There are 3 opinions on this issue:
1. Those that place complete reliance on astronomical data, negating any role of actual sighting. According to this group, the new month will begin as forecasted by astronomical data irrespective of whether actual sighting took place or not. This view goes contrary to Ahaadith of Nabi [sallallaahu alayhi wasallam] and is therefore unacceptable.
2. Those that place complete reliance on actual sighting allowing astronomical data no influence. According to this group, the ultimate decision will be based on the reliability of witnesses bearing testimony of moonsighting. If they are reliable, then their testimony will be accepted and a ruling passed accordingly irrespective of whether such a testimony appears reasonable or logical, and whether it is acceptable in terms of astronomical predictions or not. This group seek support for their view from the Ahaadith that commands the commencement and ceasing of fasting with actual sighting of the moon – and that we are a simple unlettered Ummah. Many ibaaraat of the Fuqahaa can also be found in support of this view.
3. Those that give astronomical data, persuasive influence but not conclusive authority. This group purports that issuing a ruling solely based on actual sighting even though it may be contrary to reason and logic is against the teachings of Islam. They purport that although certain aspects or rulings of our deen may be supralogical, they will never be illogical and just as Islam has embraced simplicity and a natural way it also embraces logic and reason. Allamah Jassas in al-Fusool (vol.4 pg.80) and Allaamah Shatbi in al-Muwaafaqaat (vol.3 pg.131) have brought chapters in support of this. According to this group, actual sighting of the moon will still be the basis of issuing a ruling (and not astronomical data). Astronomical data will merely be used to authenticate the veracity of testimonies given. If testimonies are given that are impossible according to astronomical data, they will be rejected. This was the view of the great Shaafi’ee scholar, Allamah al-Subki (Fataawa al-Subki vol.1 pg.209) and the Taabi’ee Mutarrif ibn Abdullah (commentary of Sahih Muslim – al-Minhaj vol.1 pg.347).
Rejecting the testimony of one, two or a few people whose collective testimony does not necessitate absolute conclusive information is not something new to Islam if it is contrary to conclusive, absolute information. This is also why the testimony of moonsighting of one or two people in the context of clear skies is not accepted.
Consider also the following from the works of the great Ulama.
A question may arise that how can the testimony of a reliable Muslim be rejected based on astronomical data whilst the astronomers are at variance with themselves. In response to this: Certain astronomical information can be proven conclusively (like time of conjunction) and some not as in the case of the minimum altitude of which moonsighting is possible.
Therefore, if a group of individuals (that has no reached the level of Tawaatur – absolute) testify to sighting the moon before conjunction time, then this testimony will be rejected. The time of conjunction as presented by astronomical data is absolute and if contradicted by that which is not absolute, then the absolute will be give preference.
By way of example: if sunset is predicted (by astronomical data) to be 5:15 pm, and a group of individuals testify under oath that they had performed Maghrib Salaat at 4:35 pm because they witnessed sunset at 4:30 pm., then their collective testimony will be rejected. This rejection will be on the basis that astronomical data, which is absolutely conclusive, is being contradicted by that which is not absolute.
However, if astronomical data which is not absolute, such as the minimum altitude for moonsighting is 5 degrees is contradicted by the testimony of a few individuals, e.g. moonsighting at 4 degrees, then their testimony will not be rejected on mere contradiction (as both contradicting sides are of equal strength). Rather, either side will be give preference due to outside factors.