# 岁差

## 历史

### 近代

${\displaystyle p_{A}=5\,028.796\,195T+1.105\,434\,8T^{2}+O(T^{3})}$

${\displaystyle p=5\,028.796\,195+2.210\,869\,6T+O(T^{2})}$

## 成因

### 方程

${\displaystyle {\overrightarrow {T))={\frac {3Gm}{r^{3))}(C-A)\sin \delta \cos \delta {\begin{pmatrix}\sin \alpha \\-\cos \alpha \\0\end{pmatrix))}$

Gm = 摄动天体的标准引力参数
r = 摄动天体的地心距离
C = 围绕地球自转轴转动的转动惯量
A = 任何环绕地球赤道直径的转动惯量
C−A = 地球赤道隆起的转动惯量(C>A)
δ = 摄动天体的赤纬 (赤道以南或北)
α = 摄动天体的赤经 (从春分点向东)

${\displaystyle T_{x}={\frac {3}{2)){\frac {Gm}{a^{3}(1-e^{2})^{3/2))}(C-A)\sin \epsilon \cos \epsilon }$

${\displaystyle a}$ = 地球(太阳)或月球的轨道半长轴
e =地球(太阳)或月球的轨道离心率

${\displaystyle {\frac {d\psi }{dt))={\frac {T_{x)){C\omega \sin \epsilon ))}$

${\displaystyle {\frac {d\psi _{S)){dt))={\frac {3}{2))\left[{\frac {Gm}{a^{3}(1-e^{2})^{3/2))}\right]_{S}\left[{\frac {(C-A)}{C)){\frac {\cos \epsilon }{\omega ))\right]_{E))$

${\displaystyle {\frac {d\psi _{L)){dt))={\frac {3}{2))\left[{\frac {Gm(1-1.5\sin ^{2}i)}{a^{3}(1-e^{2})^{3/2))}\right]_{L}\left[{\frac {(C-A)}{C)){\frac {\cos \epsilon }{\omega ))\right]_{E))$

${\displaystyle e''^{2}={\frac {\mathrm {a} ^{2}-\mathrm {c} ^{2)){\mathrm {a} ^{2}+\mathrm {c} ^{2))))$

Gm=1.3271244×1020 m³/s² Gm=4.902799×1012 m³/s² (CA)/C=0.003273763
${\displaystyle a}$=1.4959802×1011 m ${\displaystyle a}$=3.833978×108 m ω=7.292115×10−5 rad/s
e=0.016708634 e=0.05554553 ${\displaystyle \epsilon \,\!}$=23.43928°
i= 5.156690°

S/dt = 2.450183×10−12 /s
L/dt = 5.334529×10−12 /s

S/dt = 15.948788"/a   vs   15.948870"/a 取自威尔士[24]
L/dt = 34.723638"/a   vs   34.457698"/a 取自威尔士

## 数值

p = A + BT + CT² + … 只是下面公式的近似 p = A + Bsin (2πT/P)，此处P 是410个世纪的周期。

### 黄经总岁差与交角岁差

#### 岁差常数

${\displaystyle p=5\,029.0\,965''/{\text{c))\pm 0.3''/{\text{c))}$

${\displaystyle \epsilon _{0}=84\,381.412''\pm 0.005''}$

${\displaystyle p=5\,038.478\,75''/{\text{c))\pm 0.000\,40''/{\text{c))}$

${\displaystyle \epsilon _{0}=84\,381.405\,9''\pm 0.000\,3''}$

#### 数值计算

${\displaystyle p_{A}=5\,029.096\,6''t+1.111\,61t^{2}-0.000\,113t^{3))$

${\displaystyle \epsilon _{A}=\epsilon _{0}-46.815\,0''t-0.000\,59t^{2}+0.001\,813t^{3))$

## 改正

${\displaystyle \mathbf {r} (t_{0})=\left[\mathbf {P} (t_{i},t_{0})\right]\mathbf {r} (t_{i})}$

### 三次坐标旋转法

MHB2000模型使用了三个欧拉角来表示转换前后的坐标系的相对位置，并将岁差矩阵表达为三个旋转矩阵的乘积：

${\displaystyle \left[\mathbf {P} (t_{i},t_{0})\right]=\mathbf {R_{Z)) (\eta _{A})\mathbf {R_{Y)) (-\theta _{A})\mathbf {R_{Z)) (\zeta _{A})}$

