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New moon

Traditionally, the lunar phase new moon begins with the 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 doesn't depend on location. To avoid confusion with the traditional new moon, this may be called the dark moon.

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 isn't known in advance. In Saudi Arabia, observers are sent up in airplanes if the weather is cloudy when the new moon is expected.

Approximate formula

An approximate formula for the average time of new moon N (conjunction) is

D = 5.597661 + 29.5305888610*N + (102.026*10^-12)*N*N,

where D is the number of days (and fractions) since 2000-01-01 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 - (235*10^-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 - see section Explanation of the formulae for details.)

A reasonably simple method to more accurately compute the time of new moon is discussed on the page fumocy.

Explanation of the formulae

The moment of mean conjunction can easily be computed from an expression for the average ecliptic longitude of the Moon minus the average ecliptic longitude of the Sun (Delauney parameter D). The expression given is based on the paper by Chapront et al. [2], with the following corrections:

constant term:
- Applied the constant terms of the aberration to obtain the apparent difference in ecliptic longitudes:

Sun: +20.496"

Moon: -0.704"

Correction in conjunction: -0.000451 days.

- For UT: at 1 Jan. 2000, Delta-T was +63.83 s; hence the correction for the clock time of the conjunction is:

-0.000739 days.

quadratic term:

- In ELP2000-85 (see [1]), D has a quadratic term of -5.8681"*T*T; expressed in lunations N, this yields a correction of +87.403E-12*N*N days to the time of conjunction. The term includes a tidal contribution of 0.5* -23.8946 "/cy**2. The most current estimate from Lunar Laser Ranging is (see [2]): (-25.858 ±0.003) "/cy**2. Therefore the tidal correction to the quadratic term in D is -0.9817*T*T". The polynomial provided by Chapront et al. (ref. [2]) provides the same value. This translates to a correction of +14.622E-12*N*N days; the quadratic term now is:

+102.026E-12*N*N days.

- For UT: analysis of historical observations show that Delta-T has a long-term increase of +31 s/cy**2 . Converted to days and lunations, the correction from ET to UT becomes:

-235E-12*N*N days.

The theoretical tidal contribution to Delta-T is about +42 s/cy**2 ; the smaller observed value is due to changes in the shape of the Earth. The 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, or 1 s/cy**2 in the time of conjunction with the Sun.

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 (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. This range is smaller than the difference between mean and true conjunction, because during the lunation the periodic terms cannot all change to their maximum opposite value.

Literature

[1] M.Chapront-Touzé, J.Chapront: "ELP2000-85: a semianalytical lunar ephemeris adequate for hsitorical times". Astron.Astrophys. 190, 342..352 (1988)

[2] J.Chapront, M.Chapront-Touzé, G.Francou: "A new determination of lunar orbital parameters, precession contant, and tidal acceleration from LLR measurements". Astron. Astrophys. 387, 700..709 (2002)

see: "http: simbad.u-strasbg.fr/cgi-bin/cdsbib?2002A%26A...387..700C"

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