slaRcc -

SYNOPSYS

PARAMETERS

double tdb

double ut1

double wl

double u

double v

DESCRIPTION

  Relativistic clock correction:  the difference between proper time at
  a point on the surface of the Earth and coordinate time in the Solar
  System barycentric space-time frame of reference.

  The proper time is Terrestrial Time TT;  the coordinate
  time is an implementation of the Barycentric Dynamical Time TDB.

Given

    TDB   double   coordinate time (MJD: JD-2400000.5)
    UT1   double   universal time (fraction of one day)
    WL    double   clock longitude (radians west)
    U     double   clock distance from Earth spin axis (km)
    V     double   clock distance north of Earth equatorial plane (km)

Returned

    The clock correction, TDB-TT, in seconds.  TDB may be considered
    to be the coordinate time in the Solar System barycentre frame of
    reference, and TT is the proper time given by clocks at mean sea
    level on the Earth.

    The result has 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.

    The variation arises from the transverse Doppler effect and the
    gravitational red-shift as the observer varies in speed and moves
    through different gravitational potentials.

  The argument TDB is, strictly, the barycentric coordinate time;
  however, the terrestrial proper time (TT) can in practice be used.

  The geocentric model is that of Fairhead & Bretagnon (1990), in its
  full form.  It was supplied by Fairhead (private communication) as a
  FORTRAN subroutine.  The original Fairhead routine used explicit
  formulae, in such large numbers that problems were experienced with
  certain compilers (Microsoft Fortran on PC aborted with stack
  overflow, Convex compiled successfully but extremely slowly).  The
  present implementation is a complete recoding in C, with the original
  Fairhead coefficients held in a table.  To optimize arithmetic
  precision, the terms are accumulated in reverse order, smallest
  first.  A number of other coding changes were made, in order to match
  the calling sequence of previous versions of the present routine, and
  to comply with Starlink programming standards.  Under VAX/VMS, the
  numerical results compared with those from the Fairhead form are
  essentially unaffected by the changes, the differences being at the
  10-20 sec level.

  The topocentric part of the model is from Moyer (1981) and
  Murray (1983).

  During the interval 1950-2050, the absolute accuracy is better
  than +/- 3 nanoseconds relative to direct numerical integrations
  using the JPL DE200/LE200 solar system ephemeris.

  The IAU definition of TDB is that it must differ from TT only by
  periodic terms.  Though practical, this is an imprecise definition
  which ignores the existence of very long-period and secular effects
  in the dynamics of the solar system.  As a consequence, different
  implementations of TDB will, in general, differ in zero-point and
  will drift linearly relative to one other.

References

    Bretagnon P, 1982 Astron. Astrophys., 114, 278-288.
    Fairhead L & Bretagnon P, 1990, Astron. Astrophys., 229, 240-247.

    Meeus J, 1984, l'Astronomie, 348-354.
    Moyer T D, 1981, Cel. Mech., 23, 33.
    Murray C A, 1983, Vectorial Astrometry, Adam Hilger.

  Defined in slamac.h:  D2PI

  P.T.Wallace   Starlink   30 October 1993

SEE ALSO

• slalib.3