1. 将瞬时天球坐标系的X轴从瞬时平春分点移开，绕瞬时平天球坐标系的Z轴（即沿瞬时赤道面）逆时针旋转${\displaystyle \zeta _{A))$角，得到第一过渡坐标系；
2. 将第一过渡坐标系的X轴绕其Y轴（即沿子午圈）顺时针旋转${\displaystyle \theta _{A))$角，得到第二过渡坐标系，此时第二过渡坐标系的Z轴和赤道面与协议天球坐标系的重合；
3. 将第二过渡坐标系的X轴绕协议天球坐标系的Z轴（即沿协议天球坐标系的赤道面）逆时针旋转${\displaystyle \eta _{A))$角，使其与协议天球坐标系的春分点重合，此时整个坐标系与协议天球坐标系重合。

### 四次坐标旋转法

${\displaystyle \left[\mathbf {P} (t_{i},t_{0})\right]=\mathbf {R_{X)) (-\epsilon _{0})\mathbf {R_{Z)) (\psi _{A})\mathbf {R_{X)) (\omega _{A})\mathbf {R_{Z)) (-\chi _{A})}$

1. 将瞬时天球坐标系的X轴从瞬时平春分点移开，绕瞬时平天球坐标系的Z轴（即沿瞬时赤道面）顺时针旋转${\displaystyle \chi _{A))$角，得到第一过渡坐标系；
2. 保持第一过渡坐标系的X轴不变，将其赤道面绕其X轴逆时针旋转${\displaystyle \omega _{A))$角，得到第二过渡坐标系，此时第二过渡坐标系的赤道面的协议天球坐标系的黄道面重合；
3. 将第二过渡坐标系的X轴绕其Z轴（即沿协议天球坐标系的黄道面）逆时针旋转${\displaystyle \psi _{A))$角，得到第三过渡坐标系，此时第三过渡坐标系的X轴与协议天球坐标系的春分点重合；
4. 保持第三过渡坐标系的X轴不变，将其赤道面绕其X轴顺时针旋转${\displaystyle \epsilon _{0))$角，此时整个坐标系与协议天球坐标系重合。

• ${\displaystyle \chi _{A}=10.556\,403\,00''t-2.381\,429\,200''t^{2}-0.001\,211\,970\,0''t^{3}+0.000\,170\,663\,00''t^{4}-0.000\,000\,056\,000''t^{5))$
• ${\displaystyle \omega _{A}=\epsilon _{0}-0.025\,754\,00''t+0.051\,262\,300''t^{2}-0.007\,725\,030\,0t^{3}-0.000\,000\,467\,00t^{4}+0.000\,000\,333\,700t^{5))$
• ${\displaystyle \psi _{A}=5\,038.481\,507\,00t-1.079\,006\,900t^{2}-0.001\,140\,45t^{3}+0.000\,132\,851\,00t^{4}-0.000\,000\,095\,100t^{5))$
• ${\displaystyle \epsilon _{0}=84\,381.406''}$

