New moon 
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In
The original meaning of the term new moon, which is still sometimes used in nonastronomical contexts, was the first visible crescent of the Moon, after
A lunation or
This article contains

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
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 20000101 00:00:00 reckoned in the time scale known as
To obtain this moment expressed in
Periodic perturbations change the time of true conjunction from these mean values. For all new moons between 1601 and 2401, the maximum difference is 0.592 days = 14h13m in either direction. The duration of a lunation (i.e. the time from new moon to the next new moon) varies in this period between 29.272 and 29.833 days, i.e. −0.259d = 6h12m shorter, or +0.302d = 7h15m longer than average.^{ [4]}^{ [5]} This range is smaller than the difference between mean and true conjunction, because during one lunation the periodic terms cannot all change to their maximum opposite value.
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The longterm error of the formula is approximately: 1 cy^{2} seconds in TT, and 11 cy^{2} seconds in UT (cy is centuries since 2000; see section Explanation of the formulae for details.)
The moment of mean conjunction can easily be computed from an expression for the mean ecliptical longitude of the Moon minus the mean ecliptical longitude of the Sun (Delauney parameter D).
constant term:
quadratic term:
The theoretical tidal contribution to ΔT is about +42 s/cy^{2}^{ [12]} the smaller observed value is thought to be mostly due to changes in the shape of the Earth.^{ [13]} Because the discrepancy is not fully explained, uncertainty of our prediction of UT (rotation angle of the Earth) may be as large as the difference between these values: 11 s/cy^{2}. The error in the position of the Moon itself is only maybe 0.5"/cy^{2},^{ [note 8]} or (because the apparent mean angular velocity of the Moon is about 0.5"/s), 1 s/cy^{2} in the time of conjunction with the Sun.