新月

新月、月缺，指月亮無光之月相，一種天文現象。月球在繞行地球的軌道上，介合於太陽和地球之間之時，就會呈現此月相；在此刻，月球背向太陽的黑暗面朝向地球，因此從地球上以肉眼看不見月球。夏曆以「朔」定義每月初一引用错误：没有找到与<ref>对应的</ref>标签^[1]。合的真實時刻和平均值之間的差異通常都比上述的範圍小，這是因為在一個陰曆月的週期中不可能所有的攝動值全部都達到它們的最大值的緣故。

參考滿月周期的文章，那兒有一個更簡單但更準確的計算朔的時刻的公式。

公式中長期項的誤差大約是：在地球時是1 cy²秒，在世界時是11 cy²秒 (cy是2000年起的世紀數；參見公式的解釋有更詳細的說明。)

公式的解釋

合的平均時刻可以很容易的從月球平黃經減去太陽平黃經的算表中計算出來（迪羅尼參數D）。瓊·米斯在他的《天文學計算公式》一書中所給的計算公式是依據布朗和紐康的星曆表（ca. 1900），並且是他的《天文演算法》的第一版^[2]，以ELP2000-85為基礎^[3]（第二版在1998年，使用從Chaprontet al.改進的ELP2000-82），這些現在都已經過時了（2002年）^[4]。出版後改善了參數，並且米斯的公式使用可變的分數，可以做四種主要相位的計算，並且使用第二個變數做一般項目。為了讀者的方便，上述的公式根據Chapront最後修正的參數並且以單一的整數做為唯一的變數，並且加入了下列的項目：

常數項：

如同米斯，使用的常數項是來自太陽的光行差和月球的光時改正^[5]獲得在黃經度上的視黃經差：

太陽：+20.496"。^[6]

月球：−0.704"。^[7]

合的改正：−0.000451天。^[8]

對世界時：在2000年1月，ΔT (= TT − UT )是+63.83秒^[9]；因此改正合的鐘錶時間UT = TT − ΔT 為：

−0.000739天。

二次項：

在ELP2000–85（參見Chapront et alii 1988），D是一個二次項的函數，其值為 −5.8681"T²；陰曆月的數量用N表示，產生的修正式為+87.403×10^–12N²^[10]，得到與合的時刻相差的天數。這個項目內包含了0.5×(−23.8946 "/cy²)的潮汐加速。目前最佳的估計是來自月球雷射陣列的加速度（參見Chapront et alii 2002）：(−25.858 ±0.003)"/cy²。因此，新的二次項參數D是 -6.8498"T²^[11]。實際上，Chapront et alii（2002）提供了多項式的証明，在他們的表4也提供了相同的証明。這項轉換修改了到合的時刻為+14.622×10⁻¹²N²天；這個二項式現在成為：

+102.026×10⁻¹²N²天。

對世界時（UT）：對歷史上的觀測分析顯示ΔT有著+31 s/cy²的長期增量^[12]。轉換成天和陰曆月^[13]，從ET轉換成UT的修正是：

−235×10⁻¹²N²天。

理論上潮汐對ΔT的貢獻大約是+42 s/cy²^[14]，更小的觀測值被認為主要歸因於地球形狀的變化^[15]，由於誤差不能被充分的解釋（地球轉動的角度），我們對UT預測的不確定性可能大到11 s/cy²；在與太陽合時，月球位置的誤差上可能只有0.5"/cy²^[16]，或是（因為月球的平均視角速度大約是0.5"/s）1 s/cy²。

宗教上的應用

回曆保留了新月在觀測上的定義，以實際看見新月的時刻做為一個月的開始，因而使它不可能在朔之前就開始一個新的月份（特別是，齋戒月開始的確切日期無法事先就知道）。在沙烏地阿拉伯，當期望中的新月該出現時若遇上陰天，觀測人員會被送上飛機到雲層之上觀測。在巴基斯坦，有一個"中央 Ruet-e-Hilal委員會"，由國家協助巴基斯坦氣象局超過100個的觀測所，在全國各地確認是否看見新月，並且統一宣布每一個月的開始。在伊朗，由一個特別的委員會審視來自各地的新月報告，這個委員會有100個觀測委員小組，以確定每個月的開始。

