It is permissible to use telescopes etc., but not calculations, to sight the new moon
Question

It is not possible to see the new moon with the naked eye before it is 30 hours old, and in addition to that, it is sometimes not possible to see it at all because of the weather conditions. On this basis, is it permissible to resort to using astronomical information to calculate the likely time for sighting the new moon and the start of Ramadan, or do we have to actually sight the new moon before we start fasting the blessed month of Ramadan?
Praise be to Allah.It is permissible to use telescopes etc. to sight the moon, but it is not permissible to rely on astronomical data to confirm the beginning or end of the blessed month of Ramadan, because Allah has not prescribed that for us in His Book or in the Sunnah of His Prophet (peace and blessings of Allah be upon him). What He has prescribed for us is to confirm the beginning and end of Ramadan by sighting the new moon of Ramadan to start fasting, and the new moon of Shawwaal to end the fast and gather to offer the Eid prayers. Allah has made the new moons to mark fixed periods of time for mankind and for the Hajj, so it is not permissible for Muslims to use any other method to determine the times for acts of worship such as fasting, celebrating Eid, performing Hajj, fasting for two months as expiation (kafaarah) for killing someone by mistake or divorcing one’s wife by zihaar, and so on. Allah says (interpretation of the meanings):
“… So whoever among you sights (the crescent on the first night of) the month (of Ramadan), he must observe sawm (fast) that month…” [al-Baqarah 2:185]
“They ask you (O Muhammad) about the new moons. Say: these are signs to mark fixed periods of time for mankind and for the pilgrimage…” [al-Baqarah 2:189]
The Prophet (peace and blessings of Allah be upon him) said: “Fast when you see it [the new moon] and stop fasting when you see it, and if it is cloudy then complete the month with thirty days.” On this basis, the one who does not see the new moon from the time it rises on a clear or cloudy night must complete the month (of Sha’baan) with thirty days.
(Fataawa al-Lajnah al-Daa’imah, 10/100). This is the case if the sighting of the new moon is not confirmed in another country; if the moon is sighted according to the guidelines of Sharee’ah, then fasting is obligatory, according to the majority of scholars.
And Allah knows best.