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# dtdb

erfa.dtdb(date1, date2, ut, elong, u, v)

  An approximation to TDB-TT, the difference between barycentric dynamical time and terrestrial time, for an observer on the Earth.

  Parameters:
    date1 double array
    date2 double array
    ut double array
    elong double array
    u double array
    v double array
  Returns:
    c_retval double array

  Notes

  Wraps ERFA function `eraDtdb`. The ERFA documentation is:

      - - - - - - - -
       e r a D t d b
      - - - - - - - -

      An approximation to TDB-TT, the difference between barycentric
      dynamical time and terrestrial time, for an observer on the Earth.

      The different time scales - proper, coordinate and realized - are
      related to each other:

                TAI             <-  physically realized
                 :
              offset            <-  observed (nominally +32.184s)
                 :
                TT              <-  terrestrial time
                 :
        rate adjustment (L_G)   <-  definition of TT
                 :
                TCG             <-  time scale for GCRS
                 :
          "periodic" terms      <-  eraDtdb  is an implementation
                 :
        rate adjustment (L_C)   <-  function of solar-system ephemeris
                 :
                TCB             <-  time scale for BCRS
                 :
        rate adjustment (-L_B)  <-  definition of TDB
                 :
                TDB             <-  TCB scaled to track TT
                 :
          "periodic" terms      <-  -eraDtdb is an approximation
                 :
                TT              <-  terrestrial time

      Adopted values for the various constants can be found in the IERS
      Conventions (McCarthy & Petit 2003).

      Given:
         date1,date2   double  date, TDB (Notes 1-3)
         ut            double  universal time (UT1, fraction of one day)
         elong         double  longitude (east positive, radians)
         u             double  distance from Earth spin axis (km)
         v             double  distance north of equatorial plane (km)

      Returned (function value):
                       double  TDB-TT (seconds)

      Notes:

      1) The date date1+date2 is a Julian Date, apportioned in any
         convenient way between the two arguments.  For example,
         JD(TT)=2450123.7 could be expressed in any of these ways,
         among others:

                date1          date2

             2450123.7           0.0       (JD method)
             2451545.0       -1421.3       (J2000 method)
             2400000.5       50123.2       (MJD method)
             2450123.5           0.2       (date & time method)

         The JD method is the most natural and convenient to use in
         cases where the loss of several decimal digits of resolution
         is acceptable.  The J2000 method is best matched to the way
         the argument is handled internally and will deliver the
         optimum resolution.  The MJD method and the date & time methods
         are both good compromises between resolution and convenience.

         Although the date is, formally, barycentric dynamical time (TDB),
         the terrestrial dynamical time (TT) can be used with no practical
         effect on the accuracy of the prediction.

      2) TT can be regarded as a coordinate time that is realized as an
         offset of 32.184s from International Atomic Time, TAI.  TT is a
         specific linear transformation of geocentric coordinate time TCG,
         which is the time scale for the Geocentric Celestial Reference
         System, GCRS.

      3) TDB is a coordinate time, and is a specific linear transformation
         of barycentric coordinate time TCB, which is the time scale for
         the Barycentric Celestial Reference System, BCRS.

      4) The difference TCG-TCB depends on the masses and positions of the
         bodies of the solar system and the velocity of the Earth.  It is
         dominated by a rate difference, the residual being of a periodic
         character.  The latter, which is modeled by the present function,
         comprises a main (annual) sinusoidal term of amplitude
         approximately 0.00166 seconds, plus planetary terms up to about
         20 microseconds, and lunar and diurnal terms up to 2 microseconds.
         These effects come from the changing transverse Doppler effect
         and gravitational red-shift as the observer (on the Earth's
         surface) experiences variations in speed (with respect to the
         BCRS) and gravitational potential.

      5) TDB can be regarded as the same as TCB but with a rate adjustment
         to keep it close to TT, which is convenient for many applications.
         The history of successive attempts to define TDB is set out in
         Resolution 3 adopted by the IAU General Assembly in 2006, which
         defines a fixed TDB(TCB) transformation that is consistent with
         contemporary solar-system ephemerides.  Future ephemerides will
         imply slightly changed transformations between TCG and TCB, which
         could introduce a linear drift between TDB and TT;  however, any
         such drift is unlikely to exceed 1 nanosecond per century.

      6) The geocentric TDB-TT model used in the present function is that of
         Fairhead & Bretagnon (1990), in its full form.  It was originally
         supplied by Fairhead (private communications with P.T.Wallace,
         1990) as a Fortran subroutine.  The present C function contains an
         adaptation of the Fairhead code.  The numerical results are
         essentially unaffected by the changes, the differences with
         respect to the Fairhead & Bretagnon original being at the 1e-20 s
         level.

         The topocentric part of the model is from Moyer (1981) and
         Murray (1983), with fundamental arguments adapted from
         Simon et al. 1994.  It is an approximation to the expression
         ( v / c ) . ( r / c ), where v is the barycentric velocity of
         the Earth, r is the geocentric position of the observer and
         c is the speed of light.

         By supplying zeroes for u and v, the topocentric part of the
         model can be nullified, and the function will return the Fairhead
         & Bretagnon result alone.

      7) During the interval 1950-2050, the absolute accuracy is better
         than +/- 3 nanoseconds relative to time ephemerides obtained by
         direct numerical integrations based on the JPL DE405 solar system
         ephemeris.

      8) It must be stressed that the present function is merely a model,
         and that numerical integration of solar-system ephemerides is the
         definitive method for predicting the relationship between TCG and
         TCB and hence between TT and TDB.

      References:

         Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247
         (1990).

         IAU 2006 Resolution 3.

         McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
         IERS Technical Note No. 32, BKG (2004)

         Moyer, T.D., Cel.Mech., 23, 33 (1981).

         Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).

         Seidelmann, P.K. et al., Explanatory Supplement to the
         Astronomical Almanac, Chapter 2, University Science Books (1992).

         Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
         Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).

      This revision:  2021 May 11

      Copyright (C) 2013-2023, NumFOCUS Foundation.
      Derived, with permission, from the SOFA library.  See notes at end of file.