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:
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:
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 ecliptical longitude of the Moon minus the mean ecliptical 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 1st edition of Astronomical Algorithms based on the ELP2000-85 (the 2nd edition uses ELP2000-82 with improved expressions from Chapront et al. in 1998). These are now outdated: Chapront et al.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:
For UT: at 1 January 2000, ΔT (= TT − UT ) was +63.83 s; hence the correction for the clock time UT = TT − ΔT of the conjunction is:
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 +87.403×10–12N2 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 +14.622×10−12N2 days to the time of conjunction; the quadratic term now is:
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:
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.
A Single Observation
Although the new moon is typically depicted as a black circle, its actual phase is a very thin crescent, because the moon does not pass directly in front of the sun (except during an eclipse). On July 8, 2013, French astrophotographer Thierry Legault successfully photographed the new moon, although the crescent itself was not visible to the unaided eye.
In non-astronomical contexts, new moon refers to 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 ecliptical longitude with the Sun, when the Moon is invisible from the Earth. This moment is unique and does not depend on location, and in certain circumstances it coincides with a solar eclipse.
This section may require copy-editing for grammar, comprehensibility. (August 2014)
The new moon is quite significant in Hindu calendar. People generally wait for new moon to start new works. Waxing period of moon is considered good for all good works. Fifteen Moon dates each for waxing and waning period are there. Fifteen dates are classified in five categories, namely Nanda, Bhadra, Jaya, Rikta and Purna and three rotations of these five categories are there. The category rotation starts from first date of moon ending at fifth date and then starting at sixth date and so on. Nanda dates come on First, Sixth and Eleventh moon date, same can be known about others. Nanda dates are good for auspicious works. Bhadra dates can be good for works related with community, social, family, friends. Jaya dates are good where we need to deal with some conflict. Rikta dates are not considered much good and do good for works related with cruelty. Purna dates are good for every work. The first day of the Lunar Hindu calendar starts the day after the no moon day (Amavasya). Hindu astrology considers amavasya as powerful, either good or bad. The Hindu epic, Mahabharatha states that the Kurukshetra war started on the Amavasya day that too on a Tudesay (Mangalvaar, day of the week named after Mars).
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 Pakistan, there is a "Central Ruet-e-Hilal Committee" whose head is Mufti Muneeb-ur-Rehman, which takes help from 150 observatories of the Pakistan Meteorological Department all over the country and announces the decision of sighting of new moon. Since its creation in 1974, the status of the Central Ruet-e-Hilal Committee has been controversial as it refused the "Witnesses" (Shahadats) from other sects. 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.
An attempt to unify Muslims on a scientifically calculated worldwide calendar was adopted by both the Fiqh Council of North America and the European Council for Fatwa and Research in 2007. The new calculation requires that conjunction occur before sunset in Mecca, Saudi Arabia and that moon set on the following day must take place after sunset. These can be precisely calculated and therefore a unified calendar is imminent if it becomes adopted worldwide.
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. A new moon is when the sun comes out.
The new moon signifies the start of every Jewish month, and is considered an important date and minor holiday 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. According to Jewish tradition, the Jewish calendar is calculated based on mathematical rules handed down from God to Moses at the moment the command was given to make sure that Passover always falls in the springtime. More likely, this fixed lunisolar calendar was introduced by Hillel II. This calculation makes use of a mean lunation length used by Ptolemy and handed down from Babylonians (see Lunar theory#Babylon), which is still very accurate: ca. 29.530594 days vs. a present value (see below) of 29.530589 days. This difference of only 0.0000005, or five millionths of a day, adds up to about only 4 hours since Babylonian times.
The messianicPentecostal group, the New Israelites of Peru, keeps the new moon as a Sabbath of rest. As an evangelical church, it follows the Bible's teachings that God sanctified the seventh-day Sabbath, and the new moons in addition to it. See Ezekiel 46:1, 3. No work may be done from dusk until dusk, and the services run for 11 hours, although a large number spend 24 hours within the gates of the temples, sleeping and singing praises throughout the night.
^Annual aberration is the ratio of Earth's orbital velocity (around 30 km/s) to the speed of light (about 300,000 km/s), which shifts the Sun's apparent position relative to the celestial sphere toward the west by about 1/10,000 radian. Light-time correction for the Moon is the distance it moves during the time it takes its light to reach Earth divided by the Earth-Moon distance, yielding an angle in radians by which its apparent position lags behind its computed geometric position. Light-time correction for the Sun is negligible because it is almost motionless relative to the barycenter (center-of-mass) of the solar system during the 8.3 minutes that light travels between Sun and Earth. The aberration of light for the Moon is also negligible (the center of the Earth moves too slowly around the Earth-Moon barycenter (0.002 km/s); and the so-called diurnal aberration, caused by the motion of an observer on the surface of the rotating Earth (0.5 km/s at the equator) can be neglected. Although aberration and light-time are often combined as planetary aberration, Meeus separated them (op.cit. p.210).
^Derived Constant No. 14 from the IAU (1976) System of Astronomical Constants (proceedings of IAU Sixteenth General Assembly (1976): Transactions of the IAU XVIB p.58 (1977)); or any astronomical almanac; or e.g.Astronomical units and constants
^formula in: G.M.Clemence, J.G.Porter, D.H.Sadler (1952): "Aberration in the lunar ephemeris", Astronomical Journal57(5) (#1198) pp.46..47; but computed with the conventional value of 384400 km for the mean distance which gives a different rounding in the last digit.
^Apparent mean solar longitude is −20.496" from mean geometric longitude; apparent mean lunar longitude −0.704" from mean geometric longitude; correction to D = Moon − Sun is −0.704" + 20.496" = +19.792" that the apparent Moon is ahead of the apparent Sun; divided by 360×3600"/circle is 1.527×10−5 part of a circle; multiplied by 29.53... days for the Moon to travel a full circle with respect to the Sun is 0.000451 days that the apparent Moon reaches the apparent Sun ahead of time.
^see e.g.; the IERS is the official source for these numbers; they provide TAI−UTChere and UT1−UTC here; ΔT = 32.184s + (TAI−UTC) − (UT1−UTC)
^delay is − (−5.8681") / (60×60×360 "/circle) / (36525/29.530... lunations per Julian century)2 × (29.530... days/lunation) days