pure and applied geophysics

, Volume 145, Issue 3–4, pp 459–485 | Cite as

The Earth's palaeorotation, postglacial rebound and lower mantle viscosity from analysis of ancient Chinese eclipse records

  • Kevin D. Pang
  • Kevin Yau
  • Hung-Hsiang Chou


Of the forces changing the Earth's rotation, tidal braking and postglacial rebound predominate at a timescale≥102 yr (Hide andDickey, 1991;Dickey, 1992). Analysis of ancient eclipse records has given values for the clock error ΔT and the time derivative of the Earth's dynamic oblateness\(\dot J_2\) for the past 3,300 yr. Since ΔT=AT-UT=ct 2 , whereAT is Atomic (cesium clock) Time,UT is Universal (Earth rotation) Time, andt is the number of centuries before 1800, the oldest data have the most weight. Sunrise and sunset eclipses are especially valuable, as they can be retrospectively timed.

TheBamboo Annals, entombed in 299 B.C. and unearthed in A.D. 281, states that “in the first year of King Yi of the Western Zhou dynasty the day dawned twice at Zheng (34.5°N, 109.8°E)”.Kaiyuan zhanjing (Siddhartha, A.D. 724) cites this passageand adds that “in the 2nd (actually 12th) year of Sheng Ping reign period of King Shang (actually King Xi) the day began twice at Zheng”. Matching these records with the April 21, 899 B.C. and April 4, A.D. 368 sunrise eclipses (Oppolzer eclipse Nos. 732 and 3747) gave ΔT values of 5.8±0.15 and 1.7±0.1 hr, respectively. The recurrence of a central solar eclipse at the same site under almost identical circumstances accurately links up an ancient ΔT value with a more precise medieval one, and makes the statistics of such early data more robust.

The brightness changes for the magnitudes 0.95–0.97 and 0.991–0.998 eclipses were greater than those for the January 4, 1992 “double sunset” over Southern California, U.S.A. (magnitude 0.91–0.92). David H. Levy noted that “... as annularity ended. Sunset had come and gone, but the sky began to brighten not darken. For almost 15 minutes it continued to brighten until the onrushing shadow of Earth took over and darkness fell again ...” (Sky Telesc.83, 694). We have analyzed even earlier records from the Shang dynasty.

Six solar eclipse records have been identified among 160,000 oracle bones unearthed from the Shang dynasty capital Anyang (36.1°N, 114.3°E). Four of the 12th-century-B.C. inscriptions have cyclic days of 18, 42, 17 and 25. The chinese 60-day cycle is like our week in design, and has been in continuous use from time immemorial. These records have been uniquely matched to the sunrise eclipses of June 7, 1172 B.C. and October 31, 1161 B.C., and sunset eclipses of October 21, 1198 B.C. and June 27, 1163 B.C., respectively. Using visibility constraints on the rising and setting eclipsed Sun from Anyang we have derived upper or lower limits on ΔT. Three of them cluster around 7 hr 10 min, consistent with a ΔT of 7 hr 20 min, from the analysis of a record of the June 5, 1302 B.C. total solar eclipse, which states that “three flames ate the Sun, big stars were seen”.

Analysis of our data gave an equation of best-fit of ΔT=(30±2.5)t2, for the secular lunar acceleration rate\(\dot n_{moon} = - 26''/cen^2\) (Williamset al., 1992). From this we derived an\(\dot \omega /\omega\) of −(19±1.6)×10−11/yr, where ω is the angular velocity of the Earth's rotation. Subtracting a tidal\(\dot \omega /\omega\) of −27.8×10−11/yr (Lambeck, 1980) gave a nontidal\(\dot \omega /\omega\) of (9±1.6)×10−11/yr, which is equivalent to a\(\dot J_2\) of −(4.5±0.8)×10−11/yr. The average\(\dot J_2\) for the past 3,300 yr is larger than the present\(\dot J_2\) from satellite laser ranging, −3×10−11/yr (Chenget al., 1989), as expected. Both\(\dot J_2\) values are consistent with postglacial rebound from an upper mantle of viscosity 1021 Pa s, and a lower mantle of viscosity (2–4)×1021 Pa s, deformed by Pleistocene ice sheet loading (Peltier, 1985).

Our mantle viscosity values are consistent with those from the analyses of free air gravity anomalies and relative sea-level variations (Mitrovica andPeltier, 1991, 1992). Accurate values of the mantle viscosity are critical to our understanding of thermal convection patterns, that are responsible for plate tectonics (Peltier, 1986). Finally, the bounceback to its less oblate interglacial shape makes the Earth spin faster, overcoming a third of the tidal braking by the Moon and Sun. The net effect has been lengthening the day by 1.64±0.14 msec/cen.

