Precise Reference
of a Terrestrial Location
to the Solar System Barycenter

(based on this document)



  • Set of routines in FORTRAN (Top2Bary)

  • Worked out in the years 2000 to 2006

  • Earth barycenter wrt SSB
        JPL DE405/LE405 Ephemeris

  • Location wrt Earth barycenter
        Classical approach [i.e. equator & equinox (new: CIP & CEO)]

  • Precision
        Earth: ~1 - 25 m / 0.001"     (JPL)
        Detector: ~5 cm / 0.001-0.002"     (nutations)

  • XYZ coordinates & velocities wrt SSB
        frame: J2000.0 (ICRS/ICRF)
        time coverage: 1990.0 to 2011.0



    Documentation content

    www.astro.uni.torun.pl/~kb/AllSky/Docs/Top2B2.htm
    link in: www.astro.uni.torun.pl/~kb/AllSky/AllSky.html

    1. Inroduction
    2. Overview of transformations involved
            Introductory remarks on reference systems and frames
            Time scales
            Location coordinates and velocities with respect to Earth barycenter
            Barycentric coordinates of the Earth (JPL ephemeris)
    3. The Top2Bary module
    4. Configuration file
    5. Two practical examples
            SSB2Det program
            Orb program
    6. New in version 2.2
        Appendix: T2C2kA module implementing the new IAU2000 system
        Acknowledgments
        References



  • Problem with the MJD(UTC)
    Leap seconds:
     
 1990 JAN  1 =JD 2447892.5  TAI-UTC=  25.0
 1991 JAN  1 =JD 2448257.5  TAI-UTC=  26.0
 1992 JUL  1 =JD 2448804.5  TAI-UTC=  27.0
 1993 JUL  1 =JD 2449169.5  TAI-UTC=  28.0
 1994 JUL  1 =JD 2449534.5  TAI-UTC=  29.0
 1996 JAN  1 =JD 2450083.5  TAI-UTC=  30.0
 1997 JUL  1 =JD 2450630.5  TAI-UTC=  31.0
 1999 JAN  1 =JD 2451179.5  TAI-UTC=  32.0
 2006 JAN  1 =JD 2453736.5  TAI-UTC=  33.0

    MJD = day number +
        (number of seconds since 0h UTC)/86400

    Sequence of seconds (day 31 Dec or Jun 30):

    23h59m59s - MJD = 3735.999988095 (2005 Dec 31)
    23h59m60s - MJD = 3736.000000000 (2005 Dec 31)
      0h00m00s - MJD = 3736.000000000 (2006 Jan 1)

  • Remedy: use of MJD(TT)

    MJD(TT) = MJD(UTC) + (TAI – UTC + 32.184)/86400


  • Example (the last leap second of 2005/2006)

    2005 Dec 31; UTC = 23h59m58.96s => MJD = 53735.999988000, step 0.25 s

       MJD(UTC)            X               Y               Z            x           y           z
   53735.999988000 -0.172686578775  0.889619403855  0.385557954201 -1153.87849  6272.89679     0.41767
   53735.999990894 -0.172686628587  0.889619395493  0.385557950576 -1153.99285  6272.87575     0.41774
   53735.999993787 -0.172686678399  0.889619387132  0.385557946950 -1154.10721  6272.85471     0.41781
   53735.999996681 -0.172686728204  0.889619378772  0.385557943325 -1154.22155  6272.83367     0.41787
   53735.999999574 -0.172686778016  0.889619370410  0.385557939699 -1154.33591  6272.81263     0.41794
Leap second missing
   53736.000002468 -0.172687027069  0.889619328603  0.385557921572 -1154.90769  6272.70738     0.41828
   53736.000005361 -0.172687076882  0.889619320242  0.385557917946 -1155.02204  6272.68633     0.41834
   53736.000008255 -0.172687126686  0.889619311882  0.385557914321 -1155.13638  6272.66527     0.41841
   53736.000011148 -0.172687176498  0.889619303520  0.385557910696 -1155.25074  6272.64421     0.41848
   53736.000014042 -0.172687226311  0.889619295158  0.385557907070 -1155.36509  6272.62315     0.41855

   MJD(TT=UTC+64.184s)     X               Y               Z            x           y           z
   53736.000730870 -0.172686578767  0.889619403856  0.385557954202 -1153.87847  6272.89679     0.41767
   53736.000733764 -0.172686628579  0.889619395495  0.385557950576 -1153.99284  6272.87575     0.41774
   53736.000736657 -0.172686678391  0.889619387133  0.385557946951 -1154.10720  6272.85471     0.41781
   53736.000739551 -0.172686728196  0.889619378773  0.385557943326 -1154.22154  6272.83368     0.41787
   53736.000742444 -0.172686778008  0.889619370411  0.385557939700 -1154.33590  6272.81263     0.41794
Data for leap second follow:
   53736.000745338 -0.172686827820  0.889619362050  0.385557936074 -1154.45025  6272.79159     0.41801
   53736.000748231 -0.172686877633  0.889619353688  0.385557932449 -1154.56461  6272.77054     0.41808
   53736.000751125 -0.172686927437  0.889619345328  0.385557928824 -1154.67895  6272.74949     0.41814
   53736.000754018 -0.172686977249  0.889619336966  0.385557925198 -1154.79331  6272.72844     0.41821
Data after leap second:
   53736.000756912 -0.172687027061  0.889619328605  0.385557921573 -1154.90767  6272.70739     0.41828
   53736.000759805 -0.172687076874  0.889619320243  0.385557917947 -1155.02203  6272.68633     0.41834
   53736.000762699 -0.172687126686  0.889619311882  0.385557914321 -1155.13638  6272.66527     0.41841
   53736.000765592 -0.172687176490  0.889619303521  0.385557910696 -1155.25072  6272.64422     0.41848
   53736.000768486 -0.172687226303  0.889619295160  0.385557907071 -1155.36508  6272.62315     0.41855

    Rome, March 31, 2006