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  Craig B. Markwardt, NASA/GSFC Code 662, Greenbelt, MD 20770
  UPDATED VERSIONs can be found on my WEB PAGE:


  Relativistic clock corrections due to Earth motion in solar system

Major Topics

  Planetary Orbits

Calling Sequence

  corr = TDB2TDT(JD, TBASE=, DERIV=deriv)


  The function TDB2TDT computes relativistic corrections that must
  be applied when performing high precision absolute timing in the
  solar system.
  According to general relativity, moving clocks, and clocks at
  different gravitational potentials, will run at different rates
  with respect to each other. A clock placed on the earth will run
  at a time-variable rate because of the non-constant influence of
  the sun and other planets. Thus, for the most demanding
  astrophysical timing applications -- high precision pulsar timing
  -- times in the accelerating earth observer's frame must be
  corrected to an inertial frame, such as the solar system
  barycenter (SSB). This correction is also convenient because the
  coordinate time at the SSB is the ephemeris time of the JPL
  Planetary Ephemeris.
  In general, the difference in the rate of Ti, the time kept by an
  arbitrary clock, and the rate of T, the ephemeris time, is given
  by the expression (Standish 1998):
      dTi/dT = 1 - (Ui + vi^2/2) / c^2
  where Ui is the potential of clock i, and vi is the velocity of
  clock i. However, when integrated, this expression depends on the
  position of an individual clock. A more convenient approximate
  expression is:
    T = Ti + (robs(Ti) . vearth(T))/c^2 + dtgeo(Ti) + TDB2TDT(Ti)
  where robs is the vector from the geocenter to the observer;
  vearth is the vector velocity of the earth; and dtgeo is a
  correction to convert from the observer's clock to geocentric TT
  time. TDB2TDT is the value computed by this function, the
  correction to convert from the geocenter to the solar system
  As the above equation shows, while this function provides an
  important component of the correction, the user must also be
  responsible for (a) correcting their times to the geocenter (ie,
  by maintaining atomic clock corrections); (b) estimating the
  observatory position vector; and and (c) estimating earth's
  velocity vector (using JPLEPHINTERP).
  Users may note a circularity to the above equation, since
  vearth(T) is expressed in terms of the SSB coordinate time. This
  appears to be a chicken and egg problem since in order to get the
  earth's velocity, the ephemeris time is needed to begin with.
  However, to the precision of the above equation, < 25 ns, it is
  acceptable to replace vearth(T) with vearth(TT).
  The method of computation of TDB2TDT in this function is based on
  the analytical formulation by Fairhead, Bretagnon & Lestrade, 1988
  (so-called FBL model) and Fairhead & Bretagnon 1990, in terms of
  sinusoids of various amplitudes. TDB2TDT has a dominant periodic
  component of period 1 year and amplitude 1.7 ms. The set of 791
  coefficients used here were drawn from the Princeton pulsar timing
  program TEMPO version 11.005 (Taylor & Weisberg 1989).
  Because the TDB2TDT quantity is rather expensive to compute but
  slowly varying, users may wish to also retrieve the time
  derivative using the DERIV keyword, if they have many times to
  convert over a short baseline.
  This implementation has been compared against a set of FBL test
  data found in the 1996 IERS Conventions, Chapter 11, provided by
  T. Fukushima. It has been verified that this routine reproduces
  the Fukushima numbers to the accuracy of the table, within
  10^{-14} seconds.
  Fukushima (1995) has found that the 791-term Fairhead & Bretagnon
  analytical approximation use here has a maximum error of 23
  nanoseconds in the time range 1980-2000, compared to a numerical
  integration. In comparison the truncated 127-term approximation
  has an error of ~130 nanoseconds.


  JD - Geocentric time TT, scalar or vector, expressed in Julian
        days. The actual time used is (JD + TBASE). For maximum
        precision, TBASE should be used to express a fixed epoch in
        whole day numbers, and JD should express fractional offset
        days from that epoch.

Keyword Parameters

  TBASE - scalar Julian day of a fixed epoch, which provides the
          origin for times passed in JD.
          Default: 0
  DERIV - upon return, contains the derivative of TDB2TDT in units
          of seconds per day. As many derivatives are returned as
          values passed in JD.


  The correction offset(s) in units of seconds, to be applied as
  noted above.


  Find the correction at ephemeris time 2451544.5 (JD):
    IDL> print, tdb2tdt(2451544.5d)
  or 0.11 ms.


  Princeton TEMPO Program
  FBL Test Data Set
  Fairhead, L. & Bretagnon, P. 1990, A&A, 229, 240
    (basis of this routine)
  Fairhead, L. Bretagnon, P. & Lestrade, J.-F. 1988, in *The Earth's
    Rotation and Reference Frames for Geodesy and Geodynamics*,
    ed. A. K. Babcock and G. A. Wilkins, (Dordrecht: Kluwer), p. 419
    (original "FBL" paper)
  Fukushima, T. 1995, A&A, 294, 895 (error analysis)
  Irwin, A. W. & Fukushima, T. 1999, A&A, 348, 642 (error analysis)
  Standish, E. M. 1998, A&A, 336, 381 (description of time scales)
  Taylor, J. H. & Weisberg, J. M. 1989, ApJ, 345, 434 (pulsar timing)

See Also


Modification History

  Original logic from Fairhead & Bretagnon, 1990
  Drawn from TEMPO v. 11.005, copied 20 Jun 2001
  Documented and vectorized, 30 Jun 2001

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