New moon

The new moon phase

In astronomical terminology, the phrase 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 dark (unilluminated) portion of the Moon faces almost directly toward Earth, so that the Moon is not visible to the naked eye.

The original meaning of the phrase new moon was 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 is coincident with a solar eclipse.

The new moon in its original meaning 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.

On April 14, 2010, the new moon was photographed, producing what is claimed to be the first ever image at the exact moment of the start of the New Moon phase.[1]

Contents

Religious use

See also: Lunar calendar

Recently an attempt to unify Muslims on a scientifically calculated worldwide calendar has been adopted by both the Fiqh Council of North America and European Council for Fatwa and Research. 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.[2][3]

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.[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

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 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"[10]
Moon: −0.704"[11]
Correction in conjunction: −0.000451 days.[12]
−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.[18] the smaller observed value is thought to be mostly due to changes in the shape of the Earth[19] 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,[20] 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

References

  1. ↑ WORLD RECORD : THE YOUNGEST NEW MOON CRESCENT - APRIL 14 2010, Thierry Legault astrophotography
  2. ↑ Fiqh Council of North America Decision: "Fiqh Council Ramadan and Eid Announcement"
  3. ↑ Islamic Society of North America Decision:"Revised ISNA Ramadan and Eid Announcement"
  4. ↑ Jawad, Ala'a H. (November 1993). Roger W. Sinnott. ed. "How Long Is a Lunar Month?". Sky&Telescope: 76..77. 
  5. ↑ 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. 
  6. ↑ formula 47.1 in Jean Meeus (1991): Astronomical Algorithms (1st ed.) ISBN 0-943396-35-2
  7. ↑ M.Chapront-Touzé, J. Chapront (1988): "ELP2000-85: a semianalytical lunar ephemeris adequate for historical times". Astronomy & Astrophysics 190, 342..352
  8. ↑ 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
  9. ↑ 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 during 8.3 minutes relative to the barycenter (center-of-mass) of the solar system. 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).
  10. ↑ Derived Constant #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. [1]
  11. ↑ 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 [2]; but computed with the conventional value of 384400 km for the mean distance which gives a different rounding in the last digit.
  12. ↑ 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.
  13. ↑ see e.g. [3]; the IERS is the official source for these numbers; they provide TAI−UTC here and UT1−UTC here; ΔT = 32.184s + (TAI−UTC) − (UT1−UTC)
  14. ↑ delay is − (−5.8681") / (60×60×360 "/circle) / (36525/29.530... lunations per Julian century)2 × (29.530... days/lunation) days
  15. ↑ −5.8681" + 0.5×(−25.858 − −23.8946)
  16. ↑ F.R. Stephenson, Historical Eclipses and Earth's Rotation. Cambridge University Press 1997. ISBN 0-521-46194-4 . p.507, eq.14.3
  17. ↑ 31 s / (86400 s/d) / [(36525 d/cy) / (29.530... d/lunation)]2
  18. ↑ Stephenson 1997 op.cit. p.38 eq.2.8
  19. ↑ Stephenson 1997 op.cit. par.14.8
  20. ↑ from differences of various earlier determinations of the tidal acceleration, see e.g. Stephenson 1997 op.cit. par.2.2.3

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