## 参考资料

1. ^ Hohenkerk, C.Y., Yallop, B.D., Smith, C.A., & Sinclair, A.T. "Celestial Reference Systems" in Seidelmann, P.K. (ed.) Explanatory Supplement to the Astronomical Almanac. Sausalito: University Science Books. p. 99.
2. David P. Stern. Precession. From Stargazers to Starships. [2020-03-26]. （原始内容存档于2020-05-18）.
3. ^ 李征航; 魏二虎; 王正涛; 彭碧波. 空间大地测量学. 武汉大学出版社. : 46 – 52. ISBN 978-7-30-707574-0.
4. Astro 101 - Precession of the Equinox页面存档备份，存于互联网档案馆）, Western Washington University Planetarium, accessed 30 December 2008
5. ^ Robert Main, Practical and Spherical Astronomy页面存档备份，存于互联网档案馆） (Cambridge: 1863) pp.203–4.
6. ^ IAU 2006 Resolution B1: Adoption of the P03 Precession Theory and Definition of the Ecliptic (PDF). [2010-11-20]. （原始内容 (PDF)存档于2011-10-21）.
7. ^ The Earth Orientation Parameters. IERS. [2020-03-26]. （原始内容存档于2021-03-17）.
8. ^ Dennis Rawlins, Continued fraction decipherment: the Aristarchan ancestry of Hipparchos' yearlength & precession页面存档备份，存于互联网档案馆DIO (1999) 30–42.
9. ^ Neugebauer, O. "The Alleged Babylonian Discovery of the Precession of the Equinoxes", Journal of the American Oriental Society, Vol. 70, No. 1. (Jan. – Mar., 1950), pp. 1–8.
10. ^
11. ^ Siddhānta-shiromani, Golādhyāya, section-VI, verses 17-19
12. ^ http://episte.math.ntu.edu.tw/articles/sm/sm_18_01_1/index.html页面存档备份，存于互联网档案馆） 参照曹亮吉教授：印度的数学，翻译的书名。
13. ^ Translation of the Surya Siddhānta by Pundit Bāpu Deva Sāstri and of the Siddhānta Siromani by the Late Lancelot Wilkinson revised by Pundit Bāpu Deva Sāstri, printed by C B Lewis at Baptist Mission Press, Calcutta, 1861; Siddhānta Shiromani Hindi commentary by Pt Satyadeva Sharmā, Chowkhambā Surbhārati Prakāshan, Varanasi, India.
15. ^ cf. Suryasiddhanta, commentary by E. Burgess, ch.iii, verses 9-12.
16. ^ Rufus, W. C., The Influence of Islamic Astronomy in Europe and the Far East, Popular Astronomy, May 1939, 47 (5): 233–238 [236]
17. ^ Ancient records of astronomy are discussed in Baron Georges Cuvier A Discourse on the Revolutions of the Surface of the Globe (1825)页面存档备份，存于互联网档案馆） in the chapter titled "The astronomical monuments of the ancients." Part of the discussion in the chapter concerns the date of the Dendera zodiac, which Cuvier suggested is 123 AD to 147 AD page 170页面存档备份，存于互联网档案馆） and page 172页面存档备份，存于互联网档案馆）. The current consensus is around 50 BC.
18. ^ N. Capitaine et al. 2003页面存档备份，存于互联网档案馆）, p. 581 expression 39
19. Kaler, James B. The ever-changing sky: a guide to the celestial sphere (Reprint). Cambridge University Press. 2002: 152 [2020-03-30]. ISBN 978-0521499187. （原始内容存档于2021-04-08）.
20. ^ USEFUL CONSTANTS. hpiers.obspm.fr. [2020-03-30]. （原始内容存档于2018-10-12）.
21. ^ Ice Ages, Sea Level, Global Warming, Climate, and Geology. [2019-08-18]. （原始内容存档于2008-03-04）.
22. ^ The Columbia Electronic Encyclopedia, 6th ed., 2007. [2010-11-22]. （原始内容存档于2012-10-13）.
23. ^ Ivan I. Mueller, Spherical and practical astronomy as applied to geodesy (New York: Frederick Unger, 1969) 59.
24. James G. Williams, "Contributions to the Earth's obliquity rate, precession, and nutation页面存档备份，存于互联网档案馆）", Astronomical Journal 108 (1994) 711–724, pp.712&716. All equations are from Williams.
25. ^ G. Boué & J. Laskar, "Precession of a planet with a satellite", Icarus 185 (2006) 312–330, p.329.
26. ^ George Biddel Airy, Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics (third edititon, 1842) 200.
27. ^ J.L. Simon et al., "Numerical expressions for precession formulae and mean elements for the Moon and the planets页面存档备份，存于互联网档案馆）", Astronomy and Astrophyics 282 (1994) 663-683.
28. Dennis D. McCarthy, IERS Technical Note 13 – IERS Standards (1992)页面存档备份，存于互联网档案馆 (Postscript, use PS2PDF页面存档备份，存于互联网档案馆）).
29. ^ IERS - IERS CONVENTIONS (2003). www.iers.org. [2020-03-31]. （原始内容存档于2021-04-15）.
30. ^ 2000年以来国际天文学联合会(IAU)关于基本天文学的决议及其应用 - 中国期刊全文数据库. gb.oversea.cnki.net. [2020-03-31]. （原始内容存档于2021-04-08）.
31. ^ Lieske, J. H., Lederle, T., Fricke, W., & Morando, B. Expressions for the precession quantities based upon the IAU /1976/ system of astronomical constants (PDF). Astronomy and Astrophysics. 1977, 58: 1-16.
32. ^ Coppolla, V.; Seago, J.H.; Vallado, David. The IAU 2000A and IAU 2006 precession-nutation theories and their implementation 134: 919-938. 2009-01-01.
33. ^ Capitaine, N; Wallace, Patrick. High precision methods for locating the celestial intermediate pole and origin 450: 855-872. 2006-05-01. doi:10.1051/0004-6361:20054550.
34. ^ Gérard Petit; Brian Luzum. IERS Conventions (2010) (PDF). IERS Conventions Centre. 2010 [2020-03-26]. （原始内容存档 (PDF)于2021-02-03）.