Key words

Earth rotation postglacial rebound mantle rheology China eclipses chronology history 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alexander, J. C. (1983),Higher Harmonic Effects of the Earth's Gravitational Field from Postglacial Rebound as Observed by Lageos, Geophys. Res. Lett.10, 1085–1087.Google Scholar
  2. Borkowski, K. M. (1988),ELP 2000-85 and the Dynamical Time—Universal Time Relation, Astron. Astrophys.205, L8-L10.Google Scholar
  3. Chang, K. C.,Shang Civilization (Yale University Press, New Haven 1980).Google Scholar
  4. Chao, B. F. et al. (1995),Coseismic Effects on the Earth's Rotation and Gravitational Field and Their Energy Consideration, Pure and Appl. Geophys. in press.Google Scholar
  5. Chen, C. Y., andXi, Z. Z.,The Yao Dian and the origins of astronomyin China. InAstronomies and Cultures (eds. Ruggles, C. L. N., and Saunders, N. J.) (University of Colorado, Boulder 1993) pp. 32–66.Google Scholar
  6. Chen, Z. G.,History of Chinese Astronomy, Vol. 3, (Shanghai People's Press, Shanghai 1984) (in Chinese).Google Scholar
  7. Cheng, M. K., Eanes, R. J., Shum, C. K., Shutz, B. E., andTapley, B. D. (1989),Temporal Variations in Low Degree Zonal Harmonics from Starlette Orbit Analysis. Geophys. Res. Lett.16, 393–396.Google Scholar
  8. Chou, H. H.,Genealogy of the Shang and Yin Kings (privately printed, Hong Kong, 1958) (in Chinese).Google Scholar
  9. Chou, H. H. (1979),Chinese Oracle Bones, Sci. Am.240, 135–149.Google Scholar
  10. Chou, H. H., andPang, K. D.,Interpretation and Dating of Tunyi 6386 Solar Eclipse, Paper presented at the International Symposium on Xia Culture, 1990, University of California, Los Angeles.Google Scholar
  11. Christodoulidis, D. C., Smith, D. E., Williamson, R. G., andKlosko, S. M. (1988),Observed Tidal Braking in the Earth/Moon/Sun System, J. Geophys. Res.93, 6216–6236.Google Scholar
  12. Currot, D. R. (1966),Earth Deceleration from Ancient Solar Eclipses, Astron. J.71, 264–269.Google Scholar
  13. Dicke, R. H.,The secular acceleration of the Earth's rotation and cosmology. InThe Earth-Moon System (eds. Marsden, B. G., and Cameron, A. G. W.) (Plenum, New York 1966) pp. 98–163.Google Scholar
  14. Dickey, J. O. (1992),Earth Rotation: An Interdisciplinary Approach to Earth System Science, EOS, Trans. Am. Geophys. Union74 (43), 195.Google Scholar
  15. Doggett, L. E. (1987),The Acceleration of the Moon (a review of Newton's 1984 book, listed below), J. Hist. Astron.18, 68–70.Google Scholar
  16. Eubank, T. M.,Variations in the orientation of the Earth. InContributions of Space Geodesy to Geodynamics: Earth Dynamics (eds. Smith, D. E., and Turcotte, D. L.) (Am. Geophys. Union, Washington D.C. 1993) pp. 1–54.Google Scholar
  17. Fotheringham, J. K. (1920),A Solution of Ancient Eclipses of the Sun, Mon. Not. Roy. Astron. Soc.81, 104–126.Google Scholar
  18. Han, Y. B., Li, Z. S., Lin, B. S., andYang, X. H. (1984),A Derivation of the Rate of Spin-down of the Earth Using Ancient Chinese Records of Central Eclipses, Chin. Astron. Astrophys.8, 348–353.Google Scholar
  19. Harvey, O. L. (1982),Lunar Beads in a Chinese Necklace, Chin. Cult.24, 59–67.Google Scholar
  20. Hide, R. (1969),Interaction Between the Earth's Liquid Core and Solid Mantle, Nature222, 1055–1056.Google Scholar
  21. Hide, R., andDickey, J. O. (1991),Earth's Variable Rotation, Science253, 629–637.Google Scholar
  22. Hilton, J. L., Seidelmann, P. K., andLiu, C. Y. (1988),Analysis of Ancient Chinese Records of Occultations Between Planets and Stars, Astron. J.96, 1482–1493.Google Scholar
