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    Re: Delta-T
    From: Michael Dorl
    Date: 2004 Dec 5, 13:36 -0600

    At 09:54 PM 12/3/04 +0000, George wrote:
    >So where does Michael Dorl's value for delta-t in 1580, and where does
    >Omar's equation, come from?
    Here are the comments at the front of the piece of code that calculates delta T
    in the aa code I got from Mr. Mosier.  I think I added to the Delta T table
    to bring it up
    to date.
    DeltaT = Ephemeris Time - Universal Time
      * The tabulated values of deltaT, in hundredths of a second,
      * were taken from The Astronomical Almanac, page K8.  The program
      * adjusts for a value of secular tidal acceleration ndot. It is -25.8
      * arcsec per century squared for JPL's DE403 ephemeris.
      * ELP2000 and DE200 use the value -23.8946.
      * The tabulated range is 1620.0 through 2003.0.  Bessel's interpolation
      * formula is implemented to obtain fourth order interpolated values at
      * intermediate times.
      * Updated deltaT predictions can be obtained from this network archive:
      *    http://maia.usno.navy.mil
      * Currently (as of 2002) available series are
      *    tai-utc.dat  Changes by 1 whenever there is a leap second
      *    finals.all   EOP including UT1-UTC, always less than 1 second
      * from which deltaT = 32.184 + (tai-utc) - (UT1-UTC)
      * For dates earlier than the tabulated range, the program
      * calculates approximate formulae of Stephenson and Morrison
      * or K. M. Borkowski.  These approximations have an estimated
      * error of 15 minutes at 1500 B.C.  They are not adjusted for small
      * improvements in the current estimate of ndot because the formulas
      * were derived from studies of ancient eclipses and other historical
      * information, whose interpretation depends only partly on ndot.
      * A quadratic extrapolation formula, that agrees in value and slope with
      * current data, predicts future values of deltaT.
      * Input Y is the Julian epoch expressed in Julian years.  Y can be
      * found from the Julian date JD by
      *     Y = 2000.0 + (JD - 2451545.0)/365.25.
      * See AA page B4.
      * Output double deltat(Y) is ET-UT in seconds.
      * References:
      * Stephenson, F. R., and L. V. Morrison, "Long-term changes
      * in the rotation of the Earth: 700 B.C. to A.D. 1980,"
      * Philosophical Transactions of the Royal Society of London
      * Series A 313, 47-70 (1984)
      * Borkowski, K. M., "ELP2000-85 and the Dynamical Time
      * - Universal Time relation," Astronomy and Astrophysics
      * 205, L8-L10 (1988)
      * Borkowski's formula is derived from eclipses going back to 2137 BC
      * and uses lunar position based on tidal coefficient of -23.9 arcsec/cy^2.
      * Chapront-Touze, Michelle, and Jean Chapront, _Lunar Tables
      * and Programs from 4000 B.C. to A.D. 8000_, Willmann-Bell 1991
      * Their table agrees with the one here, but the entries are
      * rounded to the nearest whole second.
      * Stephenson, F. R., and M. A. Houlden, _Atlas of Historical
      * Eclipse Maps_, Cambridge U. Press (1986)

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