How can the Ramadan crescent moon be sighted with the naked eye, while observatories and modern instruments are unable to see it on the same night?

Determining the beginning of Ramadan depends on sighting the crescent moon or completing thirty days of Sha’ban, according to the Prophet, peace and blessings be upon him: "Fast when you see it [the new moon], and break your fast when you see it. If it is obscured from you, then complete the number of Sha’ban as thirty days." Astronomical calculations are not relied upon. Sighting with the naked eye is the principle, but sighting with modern instruments is acceptable. If the crescent moon is sighted by a trustworthy Muslim or two trustworthy Muslims, then this sighting must be acted upon.