  23. Hilton, J. L., Seidelmann, P. K., andLiu, C. Y. (1992),An Examination of the Change in the Earth Rotation Rate from Ancient Chinese Observations of Lunar Occultations of the Planets, Astron. J.104, 2250–2252.Google Scholar
  24. Hu, H. X. (1986).An Interpretation of the Oracle-bone Inscription Phrase: “The Sun and Moon Eclipsed,” Early China, Supplement No.1, 35–38.Google Scholar
  25. Jault, D., andLe Mouel, J.-L. (1990),Core-mantle Boundary Shape: Constraints Inferred from the Pressure Torque Acting Between the Core and the Mantle, Geophys. J. Intern.101, 233–241.Google Scholar
  26. Jong, T. de, andvan Soldt, W. H. (1989),The Earliest Known Solar Eclipse Record Redated, Nature338, 238–240.Google Scholar
  27. Keightly, D. N. (1977),On the Misuse of Ancient Chinese Inscriptions: An Astronomical Fantasy, Hist. Sci.15, 267–272.Google Scholar
  28. Kuo, M. J.,Combined Compilation of Oracle Bone Inscriptions (Zhonghua Book Publisher, Beijing 1977) (in Chinese).Google Scholar
  29. Kuo, M. J.,Historical Atlas of China, Part 1 (Cartographic Publishing House, Shanghai 1979) pp. 13, 14 and 55 (in Chinese).Google Scholar
  30. Lambeck, K.,The Earth's Variable Rotation (Oxford University Press, Oxford 1980).Google Scholar
  31. Legge, J.,The Chinese Classics, Volume 3, The Shoo King or the Book of Documents (Lane, Crawford and Co., Hong Kong, 1865; reprinted by Southern Materials Center, Inc., Taibei 1985).Google Scholar
  32. Levy, D. H. (1992),Star Trails (a monthly column), Sky Telesc.83, 694–695. Levy is a co-discoverer of Comet Shoemaker-Levy 9 that crashed into Jupiter in July, 1994.Google Scholar
  33. Li, H.,History of the Xia, Shang and Zhou Dynasties (Beijing Publishing House, Beijing, 1984) (in Chinese).Google Scholar
  34. Li, Z. S. andYang, X. H. (1985),Ancient Eclipse Records of China and Earth's Rotation, Scientia Sinica28, 1299–1307.Google Scholar
  35. Liu, C. Y. (1945),A Record of an Observation of Solar Prominences in Oracle Bone Inscriptions, Yuzhou (Universe)15, 15–16 (in Chinese).Google Scholar
  36. Liu, C. Y. (1988),Secular Acceleration of Earth's Rotation from Chinese Records of Lunar Occultation of Stars Before 600 A.D., Chin. Astron. Astrophys.12, 169–178.Google Scholar
  37. Liu, C. Y., andYau, K. K. C.,Application of early Chinese records of lunar occultations and close approaches, InEarth's Rotation from Eons to Days (eds. Brosche, P., and Sundermann, J.) (Springer-Verlag, Berlin 1990) pp. 33–39Google Scholar
  38. Liu, Y. (1982),Analysis and Identification of the Phrase “Chuji” in Bronze Vessel Inscriptions, Wen Wu (Cultural Relics)11, 76–84 (in Chinese).Google Scholar
  39. Liu, Y. L. (1978),The Yi-Mao Eclipse of Yin King Wuding, Dalu Zazhi (Continental Magazine)57, 197–206 (in Chinese).Google Scholar
  40. Lu, Y.,Astrology of the Yi National Minority (Yunnam People's Press, Kunming 1989) (in Chinese).Google Scholar
  41. Mignard, F.,Tidal and nontidal acceleration of the Earth's rotation. InEarth Rotation: Solved and Unsolved Problems (ed. Cazenave, A.) (Reidel, Dordrecht 1986) pp. 93–110.Google Scholar
  42. Mitrovica, J. X., andPeltier, W. R. (1991),Free Air Gravity Anomalies Associated Glacial Isostatic Disequilibrium: Load History Effects on the Inference of Deep Mantle Viscosity, Geophys. Res. Lett.18, 235–238.Google Scholar
  43. Mitrovica, J. X., andPeltier, W. R. (1992),Constraints on Mantle Viscosity from Relative Sea Level Variations in Hudson Bay, Geophys. Res. Lett.19, 1185–1188.Google Scholar
