[Fasting by sighting the crescent]

Answer—and Allah is the Granter of success: That is permissible. This is because, as the astronomers themselves say, it cannot be seen through the telescope unless it has separated from the sun and moved away from its rays by a defined amount; and nothing can be seen through the telescope except what could, in principle, be seen with the naked eye. When the crescent is close to the sun, it cannot be seen through the telescope due to the overpowering of the sun’s rays and their preventing it from being seen—by telescope or otherwise.
Source : Min Thimār al-ʿIlm wa al-Ḥikmah vol.1