Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions. Wa alaikum assalam wa rahmatullahi wa barakatuh. As to what follows: In response to your question, we say: Answer 1: The scholars have differed on this issue; some of them are of the opinion that calculations can be used all the time. Other scholars are of the opinion that calculations should not be considered at all. A group of scholars had a detailed opinion on the issue. The preponderant view is that calculations can be used to negate the sighting of the moon and not to establish its sighting. If reliable calculations establish that the moon cannot be seen on a certain day and someone says, “I have seen the moon,” we will not accept his statement. However, we cannot establish the presence of the moon merely because calculations establish it because of the possibility of that the moon may be born but it may not be seen. What is considered is the sighting of the moon and not the birth of the moon. And Allah knows best. In terms of action; you should fast with the people of your country and when they break their fast you should also break yours because of what has been transmitted by Abu Dawud, at-Tirmithi and others from the hadith of Abu Hurairah (peace be upon him) that he said, “The Messenger of Allah said, “The fast is the day the people fast, the breaking of the fast is the day the people break their fast.” [at-Tirmithi (697)].‘Aishah (may Allah be pleased with her) narrated the hadith with the wording, “The breaking of the fast is the day the people break their fast, and the sacrifice is the day the people sacrifice." [at-Tirmithi (802)]. At-Tirmithi said in his al-Jami’, “Indeed the  hadith means  that the beginning of fasting and its end is with the majority of the people”.   Answer 2: It is clear from the previous answer that a person should follow the people of his country in fasting or ending fasting, and it is not permissible for him to contradict them. In one narration Imam Ahmad said, “A person should fast with the Muslim ruler and the majority of the Muslims in cloudless and cloudy conditions”.  He also said, “Allah’s hand is with the majority.”