Even though visual sighting is necessary to determine the start of a month, it is useful to accurately predict when a crescent is likely to be visible in order to produce lunar calendars in advance and to guide the watchers where to look. Since ancient times, many Civilisations and Astronomers have tried to predict the likelihood of visualising the new crescent using different 'minimum visibility criteria'. It incorporates many disciplines such as physics, particularly optics, mathematics and celestial mechanics. Since ancient times, Muslim Scientists have studied astronomy, contributing greatly to human knowledge. Eclipses occur always at the same instant that the Astronomers predict.
Stars disappear or reappear at exactly the same second that it is predicted.
The Sun must not catch up the Moon, nor does the night outstrip the day. Thus the Qur an tells us quite clearly that the motions of the Celestial Bodies are fixed and so are the mathematical formulae controlling them. That is why today space crafts can be sent with such precision to explore far away planets in our Solar System. This is the moment of Astronomical NEW MOON, and it occurs at exactly the same instant regardless of where you are on earth, since it does not depend in any way on the viewer's perspective. That night and the following day are the first day of the new Islamic Month.