Skip to main content

Determination of ΔT and Lunar Tidal Acceleration from Ancient Eclipses and Occultations

  • Conference paper
  • First Online:
New Insights From Recent Studies in Historical Astronomy: Following in the Footsteps of F. Richard Stephenson

Part of the book series: Astrophysics and Space Science Proceedings ((ASSSP,volume 43))

Abstract

In order to investigate the variation of the Earth’s rotation speed we have been using ancient solar eclipses and lunar occultations. We are also studying whether or not the Moon’s tidal acceleration has been constant from ancient times.

In this paper we show that the records of solar eclipses between 198 and 181 BC in China and in Rome give a value for the lunar tidal acceleration that is consistent with the current one. We also show that the records of lunar occultations of Venus and Saturn in AD 503 and 513 in China are useful for our studies of the Earth’s rotation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Brown, E. W. (1919). Tables of the motion of the Moon. New Haven: Yale University Press.

    MATH  Google Scholar 

  • Calame, O., & Mulholland, J. D. (1978). Lunar tidal acceleration determined from laser range measures. Science, 199, 977–978.

    Article  ADS  Google Scholar 

  • Capitaine, N., Wallace, P. T., & Chapront, J. (2003). Expressions for IAU 2000 precession quantities. Astronomy and Astrophysics, 412, 567–586.

    Article  ADS  Google Scholar 

  • Chapront, J., & Chapront-Touzé, M. (1997). Lunar motion: Theory and observations. Celestial Mechanics and Dynamical Astronomy, 66, 31–38.

    Article  ADS  Google Scholar 

  • Chapront, J., Chapront-Touzé, M., & Francou, G. (1999). Determination of the lunar orbital and rotational parameters and of the ecliptic reference system orientation from LLR measurements and IERS data. Astronomy and Astrophysics, 343, 624–633.

    ADS  Google Scholar 

  • Chapront, J., Chapront-Touzé, M., & Francou, G. (2000). Contribution of LLR to the reference systems and precession. In N. Capitaine (Ed.), Journées Systèmes de Référence (pp. 96–101). Paris: Observatoire de Paris.

    Google Scholar 

  • Chapront, J., Chapront-Touzé, M., & Francou, G. (2002). A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements. Astronomy and Astrophysics, 387, 700–709.

    Article  ADS  Google Scholar 

  • Clemence, G. M. (1948). On the system of astronomical constants. Astronomical Journal, 53, 169–179.

    Article  ADS  Google Scholar 

  • Dickey, J. O., & Williams, J. G. (1982). Geodynamical application of lunar laser ranging. Eos, 63, 301.

    Google Scholar 

  • Dickey, J. O., Williams, J. G., & Yoder, C. F. (1982). Results from lunar laser ranging data analysis. In O. Calame (Ed.), High precision Earth rotations and Earth-Moon dynamics (pp. 209–216). Dordrecht: Reidel.

    Chapter  Google Scholar 

  • Dickey, J. O., Bender, P. L., Faller, J. E., Newhall, X. X., Ricklefs, R. L., Ries, J. G., Shelus, P. J., Veillet, C., Whipple, A. L., Wiant, J. R., Williams, J. G., & Yoder, C. F. (1994). Lunar laser ranging: A continuing legacy of the Apollo program. Science, 265, 482–490.

    Article  ADS  Google Scholar 

  • Ferrari, A. J., Sinclair, W. S., Sjogren, W. L., Williams, J. G., & Yoder, C. F. (1980). Geophysical parameters of the Earth-Moon system. Journal of Geophysical Research, 85, 3939–3951.

    Article  ADS  Google Scholar 

  • Morrison, L. V. (1973). Rotation of the Earth from AD 1663–1972 and the constancy of G. Nature, 241, 519–520.

    Article  ADS  Google Scholar 

  • Morrison, L. V., & Ward, C. G. (1975). An analysis of the transits of Mercury: 1677–1973. Monthly Notices of the Royal Astronomical Society, 173, 183–206.

