Equations for ΔT calculations

On this page I'm collected articles with equations for calculations of ΔT and/or related to tidal/secular acceleration of the Moon. Of course, all this articles relate to solar eclipses in ancient time.

• Newcomb, Simon, "On the dynamics of the Earth's rotation, with respect to the periodic variations of latitude", Monthly Notices of the Royal Astronomical Society, 52 (1892), 336-341 [Local PDF • ADS link].
• Newcomb, Simon, "The Elements of the four inner Planets and the fundamental Constants of Astronomy", Bulletin Astronomique, 13 (1896), 26-36 [Local PDF • ADS link].
• Newcomb, Simon, "Fluctuations in the Moon's mean motion", Monthly Notices of the Royal Astronomical Society, 69 (1909), 164-169 [Local PDF • ADS link].
• Newcomb, Simon, "Comparison of ancient eclipses of the Sun with modern elements of the Moon's motion", Monthly Notices of the Royal Astronomical Society, 69 (1909), 460-467 [Local PDF • ADS link].
• Fotheringham, J. K., "Comparison of note on the above paper", Monthly Notices of the Royal Astronomical Society, 69 (1909), 467-470 [Local PDF • ADS link].
• Fotheringham, J. K., "Moon, Note on the secular acceleration of, as determined from the ancient eclipses", Monthly Notices of the Royal Astronomical Society, 80 (1920), 578-581 [Local PDF • ADS link].
• Fotheringham, J. K., "A solution of ancient eclipses of the sun", Monthly Notices of the Royal Astronomical Society, 81 (1920), 104-126 [Local PDF • ADS link].
• Brown, Ernest William, "The Evidence for Changes in the Rate of Rotation of the Earth and their Geophysical Consequences: With a Summary and Discussion of the Deviations of the Moon and Sun from their Gravitational Orbits", Transactions of the Astronomical Observatory of Yale University, 3 (1926), 205-238 [Local PDF • ADS link].
• de Sitter, Willem, "On the Secular Accelerations and the Fluctuations of the Longitudes of the Moon, the Sun, Mercury and Venus", Bulletin of the Astronomical Institutes of the Netherlands, 4 (1927), 21-38 [Local PDF • ADS link].
• de Sitter, Willem, "On the Longitude of the Sun in the Years 1864-1900, and the Rotation of the Earth", Bulletin of the Astronomical Institutes of the Netherlands, 4 (1927), 49-50 [Local PDF • ADS link].
• de Sitter, Willem, "Further Note on the Causes of the Discontinuous Changes of the EarthòÀÙs Rotation and their Possible Effect on the Intensity of Gravity", Bulletin of the Astronomical Institutes of the Netherlands, 4 (1927), 69-70 [Local PDF • ADS link].
• de Sitter, Willem & Brouwer, Dirk, "On the System of Astronomical Constants", Bulletin of the Astronomical Institutes of the Netherlands, 8 (1938), 213-231 [Local PDF • ADS link].
• Spencer Jones, H., "The Rotation of the Earth, and the Secular Accelerations of the Sun, Moon and Planets", Monthly Notices of the Royal Astronomical Society, 99 (1939), 541-558 [Local PDF • ADS link].
• Clemence, Gerald Maurice, "On the System of Astronomical Constants", The Astronomical Journal, 53 (1948), 169-179 [Local PDF • ADS link].
• Brouwer, Dirk, "A New Discussion of the Changes in the EarthòÀÙs Rate of Rotation", Proceedings of the National Academy of Sciences of the United States of America, 38 (1952), 1-12 [JSTOR link].
• Brouwer, Dirk, "A Study of the Changes in the Rate of Rotation of the Earth", The Astronomical Journal, 57 (1952), 125-146 [Local PDF • ADS link].
• Jackson, J., "On the Standard of Time used in the Calculation of Ephemerides of the Sun and the Moon", The Observatory, 72 (1952), 233-235 [Local PDF • ADS link].
• Murray, C. A., "The secular acceleration of the Moon, and the lunar tidal couple", Monthly Notices of the Royal Astronomical Society, 117 (1957), 478-482 [Local PDF • ADS link].
• Murray, C. A., "On the determination of ephemeris time", Monthly Notices of the Royal Astronomical Society, 119 (1959), 612-615 [Local PDF • ADS link].
• Curott, David R., "Earth deceleration from ancient solar eclipses", Astronomical Journal, 71 (1966), 264-269 [Local PDF • ADS link].