參考資料

^ Meeus, Jean. The duration of the lunation, in More Mathematical Astronomy Morsels. Willmann-Bell, Richmond VA USA. 2002: 19..31. ISBN 0-943396-74-3.
^ formula 47.1 in Jean Meeus (1991): Astronomical Algorithms (1^st ed.) ISBN 978-0-943396-35-4
^ M.Chapront-Touzé, J. Chapront (1988): "ELP2000-85: a semianalytical lunar ephemeris adequate for historical times". Astronomy & Astrophysics 190, 342..352
^ 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
^ 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).
^ 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]
^ 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.
^ 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. [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)
^ delay is − (−5.8681") / (60×60×360 "/circle) / (36525/29.530... lunations per Julian century)² × (29.530... days/lunation) days
^ −5.8681" + 0.5×(−25.858 − −23.8946)
^ F.R. Stephenson, Historical Eclipses and Earth's Rotation. Cambridge University Press 1997. ISBN 978-0-521-46194-8 . p.507, eq.14.3
^ 31 s / (86400 s/d) / [(36525 d/cy) / (29.530... d/lunation)]²
^ Stephenson 1997 op.cit. p.38 eq.2.8
^ Stephenson 1997 op.cit. par.14.8
^ from differences of various earlier determinations of the tidal acceleration, see e.g. Stephenson 1997 op.cit. par.2.2.3

外部連結

[1] Meeus, Jean. The duration of the lunation, in More Mathematical Astronomy Morsels. Willmann-Bell, Richmond VA USA. 2002: 19..31. ISBN 0-943396-74-3.

[2] rmula 47.1 in Jean Meeus (1991): Astronomical Algorithms (1^st ed.) ISBN 978-0-943396-35-4

[3] M.Chapront-Touzé, J. Chapront (1988): "ELP2000-85: a semianalytical lunar ephemeris adequate for historical times". Astronomy & Astrophysics 190, 342..352

[4] 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

[5] 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).

[6] 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]

[7] rmula 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.

[8] 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.

[9] 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)

[10] y is − (−5.8681") / (60×60×360 "/circle) / (36525/29.530... lunations per Julian century)² × (29.530... days/lunation) days

[11] −5.8681" + 0.5×(−25.858 − −23.8946)

[12] F.R. Stephenson, Historical Eclipses and Earth's Rotation. Cambridge University Press 1997. ISBN 978-0-521-46194-8 . p.507, eq.14.3

[13] 31 s / (86400 s/d) / [(36525 d/cy) / (29.530... d/lunation)]²

[14] Stephenson 1997 op.cit. p.38 eq.2.8

[15] Stephenson 1997 op.cit. par.14.8

[16] rom differences of various earlier determinations of the tidal acceleration, see e.g. Stephenson 1997 op.cit. par.2.2.3

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查论编月球
物理特性	月球內部構造月球重力場月球地形學（英语：Topography of the Moon）月球磁場月球大氣層月球钠尾月光月食
月球軌道	月球距離月球軌道月相月食半影月全食日食月球日食交食周期滿月周期新月天平動月球交點潮汐潮汐力潮汐鎖定潮汐加速潮差
月球表面特徵	月面学月球表面特徵列表月球正面月球背面月球北极月球南极月海（列表）撞擊坑（列表）月谷（列表）月球山脉列表月球山脉高度列表月溪南極-艾特肯盆地沙克爾頓坑月球水（英语：Lunar water）月球土壤皱岭月岩 70017号月球玄武岩嫦娥石永昼峰永夜坑太空風化月球瞬变现象
月球科學	天平動月球運動論月球的起源大碰撞說特亞月球岩漿海月球地質年代後期重轟炸期月球隕石克里普矿物阿波羅月面實驗包（英语：Apollo Lunar Surface Experiments Package）月球激光测距实验阿波罗17号月球样本展品月震学
月球探測	前往月球的航天任务列表月球探测器列表阿波罗计划月球号系列探测器中国探月工程登陸月球月球殖民月球觀測月球旅遊
月相名字	新月满月超級月亮月食日食月球上的日食藍月黑月
报时和导航	阴历阴阳历月朔望月星期月角距
有关	衛星雙行星月球人造物体列表文化月球錯覺登月陰謀論月球协定月神維茲芬、碧爾和修奇嫦娥、玉兔、吴刚常羲月球是綠乳酪做的月球空心說月亮大骗局
分类主題共享资源专题

公式的解釋

宗教上的應用

相關條目

參考資料

外部連結