2- Astronomical calculations:
Most of the contemporary scholars disregard the astronomical calculations in ascertaining the beginning and the end of the month, however it is obligatory to act according the crescent sighting because of Allah's saying: “They ask you (O Muhammad peace be upon him) about the new crescents. Say: “They are signs to mark fixed periods of time for mankind and for the pilgrimage.” [Surat Al Baqarah: 189]. And for the saying of the Prophet (peace be upon him): "Do not fast until you see the crescent, and do not stop fasting until you see it.” [Reported by Al Bukhari and Muslim]. And because of the following Hadith: "Begin the fast for seeing it (the crescent)." [Reported by Al Bukhari and Muslim]. According to this Hadith, the International Islamic Fiqh Academy reached a decision No. (7) at its fourth session in 1401 AH with considering astronomical calculations in crescent sighting.
3 - Using observatories in crescent sighting:
Barely, scholars have agreed to the permissibility of using observatories in crescent sighting. If crescent is seen truly, the people must act according to this sight because of the Hadith: "Begin the fast when you see it," even if the crescent is not seen by naked eye on condition that the person who sees the crescent in observatories must be trustworthy. The International Islamic Fiqh Academy reached a decision No. 18 (6/3) in 19/10/1425 AH, in addition to the decision of the Senior Scholars in Saudi Arabia, and the decision of the European Council for Fatwa and Research in this regard.
4 - Traveling to another country where crescent sighting is different:
If a person travels from one country to another and the crescent sighting is different in both, whether that happened at the beginning or at the end of the month, this case has different conditions:
1- The crescent sighting may be different at the beginning of the month but is the same at the end of the month.
2- The crescent sighting is the same at the beginning of the month but differs at the end.
3- The crescent sighting is different in both.
The difference lies in: sometimes the days of the month are twenty-eight and sometimes they are thirty-one, what should a person do?
The Shari`ah stated that a person should follow the country to which he traveled. So, a person should begin the fast and end it with the country in which he is, even if this resulted in fasting a day more or less because of the stated proofs which connected the beginning and the end of the fast with the general Muslim opinion. The Prophet (peace be upon him) said: "Fast is the day when you fast, and the sacrificial animal is incumbent on you in the day when you offer the sacrifice." [Reported by At-Tirmidhy, Abu Dawud, and Ibn Majah with authentic chain of narration]. In addition to the Prophet's saying in the Two Sahih (books of authentic Hadiths, i.e., Al Bukhari and Muslim): "Begin the fast when you see it and stop fasting when you see it." the address is for all Muslims.
By analogical deduction, if someone begins his fast in a town and moves to another during daytime where their sunset delays for a while, it is incumbent on him to break the fast with the town to which he moves.
This is for the sake of unifying the Muslim nation, therefore a person must break his fast with the town to which he travels.
In case he fasted twenty-eight days, it is better for him to fast another day to complete twenty-nine days because months in Islamic calendar are not less than twenty-nine days.