• van Flandern, Thomas C., "The Secular Acceleration of the Moon", Astronomical Journal, 75 (1970), 657-658 [Local PDF • ADS link].
• Morrison, Leslie V., "The Secular Accelerations of the Moon's Orbital Motion and the Earth's Rotation", The Moon, 5 (1972), 253-264 [Local PDF • ADS link].
• Morrison, Leslie V. & Ward, C.G., "An Analysis of the Transits of Mercury: 1677-1973", Monthly Notices of the Royal Astronomical Society, 173 (1975), 183-206 [Local PDF • ADS link].
• Schmadel, Lutz D. & Zech, G., "Polynomial Approximations for the Correction ΔT = E.T. — U.T. in the Period 1800-1975", Acta Astronomica, 29 (1979), 101-104 [Local PDF • ADS link].
• Stephenson, Francis Richard & Houlden, Michael A., "The Accuracy of TuckermanòÀÙs Solar and Planetary Tables", Journal for the History of Astronomy, 12 (1981), 133-138 [Local PDF • ADS link].
• McCarthy, Dennis D. & Babcock, Alice Kay, "The Length of Day since 1656", Physics of the Earth and Planetary Interiors, 44 (1986), 281-292 [ScienceDirect link].
• Stephenson, Francis Richard & Morrison, Leslie V., "Long-Term Changes in the Rotation of the Earth: 700 B.C. to A.D. 1980", Philosophical Transactions of the Royal Society of London, Ser. A, 313 (1984), 47-70 [JSTOR link].
• Houlden, Michael A. & Stephenson, Francis Richard, "A Supplement to the Tuckerman Tables", Philadelphia: American Philosophical Society, 1986 [Local PDF • ADS link].
• Chapront-Touz†é, Michelle & Chapront, Jean, "ELP 2000-85: A Semi-Analytical Lunar Ephemeris Adequate for Historical Times", Astronomy and Astrophysics, 190 (1988), 342-352 [Local PDF • ADS link].
• Stephenson, Francis Richard & Lieske, Jay H., "Changes in the EarthòÀÙs Rate of Rotation between A.D. 1672 and 1806 as deduced from Solar Eclipse Timings", Astronomy and Astrophysics, 200 (1988), 218-224 [Local PDF • ADS link].
• Borkowski, Kazimierz M., "ELP 2000-85 and the Dynamical Time — Universal Time Relation", Astronomy and Astrophysics, 205 (1988), L8-L10 [Local PDF • ADS link].
• Schmadel, Lutz D. & Zech, G., "Emperical Transformations from U.T. to E.T. for the Period 1800 — 1988", Astronomische Nachrichten, 309 (1988), 219-221 [Local PDF • ADS link].
• Standish, E. Myles, "The Observational Basis for JPLòÀÙs DE 200, the Planetary Ephemerides of the Astronomical Almanac", Astronomy and Astrophysics, 233 (1990), 252-271 [Local PDF • ADS link].
• Hide, Raymond & Dickey, Jean O., "EarthòÀÙs Variable Rotation", Science, new series, 253 (1991), 629-637 [JSTOR link].
• Stephenson, F. R.; Said, S. S., "Non-tidal changes in the earth's rate of rotation as deduced from medieval eclipse observations", Astronomy and Astrophysics, 215 (1989), 181-189 [Local PDF • ADS link].
• Protitch-Benishek, V.; Protitch, M. B., "On the Lunar Secular Acceleration - a Possible Approach", Inertial Coordinate System on the Sky, 141 (1990), 201-202 [Local PDF • ADS link].
• Wu, Shou-Xian; Liu, Ci-Yuan, "Secular variation of Earth's rotation from ancient Chinese records of lunar occultations and approaches", Chinese Astronomy and Astrophysics, 17, 3 (1993), 337-346 [ScienceDirect link].
• Stephenson, Francis Richard & Morrison, Leslie V., "Long-Term Fluctuations in the EarthòÀÙs Rotation: 700 BC to AD 1990", Philosophical Transactions of the Royal Society of London, Ser. A, 351 (1995), 165-202 [JSTOR link].
• Bois, E.; Boudin, F.; Journet, A., "Secular variation of the Moon's rotation rate", Astronomy and Astrophysics, 314 (1996), 989-994 [Local PDF • ADS link].