  44. Morrison, L. V., andWard, C. G. (1975),An Analysis of the Transits of Mercury 1677–1973, Mon. Not. Roy. Astron. Soc.173, 183–206.Google Scholar
  45. Morrison, L. V., andStephenson, F. R.,Secular and decade fluctuations in the Earth rotation: 700 BC-AD 1978. InSun and Planetary System (eds. Fricke, W., and Teleki, G.) (Reidel, Dordrecht 1982) pp. 173–178.Google Scholar
  46. Mucke, H., andMeeus, J.,Canon of Solar Eclipses, −2003 to 2526 (Astronomisches Büro, Vienna 1983).Google Scholar
  47. Muller, P. N., andStephenson, F. R.,The acceleration of the Earth and Moon from early astronomical observations. InGrowth Rhythms and the History of the Earth's Rotation (eds. Rosenberg, G. D., and Runcorn, S. K.) (Wiley, London 1975) pp. 459–534.Google Scholar
  48. Munk, W., andRevelle, R. (1952),Sea Level and the Rotation of the Earth, Am. J. Sci.250, 829–833.Google Scholar
  49. Munk, W., andMacDonald, G. J. F.,The Rotation of the Earth (Cambridge University Press, Cambridge 1960).Google Scholar
  50. Needham, J.,Science and Civilization in China, Vol. 3 (Cambridge University Press, Cambridge 1959).Google Scholar
  51. Newton, R. R.,Ancient Astronomical Observations and the Accelerations of the Earth and Moon (Johns Hopkins University Press, Baltimore 1970).Google Scholar
  52. Newton, R. R.,Medieval Chronicles and the Rotation of the Earth (Johns Hopkins University Press, Baltimore 1972).Google Scholar
  53. Newton, R. R.,The Moon's Acceleration and its Physical Origins, Volume 1, as Deduced from Solar Eclipses (Johns Hopkins University Press, Baltimore 1979).Google Scholar
  54. Newton, R. R.,The Moon's Acceleration and its Physical Origins, Volume 2, as Deduced from General Lunar Observations (Johns Hopkins University Press, Baltimore 1984).Google Scholar
  55. Nivison, D. N., andPang, K. D. (1990),Astronomical Evidence for the Bamboo Annals' Chronology of Early Xia, Early China15, 87–95.Google Scholar
  56. Oppolzer, T. R. von,Canon of Eclipses (German ed., 1887; reprinted in English by Dover, New York 1964).Google Scholar
  57. Pang, K. D. (1985),Extraordinary Floods in Early Chinese History and their Absolute Dates, Paper presented at theU.S.-China Bilateral Symposium on the Analysis of Extraordinary Flood Events, Nanjing; also J. Hydrol.96, 139–155.Google Scholar
  58. Pang, K. D., andBangert, J. A. (1993),The Holy Grail of Chinese Astronomy: The Sun-Moon-Five-Planet Conjunction in Yingshi (Pegasus) on March 5, 1953 B.C., Bull. Am. Astron. Soc.25, 922.Google Scholar
  59. Pang, K. D., Yau, K., Chou, H. H., andWolff, R. (1988),Computer Analysis of Some Ancient Chinese Sunrise Eclipse Records to Determine the Earth's Rotation Rate, Vistas Astron.31, 833–847.Google Scholar
  60. Pang, K. D., Chou, H. H., Yau, K., Bangert, J. A., andAhluwalia, D. A. (1989),Shang Dynasty Oracle Bone Eclipse Records and the Earth's Rotation Rate in 1302 B.C., Bull. Am. Astron. Soc.21, 753.Google Scholar
  61. Peltier, W. R. (1985),The LAGEOS Constraint on Deep Mantle Viscosity: Results from a New Normal Mode Method for the Inversion of Viscoelastic Relaxation Spectra, J. Geophys. Res.90, 9411–9421.Google Scholar
  62. Peltier, W. R.,Slow changes in the Earth's shape and gravitational field: Constraints on the glaciation history and internal viscoelastic stratification. InSpace Geodesy and Geodynamics (eds. Anderson, A. J., and Cazenave, A.) (Academic Press, London 1986) pp. 75–109.Google Scholar
  63. Rogers, M. C.,The Rise of the Former Ch'in State and its Spread Under Fu Chien, Through 370 A.D. (University of California Press, Berkeley 1968) pp. 9–13.Google Scholar
