Traditionally, the new moon is first visible crescent of the Moon after conjunction with the Sun. This takes place over the western horizon in a brief period between sunset and moonset. Therefore the time and even the day depend on the actual geographical location of the observer.
Currently, the new moon is defined by astronomers to occur at the moment of conjunction in ecliptic longitude with the Sun, when the Moon is invisible and a solar eclipse may occur. This moment is unique and does not depend on location. To avoid confusion with the traditional new moon, this may be called the dark moon.
An approximate formula for the average time of new moon N (conjunction) is
D = 5.597660 + 29.5305888531*N + 102.19E-12*N*N,
where D is the number of days (and fractions) since 1 January 2000 00:00:00 TT, and N is an integer.
To obtain this moment expressed in universal time (world clock time) for future events (N>0), apply the following approximate correction:
-0.000739 -235E-12*N*N days
The true new moon may differ from this by over 14 hours due to periodic perturbations. The long-term error of the formula is approximately: 1*cy*cy seconds in TT, and 11*cy*cy seconds in UT (cy is centuries since 2000); /details.
The new moon is the beginning of the month in the Muslim calendar. For this religious purpose, the new month begins when the first crescent moon is actually seen. Thus, it is impossible to be certain in advance of when months will begin; in particular, the exact date on which Ramadan will begin is not known in advance. In Saudi Arabia, observers are sent up in airplanes if the weather is cloudy when the new moon is expected.