All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
The Sharee’ah considers only the eye sighting of the moon. So, calculations and astronomic estimations are not accepted by the scholars of Islam from their most preponderant opinion. This is so because sighting the new moon by eye is possible everywhere and at anytime while calculations and astronomy are known only to a small number of people, so they can be known in some places and unknown in others.
For, the above, we tell you that it is unlawful for you to fast according to astronomic calculation. You should only rely on your own sighting of the new moon or that of Muslims in the nearest country to yours.
For more benefit on Ramadan's crescent sighting, please refer to Fataawa 115026, 92566, 90491, 86669, 85129 and 92703.
Allah knows best.