# New moon

Image of the Moon approximately in its phase new moon. At this time it is mostly lit only by Earthshine and Starlight

In astronomy, the new moon is the first lunar phase, when the Moon and Sun have the same ecliptic longitude.[1] At this phase, the lunar disk is not visible to the unaided eye, except when silhouetted during a solar eclipse. Daylight outshines the earthlight that dimly illuminates the new moon. The actual phase is usually a very thin crescent.[note 1]

The original meaning of the term new moon, which is still sometimes used in non-astronomical contexts, was the first visible crescent of the Moon, after conjunction with the Sun.[2] This crescent moon is briefly visible when low above the western horizon shortly after sunset and before moonset.

A lunation or synodic month is the average time from one new moon to the next. In the J2000.0 epoch, the average length of a lunation is 29.530588 days (or 29 days, 12 hours, 44 minutes, and 2.8 seconds). However, the length of any one synodic month can vary from 29.26 to 29.80 days due to the perturbing effects of the Sun's gravity on the Moon's eccentric orbit.[3] In a lunar calendar, each month corresponds to a lunation. Each lunar cycle can be assigned a unique lunation number to identify it.

## Formula for New Moons

A graphic depicting the new moon phase

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 spring and neap tides (the most and least profound tidal variances respectively). An approximate formula to compute the mean moments of new moon (conjunction between Sun and Moon) for successive months is:

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

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:

${\displaystyle -0.000739-(235\times 10^{-12})\times N^{2}}$ 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.[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.

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

Approximately a new Moon in the sky of Earth during sunset

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 Astronomical Formulae for Calculators based on the ephemerides of Brown and Newcomb (ca. 1900); and in his 1st edition of Astronomical Algorithms[6] based on the ELP2000-85[7] (the 2nd edition uses ELP2000-82 with improved expressions from Chapront et al. in 1998). These are now outdated: Chapront et al. (2002)[8] 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:

Sun: +20.496"[9]
Moon: −0.704"[10]
Correction in conjunction: −0.000451 days[note 3]
• For UT: at 1 January 2000, ΔT (= TTUT ) was +63.83 s;[note 4] hence the correction for the clock time UT = TT − ΔT of the conjunction is:
−0.000739 days.

• 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[note 5] 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.[note 6] 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:
+102.026×10−12N2 days.
• For UT: analysis of historical observations shows that ΔT has a long-term increase of +31 s/cy2.[11] Converted to days and lunations,[note 7] the correction from ET to UT becomes:
−235×10−12N2 days.

The theoretical tidal contribution to ΔT is about +42 s/cy2[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/cy2. The error in the position of the Moon itself is only maybe 0.5"/cy2,[note 8] 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.

Other Languages
العربية: محاق
বাংলা: অমাবস্যা
беларуская: Маладзік
български: Новолуние
català: Lluna nova
čeština: Nov
dansk: Nymåne
Deutsch: Neumond
español: Luna nueva
Esperanto: Novluno
estremeñu: Novicionis
فارسی: ماه نو
français: Nouvelle lune
Frysk: Nijmoanne
한국어: 신월
հայերեն: Նորալուսին
हिन्दी: कृष्ण पक्ष
Bahasa Indonesia: Bulan baru
italiano: Novilunio
kaszëbsczi: Nów
Kiswahili: Mwezi mwandamo
Lëtzebuergesch: Neimound
lietuvių: Jaunatis
македонски: Млада месечина
മലയാളം: അമാവാസി
Bahasa Melayu: Anak bulan
Nederlands: Nieuwe maan
नेपाली: औंसी

Nordfriisk: Neimuun
norsk: Nymåne
norsk nynorsk: Lunasjon
occitan: Luna novèla
oʻzbekcha/ўзбекча: Yangi oy
Plattdüütsch: Neemaand
polski: Nów
português: Lua nova
Ripoarisch: Neumond
română: Lună nouă
Runa Simi: Killa wañuy
русский: Новолуние
Scots: New muin
slovenčina: Nov (fáza Mesiaca)
suomi: Uusikuu
svenska: Nymåne
Tagalog: Bagong buwan
Türkçe: Yeni ay
українська: Новий Місяць
Tiếng Việt: Mặt Trăng mới
walon: Tinre lune