Hadith - local moonsighting
A narration of Ibn Abbas in Sahīh Muslim indicates that local moonsighting alone was the prevailing method in the time of the Blessed Prophet (صلى الله عليه وسلم) and was a part of the teachings of the Blessed Prophet (صلى الله عليه وسلم) to the Sahābah. The narration goes like this:
Kurayb narrates that Umm al-Fadl sent him to Muāwiyah in Sham for something. Kurayb says, "I went to Sham and finished the job. I was in Sham when the month of Ramadān began and we saw the moon the night of Friday. When I reached Madinah at the end of the blessed month, Ibn Abbas asked me about Sham. (After answering him) He then asked me when we saw the moon.
I said, 'We saw the moon the night of Jumuah.'
He asked, 'Did you see it as well?'
I said, 'Yes, I saw it too and many others saw it and we all kept fasting and so did Muāwiyah (that is according to that moonsighting).'
Ibn Abbas said, 'But we saw the moon on Saturday night, therefore, we will keep fasting for thirty days according to that unless we sight the moon on the 29th.'
I asked, 'You don’t think the moonsighting of Muāwiyah and his fasting is enough for you?'
Ibn Abbas replied, 'No, this is how the Blessed Prophet (صلى الله عليه وسلم) taught us.'" (Muslim H.1819, Tirmiðī H.629, Nasa'i H.2084, Abū-Dāwūd H.1985, Musnad Ahmad H.2653 Dar-qutni H.2234)
This hadith is clear evidence. When Ibn Abbas was informed by the person who himself sighted the moon that the people of Sham had begun Ramadān one day before, he responded that it was not only his opinion, but also the teachings of the Blessed Prophet (صلى الله عليه وسلم) that the moonsighting of another locality was not compulsory upon them.