text: 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.\n\nNew 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.\n\nThe 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.\n\n\nAn approximate formula for the average time of New Moon N (conjunction) is\n\n, \nwhere D is the number of days (and fractions) since 2000-01-01 00:00:00 TT, and N is an integer.\n\n(Note that the number 29.53.. is the synodic month.)\n\nTo obtain this moment expressed in Universal Time (world clock time) for future events (N>0), apply the following approximate correction:\n\n days \nPeriodic 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.\n\nThe 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.\n\nSee the paper on the full moon cycle for a fairly simple method to compute the moment of New Moon more accurately.\n\nThe 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.)\n\nThe 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:\n\nconstant term:\n\nApplied the constant terms of the aberration to obtain the apparent difference in ecliptic longitudes: \nSun: +20.496" \nMoon: −0.704" \nCorrection in conjunction: −0.000451 days. \nFor UT: at 1 Jan. 2000, ΔT was +63.83 s; hence the correction for the clock time of the conjunction is: \n−0.000739 days. \nquadratic term:\n\nIn ELP2000–85 (see [1]), 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 is (see [2]): (−25.858 ±0.003) "/cy2. Therefore the tidal correction to the quadratic term in D is −0.9817*T2". The polynomial provided by Chapront et al. (ref. [2]) provides the same value. This translates to a correction of +14.622E−12*N2 days; the quadratic term now is: \n+102.026E−12*N2 days. \nFor UT: analysis of historical observations show that ΔT has a long-term increase of +31 s/cy2. Converted t