    Article  ADS  Google Scholar 

  • Muller, P. M. (1976). Determination of the cosmological rate of change of G and the tidal accelerations of Earth and Moon from ancient and modern astronomical data (Special publication 43–36). Pasadena: Jet Propulsion Laboratory.

    Google Scholar 

  • Newhall, X. X., Williams, J. G., & Dickey, J. O. (1988). Earth rotation from lunar laser ranging. In A. K. Babcock & G. A. Wilkins (Eds.), The Earth’s rotation and reference frames for geodesy and geodynamics (pp. 159–164). Dordrecht: Reidel.

    Google Scholar 

  • Oesterwinter, C., & Cohen, C. J. (1972). New orbital elements for Moon and planets. Celestial Mechanics, 5, 317–395.

    Article  ADS  Google Scholar 

  • Sôma, M. (1985). An analysis of lunar occultations in the year 1955–1980 using the new lunar ephemeris ELP2000. Celestial Mechanics, 35, 45–88.

    Article  ADS  Google Scholar 

  • Sôma, M., & Tanikawa, K. (2005). Variation of ΔT between AD 800 and 1200 derived from ancient solar eclipse records. In N. Capitaine (Ed.), Journées 2004, Systèmes de Référence Spatio-Temporels (pp. 265–266). Paris: Observatoire de Paris.

    Google Scholar 

  • Sôma, M., Tanikawa, K., & Kawabata, K. (2004). Earth’s rate of rotation between 700 BC and 1000 AD derived from ancient solar eclipses. In A. Finkelstein & N. Capitaine (Eds.), Journées 2003, astrometry, geodynamics and solar system dynamics: From milliarcseconds to microarcseconds (pp. 122–127). St. Petersburg: Institute of Applied Astronomy of the Russian Academy of Sciences.

    Google Scholar 

  • Spencer Jones, H. (1939). The rotation of the earth, and the secular accelerations of the Sun, Moon and planets. Monthly Notices of the Royal Astronomical Society, 99, 541–558.

    Article  ADS  Google Scholar 

  • Standish, E. M. Jr. (1998). JPL planetary and lunar ephemerides, DE405/LE405, JPL IOM 312.F-98-048. Pasadena: Jet Propulsion Laboratory.

    Google Scholar 

  • Stephenson, F. R. (1997). Historical eclipses and Earth’s rotation. Cambridge, MA: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Tanikawa, K., & Sôma, M. (2004). ΔT and the tidal acceleration of the lunar motion from eclipses observed at plural sites. Publications of the Astronomical Society of Japan, 56, 879–885.

    Article  ADS  Google Scholar 

  • Van Flandern, T. C. (1970). The secular acceleration of the Moon. Astronomical Journal, 75, 657–658.

    Article  ADS  Google Scholar 

  • Van Flandern, T. C. (1975). A determination of the rate of change of G. Monthly Notices of the Royal Astronomical Society, 170, 333–342.

    Article  ADS  Google Scholar 

  • Williams, J. G., Sinclair, W. S., & Yoder, C. F. (1978). Tidal acceleration of the Moon. Geophysical Research Letters, 5, 943–946.

    Article  ADS  Google Scholar 

  • Yardley, J. C. (Ed.). (2000). Livy: The dawn of the Roman Empire (Books 31–40). Oxford: Oxford University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mitsuru Sôma .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Sôma, M., Tanikawa, K. (2015). Determination of ΔT and Lunar Tidal Acceleration from Ancient Eclipses and Occultations. In: Orchiston, W., Green, D., Strom, R. (eds) New Insights From Recent Studies in Historical Astronomy: Following in the Footsteps of F. Richard Stephenson. Astrophysics and Space Science Proceedings, vol 43. Springer, Cham. https://doi.org/10.1007/978-3-319-07614-0_2

Download citation

Publish with us

Policies and ethics