Lunation

In astronomy, new moon is the first phase of the Moon, when it orbits not seen from the Earth, the moment when the Moon and the Sun have the same ecliptical longitude. The Moon is not visible at this time except when it is seen in silhouette during a solar eclipse when it is illuminated by earthshine. See the article on phases of the Moon for further details.

A lunation or synodic month is the mean (average) time from one new moon to the next. In the J2000.0 epoch, the average length of a lunation is 29.530588 days (or 29 days, 12 hours, 44 minutes, and 3 seconds). However, the length of any one synodic month can vary from 29.26 to 29.80 days due to the perturbing effects of the Sun's gravity on the Moon's eccentric orbit. In a lunar calendar, each month corresponds to a lunation. Each lunar cycle can be assigned a unique Lunation Number to identify it.

The length of a lunation is about 29.53 days. Its precise duration is linked to many phenomena in nature, such as the variation between spring and neap tides (the extreme highest and lowest tides, respectively). An approximate formula to compute the mean moments of new moon (conjunction between Sun and Moon) for successive months is:

where N is an integer, starting with 0 for the first new moon in the year 2000, and that is incremented by 1 for each successive synodic month; and the result d is the number of days (and fractions) since 2000-01-01 00:00:00 reckoned in the time scale known as Terrestrial Time (TT) used in ephemerides.

To obtain this moment expressed in Universal Time (UT, world clock time), add the result of following approximate correction to the result d obtained above:

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