3.  Evidence for the probability of a moon sighting occurring according to calculations is also reviewed, although it is not the sole reason for determining a new month.  Islamic law has made clear the necessity of an actual visual, unaided sighting of the moon.  However, there are no restrictions to use calculations in determining the probability of a moon sighting.  The following has been taken from an article written by Mufti Taqi Usmani in regards to calculations:

“Thank you for your letter asking me about the issue of sighting of moon at the occasion of Eid-ul-Fitr and about the acceptability of evidence despite its being impossible according to the astronomical calculations. In fact the contemporary scholars have different views on this point. I personally believe that if it is certainly proved that the moon is not yet born and its sighting is not at all possible on a particular evening, the evidence of only a few persons should not be taken as a proof of existence of moon at the horizon and the Ramadan or Eid should not be started on that basis alone unless there is evidence of people in overwhelming numbers that they themselves have seen the moon in which case it may be said that there was something wrong in the astronomical calculation. But in the absence of such an evidence, the only evidence of two or some more persons should not be relied upon. This view of mine is based on the ruling given by a large number of jurists that if the Horizon is clear the evidence of two persons is not enough for proving a crescent moon unless it is established by the evidence of a great number of people about whom it is not is not imaginable that they may have connived to give a false evidence. The requirement of such an overwhelming evidence in this case is based on the common sense that if the horizon is clear the moon must have been seen by a large number of people and merely the evidence of two persons is doubtful. By the analogy, if the astronomical calculation proved that new moon cannot be sighted on a particular day the evidence of a few people should not be relied upon.

"However, there are some contemporary scholars who totally disregard the astronomical calculations in the matter of sighting the moon and base their view on the famous Hadith of the Holy Prophet 'sallallahu alaihi wa sallam' Keep fast after seeing it (moon) and give up fasting after seeing it (moon)." Their argument is that the Shariah does not base its findings on the astronomical calculations because it is meant for all the Muslims the majority of whom have no means to know the results of such calculations. Therefore, they say, reliance can be placed only on the evidence of the persons who claim to have seen the moon. This is the view which has found favor with the Saudi authorities who are responsible for declaring the sighting or otherwise of the moon. Although I do not endorse this view, nor do other scholars of many Muslims countries accept it, yet the issue being a matter of Ijtihad, the decision given by Saudi authorities is enforceable in their own jurisdiction. That is why, despite having a different view, we validate the Hajj and Ramadan etc, as announced by the Saudi authorities [for applicability within Saudi Arabia]. The Muslims living in other parts of the world should desirably arrange their own system of sighting the moon, as is done in Pakistan and many other countries, because the system adopted in Saudi Arabia is not based on the stronger view. However, as I mentioned earlier this is not an issue which has been specifically mentioned in the Holy Qur'an or Sunnah in express terms but it is a matter of Ijtihad, therefore, we should not hold that any decision taken on that basis, whether in Saudi Arabia or in any other country, is totally against Shariah and the worship or celebrations held on that basis are invalid. This is my humble opinion regarding this issue and according to me the Muslims living in UK etc. should preferably make their own arrangement for sighting of the moon. However, if the dissension of the Muslims cannot be removed except by declaring the beginning of the months on the basis of the announcement of the Saudi authorities then the adoption of Saudi view is less harmful than inculcating the dissension among the Muslims, particularly, in a non-Muslim country."