SGP4 and TLE accuracy

From: Thomas Fly (thomasfly@j2ee-consultants.com)
Date: Wed Apr 23 2003 - 15:47:46 EDT

  • Next message: Björn Gimle: "Obs Apr 23 #5918"

    I recently did some comparison calculations relating to the SGP4 model; for
    easier viewing, this is also online at
    http://j2ee-consultants.com/iss-transit/sgp4.htm
    
    When observing a transit of the space station that's nearly overhead, the
    "transit radius" is about 2 miles in diameter (the sun & moon have angular
    diameters of about 1/120 radian, and the ISS is about 250 miles up).  If you
    want to be within a bullseye of 20% of the diameter of the sun or moon, you
    therefore can deviate laterally from the transit path by only about +/- .2
    miles, or 1000 feet -> 300 meters (proportionately more, if the transit
    occurs at a low elevation angle).
    
    Below, I ran some comparisons.  I found significant differences between the
    ancient CelesTrak reference, and my own values, though my values (computed
    by Java code) compare quite well with some tests done by Bill Gray (C++
    code).
    
    More worrisome are the differences I found between my computations, and
    those given on the NASA web page, since they amount to much of the allowable
    error (only errors that are lateral to the line of sight matter, of course).
    
    Does anyone else have any calculations, for comparison?
    
         TSINCE         X (km)         Y               Z
            0.          2328.96594238  -5995.21600342  1719.97894287
    http://celestrak.com/NORAD/documentation/spacetrk.pdf
                        2328.97070292  -5995.22083201  1719.9706582  WorldView;
    EARTH_RADIUS = 6378.135, EARTH_FLATTENING = 1 : 298.26
                        2328.97070411  -5995.22083267  1719.97065591 Bill Gray
    http://www.projectpluto.com/sat_code.zip (TEST2.OUT)
    
          360.00000000  2456.00610352  -6071.94232177  1222.95977784
                        2456.1078549   -6071.93868494  1222.89555536
                        2456.10787315  -6071.93868109  1222.89554062
    
          720.00000000  2567.39477539  -6112.49725342   713.97710419
                        2567.56292733  -6112.50381173   713.96185309
                        2567.56296196  -6112.50380107   713.96182567
    
         1080.00000000  2663.03179932  -6115.37414551   195.73919105
                        2663.09012478  -6115.48276372   196.39911433
                        2663.09017487  -6115.48274400   196.39907429
    
         1440.00000000  2742.85470581  -6079.13580322  -328.86091614
                        2742.55433733  -6079.66987202  -326.39144567
                        2742.55440172  -6079.66984111  -326.39149805
    
         XDOT (km/s)  YDOT         ZDOT
         2.91110113  -0.98164053  -7.09049922  CelesTrak
         2.91207225  -0.98341531  -7.09081697  WorldView
         2.91207225  -0.98341531  -7.09081697  Project Pluto
    
         2.67852119  -0.44705850  -7.22800565
         2.67938906  -0.4482884  -7.22879264
         2.67938906  -0.44828838  -7.22879265
    
         2.43952477   0.09884824  -7.31889641
         2.44024486  0.09811113  -7.31995951
         2.44024485   0.09811117  -7.31995951
    
         2.19531813   0.65333930  -7.36169147
         2.19612078  0.65241689  -7.36282421
         2.19612076   0.65241695  -7.36282421
    
         1.94707947   1.21346101  -7.35499924
         1.94849699  1.21107414  -7.35619305
         1.94849696   1.21107421  -7.35619305
    
    Below, from
    http://spaceflight.nasa.gov/realdata/sightings/SSapplications/Post/JavaSSOP/
    orbit/ISS/SVPOST.html
    
           ISS  TRAJECTORY DATA
    
           Lift off time (UTC)  :  N/A
           Area (sq ft)  :  3325.0
           Drag Coefficient (Cd) :   2.36
           90 day mean solar flux (jansky)  :   172.4
           12 month mean earth geomagnetic index  :   2.35
    
           Maneuvers contained within the current ephemeris are as follows:
    
           IMPULSIVE TIG (GMT)   M50 DVx(FPS)      LVLH DVx(FPS)      DVmag(FPS)
           IMPULSIVE TIG (MET)   M50 DVy(FPS)      LVLH DVy(FPS)      Invar Sph
    HA
           DT                    M50 DVz(FPS)      LVLH DVz(FPS)      Invar Sph
    HP
           ---------------------------------------------------------------------
    ---
           There are no maneuvers.
    
