question #3 Sahih Muslim 1133a, Book 13, Hadith 170 : What role does the sighting of the new moon play in determining the timing of Islamic observances?

I went to Ibn ‘Abbas (Allah be Pleased with both of them) and he was reclining using his mantle as a pillow near the fountain of Zamzam. I said to him: Tell me about fasting on Ashura. He said: When you see the new moon of Muharram then count the (days) and observe fast on the 9th. I said to him: Is it how the Messenger of Allah (ﷺ) observed the fast? He said: Yes.