Abstract
In this paper, we review the current state of knowledge about the acceleration of the Earth's spin, and about the closely related acceleration of the Moon. It is now established at a high confidence level that the acceleration of the Moon, when taken respect to Universal time, has changed by a large amount, and that it has even changed sign, within historic times. This almost certainly means that the acceleration of the Earth's spin has also changed by a large amount. At present we do not have enough information to say whether the changes have been in the contributions from tidal friction, in the contributions that do not arise from tidal friction, or both. Further, we do not know yet whether or not the variations in the Earth's rotation can account for the observed fluctuations in the longitudes of the Sun, the Moon, and the planets.
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Abbreviations
- ET:
-
ephemeris time
- UT:
-
Universal time
- T :
-
ET in centuries from 1900 January 0.5 ET
- τ:
-
UT in centuries from 1900 January 0.5 UT
- Δt :
-
=ET-UT
- n :
-
orbital angular velocity, in ET
- ν:
-
orbital angular velocity, in UT
- \(\dot n_M ,\dot n_S \) :
-
derivatives with respect to ET (Moon and Sun, resp.)
- v ' M ,v ' S :
-
derivatives with respect to UT (Moon and Sun, resp.)
- ω e :
-
spin velocity of Earth with respect to ET
- \(\dot \omega _e \) :
-
spin acceleration of Earth with respect to ET
- y :
-
=109 (\({{\dot \omega _e } \mathord{\left/ {\vphantom {{\dot \omega _e } {\omega _e }}} \right. \kern-\nulldelimiterspace} {\omega _e }}\)); Earth spin acceleration parameter
- y f :
-
portion ofy due to tidal friction (solid Earth and ocean)
- y nf :
-
non-tidal portion ofy
- L :
-
celestial longitude
- <>:
-
symbol forepochal average acceleration.
References
Adams, J. C.: 1853,Proceedings of the Royal Society 6, 321.
al-Battani, Abdallah Muhammad: ca. 925,Az-Zij as-Sabi. There is a translation into Latin, with commentary, by C. A. Nallino, under the titleAl-Battani sive Albatenii Opus Astronomicum, Reale Osservatore di Brera, Milan, 1903.
al-Biruni, Abu-Raihan bin Ahmad: 1025,Kitab Tahdid Nihayat al-Amakin Litashih Masafat al-Masakin. There is a translation into English by Jamil Ali under the titleThe Determination of the Coordinates of Positions for the Correction of Distances between Cities, American University of Beirut, Beirut, Lebanon, 1967.
Brouwer, Dirk: 1952,Astron. J. 57, 125.
Fotheringham, J. K.: 1918,Monthly Notices Roy. Astron. Soc. 78, 406.
Fotheringham, J. K. and Longbottom, Gertrude: 1915,Monthly Notices Roy. Astron. Soc. 75, 377.
Halley, E.: 1695,Philos. Trans. Roy. Soc. 19, 160.
Ibn Yunis (also spelled Ebn Iounis): 1008,Az-Zij al-Kabir al-Hakimi. There is an edition of part of this work, with a parallel translation into French, under the titleLe Livre de la Grande Table Hakémite, by le C.en Caussin, Imprimerie de la République, Paris, 1804.
Jeffreys, Sir Harold: 1970,The Earth, Fifth Edition, Cambridge University Press, Cambridge.
Laplace, P. S. de: 1786,Mémoires de l'Académie Royale des Sciences, p. 235. In 1786, theMémoires did not have volume numbers, at least not in the collection that I used.
MacPike, E. F.: 1932,The Correspondence and Papers of Edmund Halley, Oxford University Press, Oxford.
Markowitz, W.: 1970, ‘Sudden Changes in Rotational Acceleration of the Earth and Secular Motion of the Pole’, inEarthquake Fields and the Rotation of the Earth (ed. by L. Mansinha, D. E. Smylie, and A. E. Beck), D. Reidel Publ. Co., Dordrecht, Holland, pp. 69–81.
Martin, C. F.: 1969, ‘A Study of the Rate of Rotation of the Earth from Occultations of Stars by the Moon, 1627–1860’, a dissertation presented to Yale University; intended for publication in theAstronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac.
Miller, G. R.: 1966,J. Geophys. Res. 71, 2485.
Munk, W. H. and MacDonald, G. J. F.: 1960,The Rotation of the Earth, Cambridge University Press, Cambridge.
Newcomb, S.: 1875, ‘Researches on the Motion of the Moon,’Washington Observations, U.S. Naval Observatory, Washington.
Newcomb, S.: 1912, ‘Researches on the Motion of the Moon, Part II,’Astronomical Papers Prepared for the Use of the American Ephemeris and Nautical Almanac IX, U.S. Government Printing Office, Washington.
Newton, R. R.: 1968,Geophys. J. Roy. Astron. Soc. 14, 505.
Newton, R. R.: 1970,Ancient Astronomical Observations and the Accelerations of the Earth and Moon, The Johns Hopkins Press, Baltimore and London.
Newton, R. R.: 1972a,Mem. Roy. Astron. Soc. 76, 99.
Newton, R. R.: 1972b,Astrophys. Space Sci. 16, 179.
Newton, R. R.: 1972c,Medieval Chronicles and the Rotation of the Earth, The Johns Hopkins Press, Baltimore and London.
Oesterwinter, C. and Cohen, C. J.: 1972,Celest. Mech. 5, 317
Ptolemy, C.: ca. 152,'E Mathematike Syntaxis. There is an edition of the text by J. L. Heiberg in C. Ptolemaei Opera Quae Exstant Omnia, B. G. Teubner, Leipzig, 1898. There is a translation into German, with commentary by K. Manitius, B. G. Teubner, Leipzig, 1913. There is another edition of the text, with a parallel translation into French, by N. B. Halma, Henri Grand Libraire, Paris, 1813.
Spencer Jones, H.: 1939,Monthly Notices Roy. Astron. Soc. 99, 541.
Van Flandern, T. C.: 1970,Astron. J. 75, 657.
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Newton, R.R. The historical acceleration of the earth. Geophysical Surveys 1, 123–145 (1973). https://doi.org/10.1007/BF01449760
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DOI: https://doi.org/10.1007/BF01449760