Praise be to Allaah.
What counts with regard to confirming the beginning of the
month of Ramadan is sighting of the new moon or the completion of 30 days of
Sha’baan if the moon is not sighted. This is what is indicated by the saheeh
Sunnah, and the scholars are unanimously agreed on it. Al-Bukhaari (1909)
and Muslim (1081) narrated that Abu Hurayrah (may Allah be pleased with him)
said: The Prophet (blessings and peace of Allah be upon him) said: “Fast
when you see it and break the fast when you see it, and if it is cloudy then
reckon the month as thirty.”
Astronomical calculations do not count. The basic principle
with regard to sighting is that it should be done with the naked eye, but if
the crescent moon is sighted with modern equipment, then this sighting may
be acted upon, as stated in the answer to question number 106489. With
regard to how the new moon is sighted with the naked eye when it is not seen
with telescopes and equipment, this may be due to differences in the place
and time of sighting.
Whatever the case, the ruling depends on sighting of the new
moon. So long as it has been seen by one or two trustworthy Muslims, then it
is obligatory to act upon this sighting.
Shaykh Saalih ibn Muhammad al-Lahaydaan, the head of the
Higher Judiciary Council (may Allah preserve him) said: There is a brother
called ‘Abd-Allaah al-Khudayri who is famous for sighting the moon and he is
one of those who are known to be involved in sighting the moon at different
stages, even at times other than the new moon. Some astronomers went to him
and met with him in the region of Hawtah Sadeer. And he told me that they
estimated that the moon would appear on that night in a certain place
according to the calculations they did on their computers, but he told them
that it would not appear from the place that they said, because he had seen
it before them the night before, and he knew the stations of the moon and
from where it would rise every night. Then when the moon appeared, it rose
from the place he mentioned and not they place they mentioned. But he
excused them because their conclusion was not based on direct moon sighting;
rather it was based on calculations with the computers they had. End quote
from an interview with him in al-Riyadh newspaper.
http://www.alriyadh.com/2007/10/12/article286271_shtml
And Allah knows best.