot it on the horizontal scale of the graph. (Fig 5)

Step 5

Plot the altitude of the Moon on the vertical scale of the graph. (Fig 5)

If the plotted point lies below the visibility curve, the Moon crescent will not be visible, and if it lies above the curve the Moon crescent can be sighted, provided the weather is clear. If the point lies on or extremely near the visibility curve, the crescent may or may not be visible due to the atmospheric factors and the human eye limitations, as discussed earlier. Points plotted for several locations on the Earth on a given date can be used to draw parabolic curves across the world map, by which anyone can tell at a glance that in which areas of the world the new Moon crescent will be visible or, more importantly, not visible at a certain date. For example, the prediction of the new Moon sighting for Zilhajja 1427 A.H. is shown by means of the visibility lines drawn on a world map that I had made in 1955 (Fig 6). The new Moon crescent will be visible in the south of the visibility line on the dates written on these lines. It can be seen that in Pakistan, the Zilhajja new Moon crescent will be visible in the 22^nd December 2006, so that the first of Zilhajja will be on 23^rd December 2006.

In the end I must add that the matter of the new Moon crescent sighting for religious purposes is ultimately the responsibility of the religious scholars. All that science can do is to help them ignore the claims of Moon crescent sighting from the areas were it is absolutely impossible to sight the new Moon crescent.

Predicting the Chaand Raat by Samad Husain Rizvi