Sighting the new moon is compulsory and it cannot be replaced by astronomical calculations.
Allah says, "So whoever of you sights (the crescent of the first night of) the month (of Ramadaan), he must fast that month." [Soorah al-Baqarah (2): 185]Fasting begins with the sighting of the new moon. It is sufficient that a trustworthy Muslim testifies to those in authority of seeing the new moon. Thereby, everyone should observe the fasts.
Abu Hurayrah (radhi allahu anhu) narrated, "A bedouin came to the Messenger of Allah (sallallahu alaihi wasallam) and reported, 'O Messenger of Allah (sallallahu alaihi wasallam), I have seen the new moon of Ramadaan.' Thereupon, the Prophet (sallallahu alaihi wasallam) asked him, 'Do you bear witness that 'Laa ilaha illAllah.' (i.e., there is no god worthy of worship except Allah)?', 'I do,' said the bedouin.The Prophet (sallallahu alaihi wasallam) further asked him whether he testifies that Muhammad (sallallahu alaihi wasallam) is the Messenger of Allah. The bedouin affirmed that again. Thereupon, the Prophet (sallallahu alaihi wasallam) asked Bilal (radhi allahu anhu) to announce the beginning of Ramadaan." [Sunan Abu Dawood no. 2333 and 2334]
Ibn Umar (radhi allahu anhu) said, "The people were seeking the new moon. Having sighted it myself, I reported to the Prophet. He (sallallahu alaihi wasallam) began his fast and ordered the people to begin theirs, too." [Sunan Abu Dawood no, 2335 (saheeh)]Sighting the new moon is compulsory and it cannot be replaced by astronomical calculations. The Messenger of Allah (sallallahu alaihi wasallam) said: "We are an unlettered nation; we neither write, nor know accounts. The month is like this and this, i.e., sometimes of 29 days and sometimes of 30 days." [Saheeh al-Bukharee]If it becomes difficult to see the moon due to bad weather conditions, then 30 days of the month of Shabaan are completed. He (sallallahu alaihi wasallam) said, "Fast when it (the moon) is seen and cease fasting when it is seen, so if it is concealed by clouds, then complete thirty days of Shabaan." [Saheeh al-Bukharee (vol. 4 number 106) and Saheeh Muslim (no. 1081)] It is not permissible to fast a day or two before Ramadaan (the day of doubt) in anticipation of Ramadaan. The Messenger of Allah (sallallahu alaihi wasallam) said, "None of you should start Ramadaan by fasting a day or two before it, except for a man who usually fasts (on those days), then let him fast that day." [Saheeh al-Bukharee (vol. 3, no. 138)]
FATAWADifferences in Moon Sighting between Countries and its Effect on those who Travel in RamadaanQuestion: What should a Muslim do if he moves from one country to another, where the people have started fasting Ramadaan on a different day?
Answer: Praise be to Allah. If a person finds himself in a country where the people have already started fasting, he must fast with them, because he must follow the ruling of the country he is in. The Prophet (sallallahu alaihe wasallam) said, "Fast when the people fast, break your fast when the people break their fast, and offer your sacrifice when the people offer their sacrifice." [Reported by Abu Dawood with a jayyid isnad. There are corroborating reports narrated by Abu Dawood and others]
Suppose that he moved from a country where he had begun fasting with the people there, and went to another country. He has to either break his fast or continue fasting according to the ruling of the people in the country to which he has traveled, even if they end their fast earlier than the country where he started fasting. But if it turns out that he has fasted less than twenty-nine days, he must make up the fasts later on, because the Hijri month cannot be less than twenty-nine days." Fatawa al-Lajnah al-Daa'imah, 10/124Taken from As-Sunnah Newsletter