New moon

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A graphic depicting the new moon phase

In astronomy, new moon is the first phase of the Moon, when it lies closest to the Sun in the sky as seen from the Earth. More precisely, it is the instant when the Moon and the Sun have the same ecliptical longitude [1] The Moon is not normally visible at this time except when it is seen in silhouette during a solar eclipse. See the article on phases of the Moon for further details.

The original meaning of the phrase new moon, sometimes still used in non-astronomical contexts, was the first visible crescent of the Moon, after conjunction with the Sun.[2] 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.

The new moon in its original meaning[citation needed] of first crescent marks the beginning of the month in lunar calendars such as the Muslim calendar, and in lunisolar calendars such as the Hebrew calendar, Hindu calendars, and Buddhist calendar. But in the Chinese calendar, the beginning of the month is marked by the dark moon.

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.[3]

Religious use[edit]

Determining new moons: an approximate formula[edit]

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.[6][7] 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[edit]

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[8] based on the ELP2000-85[9] (the 2nd edition uses ELP2000-82 with improved expressions from Chapront et al. in 1998). These are now outdated: Chapront et al. (2002)[10] 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"[12]
Moon: −0.704"[13]
Correction in conjunction: −0.000451 days[14]
−0.000739 days.

quadratic term:

+102.026×10−12N2 days.
−235×10−12N2 days.

The theoretical tidal contribution to ΔT is about +42 s/cy2 [20] the smaller observed value is thought to be mostly due to changes in the shape of the Earth.[21] 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,[22] 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.

See also[edit]

References[edit]

  1. ^ Meeus, Jean (1991). Astronomical Algorithms. Willmann-Bell. ISBN 0-943396-35-2. 
  2. ^ "new moon". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. 
  3. ^ http://legault.perso.sfr.fr/new_moon_2013july8.html
  4. ^ Fiqh Council of North America Decision: "Astronomical Calculations and Ramadan"
  5. ^ Islamic Society of North America Decision:"Revised ISNA Ramadan and Eid Announcement"
  6. ^ Jawad, Ala'a H. (November 1993). "How Long Is a Lunar Month?". In Roger W. Sinnott. Sky&Telescope: 76..77. 
  7. ^ Meeus, Jean (2002). The duration of the lunation, in More Mathematical Astronomy Morsels. Willmann-Bell, Richmond VA USA. pp. 19..31. ISBN 0-943396-74-3. 
  8. ^ formula 47.1 in Jean Meeus (1991): Astronomical Algorithms (1st ed.) ISBN 0-943396-35-2
  9. ^ M.Chapront-Touzé, J. Chapront (1988): "ELP2000-85: a semianalytical lunar ephemeris adequate for historical times". Astronomy & Astrophysics 190, 342..352
  10. ^ J.Chapront, M.Chapront-Touzé, G. Francou (2002): "A new determination of lunar orbital parameters, precession constant, and tidal acceleration from LLR measurements". Astronomy & Astrophysics 387, 700–709
  11. ^ 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).
  12. ^ 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
  13. ^ formula in: G.M.Clemence, J.G.Porter, D.H.Sadler (1952): "Aberration in the lunar ephemeris", Astronomical Journal 57(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.
  14. ^ 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.
  15. ^ see e.g. [1]; the IERS is the official source for these numbers; they provide TAIUTC here and UT1−UTC here; ΔT = 32.184s + (TAI−UTC) − (UT1−UTC)
  16. ^ delay is − (−5.8681") / (60×60×360 "/circle) / (36525/29.530... lunations per Julian century)2 × (29.530... days/lunation) days
  17. ^ −5.8681" + 0.5×(−25.858 − −23.8946)
  18. ^ F.R. Stephenson, Historical Eclipses and Earth's Rotation. Cambridge University Press 1997. ISBN 0-521-46194-4 . p.507, eq.14.3
  19. ^ 31 s / (86400 s/d) / [(36525 d/cy) / (29.530... d/lunation)]2
  20. ^ Stephenson 1997 op.cit. p.38 eq.2.8
  21. ^ Stephenson 1997 op.cit. par.14.8
  22. ^ from differences of various earlier determinations of the tidal acceleration, see e.g. Stephenson 1997 op.cit. par.2.2.3

External links[edit]