## 参考书籍

• Explanatory supplement to the Astronomical ephemeris and the American ephemeris and nautical almanac
• Precession and the Obliquity of the Ecliptic has a comparison of values predicted by different theories
• A.L. Berger (1976), "Obliquity & precession for the last 5 million years", Astronomy & astrophysics 51, 127
• J.H. Lieske et al. (1977), "Expressions for the Precession Quantities Based upon the IAU (1976) System of Astronomical Constants". Astronomy & Astrophysics 58, 1..16
• W.R. Ward (1982), "Comments on the long-term stability of the earth's obliquity", Icarus 50, 444
• J.L. Simon et al. (1994), "Numerical expressions for precession formulae and mean elements for the Moon and the planets", Astronomy & Astrophysics 282, 663..683
• N. Capitaine et al. (2003), "Expressions for IAU 2000 precession quantities页面存档备份，存于互联网档案馆）", Astronomy & Astrophysics 412, 567..586
• J.L. Hilton et al. (2006), "Report of the International Astronomical Union Division I Working Group on Precession and the Ecliptic页面存档备份，存于互联网档案馆）" (pdf, 174KB). Celestial Mechanics and Dynamical Astronomy (2006) 94: 351..367
• Rice, Michael (1997), Egypt's Legacy: The archetypes of Western civilization, 3000-30 BC, London and New York.
• Dreyer, J. L. E.. A History of Astronomy from Thales to Kepler. 2nd ed. New York: Dover, 1953.
• Evans, James. The History and Practice of Ancient Astronomy. New York: Oxford University Press, 1998.
• Pannekoek, A. A History of Astronomy. New York: Dover, 1961.
• Parker, Richard A. "Egyptian Astronomy, Astrology, and Calendrical Reckoning." Dictionary of Scientific Biography 15:706-727.
• Tomkins, Peter. Secrets of the Great Pyramid. With an appendix by Livio Catullo Stecchini. New York: Harper Colophon Books, 1971.
• Toomer, G. J. "Hipparchus." Dictionary of Scientific Biography. Vol. 15:207-224. New York: Charles Scribner's Sons, 1978.
• Toomer, G. J. Ptolemy's Almagest. London: Duckworth, 1984.
• Ulansey, David. The Origins of the Mithraic Mysteries: Cosmology and Salvation in the Ancient World. New York: Oxford University Press, 1989.
• Schütz, Michael: Hipparch und die Entdeckung der Präzession. Bemerkungen zu David Ulansey, Die Ursprünge des Mithraskultes, in: ejms = Electronic Journal of Mithraic Studies, www.uhu.es/ejms/Papers/Volume1Papers/ulansey.doc

## 外部链接

This browser is not supported by Wikiwand :(
Wikiwand requires a browser with modern capabilities in order to provide you with the best reading experience.

Back to homepage

Please click Allow in the top-left corner,
then click Install Now in the dialog
then click Install
then click Install

#### Install Wikiwand

Install on Chrome Install on Firefox

#### Enjoying Wikiwand?

Share on Gmail Share on Facebook Share on Twitter Share on Buffer