  64. Rubincam, D. P. (1984),Postglacial Rebound Observed by Lageos and the Effective Viscosity of the Lower Mantle, J. Geophys. Res.89, 1077–1087.Google Scholar
  65. Stephenson, F. R., andMorrison, L. V. (1984),Long-term Changes in the Rotation of the Earth: 700 B.C. to A.D. 1980, Phil. Trans. Roy. Soc. Lond. A313, 47–70.Google Scholar
  66. Stephenson, F. R., andYau, K. K. C. (1992),Astronomical Records in the Ch'un-Ch'iu Chronicle, J. Hist. Astron.23, 31–51.Google Scholar
  67. Tung, T. P.,Xiatun II: Yinxu wenzi yipien (Second Collection of Writings from the Yin Ruin Xiaotun)Part 3 (Historical and Philological Research Institute, Academia Sinica, Taibei 1953) (in Chinese).Google Scholar
  68. Tung, T. P.,Chronological Tables of Chinese History, 2 volumes (Hong Kong University Press, Hong Kong 1960).Google Scholar
  69. Tung, T. P.,Fifty Years of Studies in Oracle Inscriptions (Centre for East Asian Cultural Studies, Tokyo 1964).Google Scholar
  70. Wang, P. K., andSiscoe, G. L. (1980),Ancient Chinese Observations of Physical Phenomena Attending Solar Eclipses, Solar Phys.66, 187–193.Google Scholar
  71. Wang, R. (this volume),Mechanical Problems in Geodynamics—Work Done in China, Pure and Appl. Geophys.145.Google Scholar
  72. Williams, J. G., Newhall, X. X., andDickey, J. O. (1992),Diurnal and Semidiurnal Tidal Contributions to Lunar Secular Acceleration, EOS, Trans. Am. Geophys. Union73 (43), 126.Google Scholar
  73. Xi, Z. Z. (1984),New Archaeoastronomical Discoveries in China, Archaeoastron.7, 34–45.Google Scholar
  74. Xi, Z. Z. (1986),The Astronomical Material in the Dunhuang Grotto Texts, China Hist. Mater. Sci. Tech.7, 63 (in Chinese).Google Scholar
  75. Xinjiang Yugur Autonomous Region Museum (1973),A Brief Report on the Excavation of a Group of Ancient Tombs in Turpan Prefecture, Astagna, Karahejo (1963–1965), Wen Wu (Cultural Relics)10, 7–23 (in Chinese).Google Scholar
  76. Xu, Z. T. (1990),Solar Observations in Ancient China and Solar Variability, Phil. Trans. Roy. Soc. Lond. A330, 513–515.Google Scholar
  77. Xu, Z. T., Yau, K. K. C., andStephenson, F. R. (1989),Astronomical Records on the Shang Dynasty Oracle Bones, J. Hist. Astron.20, S61-S72.Google Scholar
  78. Yao, X. S., andXiao, D.,A General Compilation of Copies and Explanations of Oracle Bone Inscriptions from Yinxu (Zhonghua Book Publisher, Beijing 1988) (in Chinese).Google Scholar
  79. Yau, K., Yeomans, D., andWeissman, P. (1994),The Past and Future Motion of Comet P/Swift-Tuttle, Mon. Not. Roy. Astron. Soc.266, 305–316.Google Scholar
  80. Yeomans, D. K., andKiang, T. (1981),The Long-term Motion of Comet Halley, Mon. Not. Roy. Astron. Soc.197, 633–646.Google Scholar
  81. Yoder, C. F., Williams, J. G., Dickey, J. O., Schultz, B. E., Eanes, R. J., andTapley, B. D. (1983),Secular Variation of Earth's Gravitational Harmonic J 2 Coefficient from Lageos and Nontidal Acceleration of Earth Rotation, Nature303, 757–762.Google Scholar
  82. Zhang, P. Y. (1975),A Study of Records of the Solar and Lunar Eclipses in Scripts on Tortoise-shells or Ox-bones, Acta Astron. Sinica16, 210–224 (in Chinese with English abstract).Google Scholar
  83. Zhuang, W. F., andWang, L. Z.,Union Compilation of Ancient Chinese Records of Celestial Phenomena (Jiangsu Science and Technology Press, Jiangsu Province 1988) (in Chinese).Google Scholar

Copyright information

© Birkhäuser Verlag 1995

Authors and Affiliations

  1. 1.Jet Propulsion LaboratoryPasadenaUSA
  2. 2.Department of East Asian Languages and CulturesUniversity of CaliforniaLos AngelesUSA

Personalised recommendations