In the Name of Allah, The Most Gracious, Ever Merciful.
Love for All, Hatred for None.
Islamic Month Defined - Many Muslim communities make a calendar predicting the dates of Islamic months (like Ramadan and Dhul Hijja) based upon scientific predictions of when the moon/crescent should be visible. The actual start and end of the month of Ramadan is (just like every other month on the Islamic calendar) based upon the sighting of the moon. Do not confuse the Islamic new moon, which is when the moon is first visible, to the "astronomical new moon". The astronomical new moon, as listed on newspapers and most astronomical sites (such as the US Naval Observatory site), is when conjunction occurs, and the moon is dark; the age of the moon starts from this point. The Islamic new moon is when that first little sliver of the moon (the crescent or "hilal") is first visible. That night starts a new Islamic month, and the following day would be considered the first day of the new Islamic month.
Visibility of Moon/Crescent Explained - The visibility of the crescent is not a function of the age of the moon (time elapsed since conjunction, or "astronomical new moon"). The visibility of the new moon/crescent is a function primarily of the angle between the moon, observer, and sun (which affects the brightness of the crescent) and the apparent altitude of the moon above the horizon and of the sun below the horizon (which affects the background brightness against which the moon is to be observed). Of course, as the moon "grows older" these angles do increase, so the more time that elapses, the more likely it is to see the moon. But one cannot ignore the actual position of the moon in the sky. Thus, the age of the moon does not automatically predict new moon/crescent visibility; so if the new moon (conjunction) occurs on one day, then the crescent will not necessarily be visible the following evening (or even the one after that!).
Scientific Calculations for Moon/Crescent Visibility Prediction - There are many conditions for the sighting of the moon in any location. However, as time has progressed and technology has advanced, the ability to predict the sighting of the moon has increased. Without getting into the debate as to which set of criteria to use, a consensus among scientists has developed to use the method developed by astronomer B. D. Yallop, which is currently one of the most accurate methods available. In Britain, the H.M. Nautical Almanac Office has adopted this formula for determining the visibility of the moon. This formula results in a visibility parameter given in a range of A to F. The range of the parameter corresponds to the following visibility types for the new crescent moon:
(see "NAO Technical Note No. 69 - A Method for Predicting the First Sighting of the New Crescent Moon by BD Yallop").
Next new moon world map - http://astro.ukho.gov.uk/moonwatch/nextnewmoon.html
(As a side note, the U.S. Naval Observatory also publishes astronomical data which is very useful. However, when it mentions "x% of the Moon's visible disk illuminated", this doesn't always directly translate to visibility from the earth. Although this is a factor and can be an indicator, the moon may still not be visible from the earth even though part of it is illuminated. See above "Visibility of Moon/Crescent Explained".)
The old style is preferred by many, though, and common sense seems to dictate that if one actually sees the moon with one's eyes, then an ounce of observation is worth a ton of calculation! Of course, you have to be careful that people will often make an honest mistake in seeing things that aren't there. (There was an experiment where astronomers took people out in the field and told them to look for a particular very faint star. About 15-20% of the people saw the star. However, it was really a trick. There was no star! It may be somewhat analogous to the placebo effect in medicine.)
Conclusion - With all of these factors taken into consideration, most Muslim communities make a calendar predicting the dates of Islamic months (like Ramadan, or the 2 "Eids"). Since sunrise and sunset can be calculated with great accuracy, along with the precise positions of planets, comets and other heavenly bodies, it should be no shock that science has progressed to where we can predict (with greater accuracy than in the past) when the moon should first be visible also. Given the visibility parameter published by H.M. Nautical Almanac Office, visibility types A, B, and C correspond well with the Islamic concept of being able to see the moon by eye for the commencement of the Islamic month. This parameter can be obtained through the use of the Websurf service of H.M. Nautical Almanac Office.
Therefore, although many believe that you should only make the official start of an Islamic month after actually seeing the moon with your eyes, the use of these proven scientific calculations from the latest, state of the art tools, has coincided with the actual observations we have made in the sky for years. This may be just one more example of how there is no clash between traditional Islamic principles and the modern age, they can be in complete agreement; and the traditions of Islam are just as relevant and valid today as they have been for centuries.