New moon

This article is about the lunar phase; for other uses, see New Moon (disambiguation).

The lunar phase depends on the Moon's position in orbit around Earth. This diagram looks down on the North pole;

The New Moon is the lunar phase that occurs when the Moon, in its monthly orbital motion around Earth, lies between Earth and the Sun, and is therefore in conjunction with the Sun as seen from Earth. At this time, the illuminated half of the Moon faces directly toward the Sun, and the dark or unilluminated portion of the Moon faces directly toward Earth, so that the Moon is invisible as seen from Earth.

New Moon is often considered to occur at the time of the appearance of 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, and therefore the precise time and even the date of the appearance of the New Moon by this definition will be influenced by the geographical location of the observer. The astronomical New Moon, sometimes known as the dark moon to avoid confusion, occurs by definition at the moment of conjunction in ecliptic longitude with the Sun, when the Moon is invisible from the Earth. This moment is unique and does not depend on location, and under certain circumstances it may be coincident with a solar eclipse.

The New Moon is the beginning of the month in lunar calendars such as the Muslim calendar, and in lunisolar calendars such as the Hebrew calendar, Hindu calendars, Buddhist calendar, and Chinese calendar.

Approximate formula

An approximate formula for calculating the occurence of the 'Nth' New Moon ('N') (the moment of astronomical conjunction) is given in units known as Terrestrial Time (TT), which by current conventions is calculated with a base universal time from the instant of the new years day in the current millenium, which is to say from the year two thousandths (2000 AD) very first second. The formula gives only what is known as the average time, for orbital perturbations (slight variations) will cause a similar slight error from an astronomically exact moment. The offset or adjustment termed 'd' (for difference) is:

$d=5.597661+29.5305888610\times N+(102.026\times 10^{-12})\times N^{2}$,

where d is the number of days (and fractions of a day) since January first 2000 at the hour 00:00:00 TT, and 'N' is an integer representing the successive new moon thereafter. Given this number of days as a result, the actual calander date is easy to calculate down to the nearest ten minutes or so.

(Note that the number 29.53.. is the synodic month.)

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.

See the article on the full moon cycle for a fairly simple method to compute the moment of New Moon more accurately.

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.)

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). Jean Meeus gave formulae to compute this in his popular Astronomical Formulae for Calculators based on the ephemerides of Brown and Newcomb (ca. 1900); and in his Astronomical Algorithms based on the ELP2000-85 . These are now obsolete: Chapront et al. (2002) published improved parameters. Also Meeus' formula uses a fractional variable to allow computation of the four main phases, and uses a second variable for the secular terms. For the convenience of the reader, the formula given above is based on Chapront's latest parameters and expressed with a single integer variable, and following additional terms are added:

constant term:

• Like Meeus, applied the constant terms of the aberration of light 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, ΔT (= TT - UT ) was +63.83 s ; hence the correction for the clock time UT = TT - ΔT of the conjunction is:

−0.000739 days.

quadratic term:

• In ELP2000–85 (see Chapront et alii 1988), D has a quadratic term of −5.8681"×T²; expressed in lunations N, this yields a correction of +87.403E–12*N² days to the time of conjunction. The term includes a tidal contribution of 0.5×(−23.8946 "/cy²). The most current estimate from Lunar Laser Ranging for the acceleration is (see Chapront et alii 2002): (−25.858 ±0.003) "/cy². Therefore the new quadratic term of D is = -6.8498"×T² . Indeed the polynomial provided by Chapront et alii (2002) provides the same value (their Table 4). This translates to a correction of +14.622E−12*N² days to the time of conjunction; the quadratic term now is:

+102.026E−12*N² days.

• For UT: analysis of historical observations show that ΔT has a long-term increase of +31 s/cy². Converted to days and lunations, the correction from ET to UT becomes:

−235E−12*N² days.

The theoretical tidal contribution to ΔT is about +42 s/cy²; 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/cy². The error in the position of the Moon itself is only maybe 0.5 "/cy², or 1 s/cy² in the time of conjunction with the Sun.

Religious use

The Islamic calendar has retained an observational definition of the New Moon, marking the new month when the first Crescent Moon is actually seen, and making it impossible to be certain in advance of when a specific month will begin (in particular, the exact date on which Ramadan will begin is not known in advance). In Saudi Arabia, if the weather is cloudy when the New Moon is expected, observers are sent up in airplanes. In Iran a special committee receives observations of every new moon to determine the beginning of each month. This committee uses one hundred groups of observers.

The New Moon is the beginning of the month in the Chinese calendar. Some Buddhist Chinese keep a vegetarian diet on the New Moon and Full Moon each month.

Trivia

• In the anime and manga InuYasha, this is the time where the hanyō Inuyasha loses his yōkai powers temporarily and turns full human for the night.

See also

• Black moon
• Blue moon
• Ecclesiastical new moon
• Full moon
• Half moon
• Metonic cycle

External links

• Moon sighting Committee World-wide of Khalid Shaukat
• Moon Sighting from Committee For Crescent Observation, Intl.
• Islamic Crescent Observation Project
• Saber's Beads