• Pang, K. D.; Yau, K. K., "The need for more accurate 4000year ephemerides using lunar and spacecraft ranging, ancient eclipse and planetary data", Dynamics, ephemerides, and astrometry of the solar system: proceedings of the 172nd Symposium of the International Astronomical Union, 1995, 113-116 [Local PDF • ADS link].
• Stephenson, F. R.; Jones, J. E.; Morrison, L. V., "The solar eclipse observed by Clavius in A.D. 1567.", Astronomy and Astrophysics, 322 (1997), 347-351 [Local PDF • ADS link].
• Steele, J. M.; Stephenson, F. R.; Morrison, L. V., "The Accuracy of Eclipse Times Measured by the Babylonians", Journal for the History of Astronomy, 28 (1997), 337-345 [Local PDF • ADS link].
• Said, S. S.; Stephenson, F. R. "Solar and Lunar Eclipse Measurements by Medieval Muslim Astronomers, II: Observations", Journal for the History of Astronomy, 28 (1997), 29-48 [Local PDF • ADS link].
• Meeus, Jean, "The Effect of Delta T on Astronomical Calculations", The Journal of the British Astronomical Association, 108 (1998), 154-156 [Local PDF • ADS link].
• Stephenson, Francis Richard, "Historical Eclipses and the Rotation of the Earth", Physics and Chemistry of the Earth, 23 (1998), 715-724 [[ScienceDirect link].
• Chapront, Jean, Chapront-Touz†é, Michelle & Francou, Gerard, "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 (1999), 624-633 [Local PDF • ADS link].
• Meeus, Jean & Simons, Larry, "Polynomial Approximations to Delta T, 1620-2000 AD", The Journal of the British Astronomical Association, 110 (2000), 323-324 [Local PDF • ADS link].
• Protitch-Benishek, V.; Protitch, M. B., "Newcomb's Data on Ancient Eclipses Revisited", Serbian Astronomical Journal, 162 (2000), 127-133 [Local PDF • ADS link].
• Morrison, Leslie V. & Stephenson, Francis Richard, "Historical Eclipses and the Variability of the EarthòÀÙs Rotation", Journal of Geodynamics, 32 (2001), 247-265 [ScienceDirect link].
• Nelson, R.A., McCarthy, Dennis D., Malys, S., Levine, J., Guinot, B., Fliegel, H.F., Beard, R.L. & Bartholomew, T.R., "The Leap Second: Its History and Possible Future", Metrologia, 38 (2001), 509-529 [Local PDF • HP link].
• Morrison, L. V.; Stephenson, F. R., "Ancient eclipses and the Earth's rotation", Highlights of Astronomy, 12 (2002), 338-341 [Local PDF • ADS link].
• Liu, Ci-Yuan, "An Ancient Solar Eclipse Record "Tian-da-yi" in the 10th Century BC", Chinese Journal of Astronomy & Astrophysics, 2 (2002), 391-395 [Local PDF • ADS link].
• Han, Yan-Ben; Qiao, Qi-Yuan, "A Check on the Variations of Earth's Rotation with an Ancient Solar Eclipse", Chinese Journal of Astronomy & Astrophysics, 3 (2003), 569-575 [Local PDF • ADS link].
• Morrison, L. V.; Stephenson, F. R., "Historical values of the Earth's clock error ΔT and the calculation of eclipses", Journal for the History of Astronomy, 35(2004), 327-336 [Local PDF • ADS link] — addendum in ibid., 36 (2005), 339 [Local PDF • ADS link].
• Stephenson, F. R.; Morrison, L. V., "Historical Eclipses", The Light-Time Effect in Astrophysics, 335 (2005), 159-180 [Local PDF • ADS link].
• Banjevic, B., "Ancient eclipses and dating the fall of Babylon", Publications of the Astronomical Observatory of Belgrade, 80 (2006), 251-257 [Local PDF • ADS link].
• Sana Islam, Muhammad Sadiq and Muhammad Shahid Qureshi, "Asessing Polynomial Approximation for ΔT", Journal of Basic and Applied Sciences, 4 (2008), 1-4 [Local PDF].
• Sana Islam, Muhammad Sadiq and Muhammad Shahid Qureshi, "Error Minimization of Polynomial Approximation of Delta T", Journal of Astrophysics and Astronomy, 29 (2008), 363-366 [Local PDF].
• Henriksson, G., "A New Test of Einstein's Theory of Relativity by Ancient Solar Eclipses", Cosmology Across Cultures ASP Conference Series, 409 (2009), 166-171 [Local PDF • ADS link].