Is it permissible to rely on astronomical observatories' calculations for establishing the beginning and end of the month? Is it permissible for a Muslim to use modern instruments to sight the crescent, or must the sighting be with the naked eye?

The legitimate method for establishing the new month is by sighting the crescent moon, and this must be done by someone trustworthy in their religiosity and sharpness of sight. Relying solely on astronomical calculations is not permissible; rather, visual sighting must occur. Using binoculars (a magnifying scope) to sight the crescent moon is permissible but not obligatory. Whenever its sighting is confirmed by any reliable means, it becomes obligatory to act upon it, as the Prophet (peace be upon him) said: "When you see it, fast, and when you see it, break your fast."