New moon

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

In astronomical terminology, 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.

Determining New Moons: an approximate formula

The time interval between New Moons - a lunation - is variable. The mean time between New Moons, the synodic month, is about 29.53... days. An approximate formula to compute the mean moments of New Moon (conjunction between Sun and Moon) for successive months is:

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

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:

$-0.000739 - (235 \times 10^{-12})\times N^2$ days

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 . 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.

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 cy² seconds in TT, and 11 cy² seconds in UT (cy is centuries since 2000; see section Explanation of the formulae for details.)

Explanation of the formula

The moment of mean conjunction can easily be computed from an expression for the mean ecliptic longitude of the Moon minus the mean 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 outdated: Chapront et al. (2002) published improved parameters. Also Meeus's 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 the following additional terms have been added:

constant term:

• Like Meeus, apply the constant terms of the aberration of light for the Sun and light-time correction for the Moon 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 +87.403^–12N² 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 +14.622⁻¹²N² days to the time of conjunction; the quadratic term now is:

+102.026⁻¹²N² 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 :

−235⁻¹²N² days.

The theoretical tidal contribution to ΔT is about +42 s/cy² ; the smaller observed value is thought to be mostly due to changes in the shape of the Earth . 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/cy². The error in the position of the Moon itself is only maybe 0.5 "/cy² , or (because the apparent mean angular velocity of the Moon is about 0.5"/s), 1 s/cy² in the time of conjunction with the Sun.

Religious use

See also: Lunar calendar

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.

The New Moon signifies the start of every Jewish month, and is considered the most important date in the Hebrew calendar. The modern form of the calendar is a rule-based lunisolar calendar, akin to the Chinese calendar, measuring months defined in lunar cycles as well as years measured in solar cycles, and distinct from the purely lunar Islamic calendar and the almost entirely solar Gregorian calendar.

The new moon is also an important entity in Wiccans' practice.

The new moon is also important in astrology, as is the full moon.

See also

• Black moon
• Blue moon
• Ecclesiastical new moon
• Full moon
• Half moon
• Dark moon
• Metonic cycle
• Lunar Cycle

External links

• Moon sighting Committee World-wide of Khalid Shaukat
• Moon Sighting from Committee For Crescent Observation, Intl.
• Islamic Crescent Observation Project
• The Length of the Lunar Cycle (numerical integration analysis)
• Predicting the First Visibility of the Lunar Crescent