            Coasting Arc #1 (begining on orbit 1211)
            ---------------------------------------
    
            Vector Time (GMT): 2003/111/04:16:12.228
            Vector Time (MET): N/A
            Weight (LBS)     : 396133.0
    
                      M50 Cartesian                         M50 Keplerian
            -----------------------------------       --------------------------
    ------
             X    =        4825000.71                 A    =         6776030.81
    meter
             Y    =       -4469367.23  meter          E    =           .0020221
             Z    =        1585585.64                 I    =           51.40937
             XDOT =       2329.384698                 Wp   =           56.30435
             YDOT =       4560.772825  meter/sec      RA   =          306.09898
    deg
             ZDOT =       5725.744991                 TA   =          321.14417
                                                      MA   =          321.28937
                                                      Ha   =            216.422
    n.mi
                                                      Hp   =            206.252
    
    * My results (with differences from NASA's values):
    *
    *  Calendar is: 21 Apr 2003 / 4:16:12.228 UTC
    *  julianDay = 2452750.67791931
    *  year = 2003, dayOfYear = 111.17791931
    *  timeElapsed since TLE epoch = -0.06098661 (fraction of day = -1.5 hours,
    or about -1 orbit)
    *
    * Raw values (epoch of date)    J2000                                  M50
    *
    *  x =  4869714.11 meters         x =  4866972.63  diff. =  71.96      x =
    4825071.69  diff. =  70.98
    *  y = -4411611.02                y = -4415204.63          -11.99      y
    = -4469379.80          -12.57
    *  z =  1610483.26                z =  1608921.70         -211.30      z =
    1585374.09         -211.55
    
                      M50 Cartesian                         J2K Cartesian
            -----------------------------------       --------------------------
    ------
             X    =       15830054.83                 X    =         4866900.67
             Y    =      -14663278.32  feet           Y    =        -4415192.64
    meter
             Z    =        5202052.64                 Z    =         1609133.00
             XDOT =       7642.338249                 XDOT =        2250.405630
             YDOT =      14963.165437  feet/sec       YDOT =        4586.372359
    meter/sec
             ZDOT =      18785.252594                 ZDOT =        5736.872024
    
            The mean element set is posted at the UTC for which position is just
    north of the
            next ascending node relative to the above vector time
    
            TWO LINE MEAN ELEMENT SET
    
            ISS
            1 25544U 98067A   03111.23890592  .00041100  00000-0  34010-3 0
    9003
            2 25544  51.6314 306.3227 0006560  42.4273 317.7388 15.58334166
    12129
    
    Here, I computed the values for the start of the TLE epoch, day of year
    111.23890592:
    
      x =  4035830.69
      y = -5432723.81
      z =      210.36
    
    As indicated by the NASA note, the space station is slightly north (210
    meters) of the earth's equatorial plane at that time.
    
    
    EARTH_RADIUS
      6378.135 km -
    http://dgfi2.dgfi.badw-muenchen.de/geodis/REFS/ellipsoid.html
      6378.137    - http://dgfi2.dgfi.badw-muenchen.de/geodis/REFS/grs80.html
      6378.1363   - http://www.ngs.noaa.gov/GRD/GPS/DOC/files/ac_noaa.html (9
    Feb 2003)
    
    EARTH_FLATTENING
      1 : 298.26    -
    http://dgfi2.dgfi.badw-muenchen.de/geodis/REFS/ellipsoid.html
      1 : 298.2572  - http://dgfi2.dgfi.badw-muenchen.de/geodis/REFS/grs80.html
    
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