Known as the Umm al-Qura calendar the Saudi Arabian government uses the following criteria for determining the beginning of the Islamic month. These criteria apply since the Islamic year 1423 (current Islamic year: 1432):

If on the 29th day of the lunar month the two following conditions are satisfied, then the next day is the first day of the new lunar month:

1. The geocentric conjunction occurs before sunset2. The moon sets after the sun

Otherwise, the current lunar month will last 30 days.

It is obvious that the actual sighting of the young crescent is not taken into account. Many discrepancies have been reported about the beginning of the lunar month under these circumstances. Even if the conjunction is shortly before sunset, with no possibility of viewing the crescent on that particular evening, the month will be declared as over, contrary to Islamic tradition.

Low on the horizon, faint and thin, the young crescent is indeed difficult to observe. The following scientific criteria determine the actual observation of the crescent:

1. The arc of light (elongation, meaning separation of the moon from the sun),2. The arc of vision (the altitude the of moon from the sun),

3. The altitude of the moon above the local horizon,

4. The width of the crescent,

5. The distance of the moon from earth,

6. The distance of the earth from the sun.

We will exploit these terms in greater detail in the course of this article. In practice, at least ten hours must elapse after conjunction before the angular separation between sun and moon will be sufficient to give a chance to observe the crescent. Local atmospheric conditions will also obviously play a role.

Obviously, the traditional method would be to try to observe the crescent in Makkah itself. Normally, if the crescent is not visible on the 29th lunar day, the month would be extended to 30 days. The revolutionary new idea we have developed is the following: if, after conjunction, the new moon is sighted to the west of *Makkah before the morning prayer*, the sighting can be considered as having taken place in Makkah itself. The month will be ended at 29 days in this case. Otherwise it will be prolonged to 30 days. Instead of the narrow interval of time around sunset in order to observe the crescent, we now dispose of the whole night (until the morning prayer) to observe the crescent anywhere west of Makkah. This leads to the concept of the *limiting horizon* and of an *intermediate horizon* developed in the next paragraph. We might add, that the time of the morning prayer in Islam, called *fajr* in Arabic, is of solar nature, defined as the moment of early dawn.

The earth rotates around its axis once every 24 hours. This means that every point on any given longitude describes a circle of 360° around the axis of rotation defined by the straight line which traverses the North and the South poles. We can thus affirm that 24 hours (or 24 x 60 = 1440 minutes) correspond to 360°.Knowing the time of sunset in Makkah on the evening after the birth of the new moon, as well as the time of the fajr prayer which follows – meaning the fajr of the day which follows that of the birth of the new moon – it is very simple to calculate the time difference between the two. In fact, this interval of time varies between roughly 12 hours when the nights are the longest and 9 hours when they are the shortest. The simple rule of three tells us that if 24 hours correspond to 360°, then 12 hours correspond to 180° and 9 hours to 135°. For each day of birth of the new moon, this elementary rule of proportionality thus allows us to convert into a space interval – or, more precisely, into an interval of longitudinal degrees – the time interval between sunset at Makkah and the fajr of the next day, both referred to the new moon.

The calculation of the ** Limiting Horizon (LH) **is now very easy : it is the visibility to the extreme West of Makkah, circumscribed by fajr in this town.

Now Makkah is situated at a longitude of 39.8° East of the Greenwich meridian. Let us simplify this figure to 40° East and let us give a concrete example: suppose that the duration between sunset in Makkah on the day of the new moon birth and the prayer of fajr on the next day is 12 hours, which corresponds to 180° of longitude. Towards the West of Makkah, we will have to cover 40° in order to reach the Greenwich meridian and again cover a further 140° in order to reach our limiting horizon. In this case, LH = 140° West.

In practice, we have used the visibility curves provided by Syed Khalid Shaukat . Some examples of recent visibility curves are given below, whereas the method of plotting the visibility curves is given in the last section of this article. [More such visibility curves are also available at Crescent Visibility Predictions Section.]

The different colours represent extended zones of different patterns of visibility on earth between the latitudes 60° North and 60° South. The curves are plotted for the day of birth of the new moon (except when visibility is impossible on earth on this day) and the two following days.

We have retained the most convenient visibility, represented by the green and the blue fields. We have avoided the exclusive use of the green fields, because this leads to an impossible result: in 1430, for instance, we would end up with too many months of 30 days and a Hegirian year of close to 360 days.

One also has to emphasize that the blue fields represent vast regions of the globe and perfect conditions of visibility will certainly be achieved at some place or another. We further point out that the use of an optical instrument in case of necessity is hardly contrary to Islamic law.