Equations for ΔT

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 Earth��s 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 Earth��s 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 Tuckerman��s 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��, 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 Earth��s 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 JPL��s 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., "Earth��s 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 Earth��s 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��, 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 Earth��s 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].