Re: 2.2' of arc discrepancy between CalSKY and SkyMap ISS tracks

From: Thomas Fly (tfly@alumni.caltech.edu)
Date: Wed Jun 30 2004 - 17:53:54 EDT

  • Next message: Steve Newcomb: "28366 current el"

    Here are all the gory details from my computation:
    
    8 June 2004, 10:09:17 UTC
    48.2579 N, 17.0272 E, elevation 208 meters above the (WGS72) ellipsoid
    
    dayOfYear = 160.42311342592592
    julianDay = 2453164.923113426
    DELTA_T = 67.9325624255297 (not actually used in computation of Venus' position)
    Greenwich Mean Sidereal Time = 11869.056696145504
    SIDEREAL_RADIANS = 2 * Math.PI * gmst / SECONDS_PER_DAY = 0.8631421602234133
    
    Venus (equinox of date?)
      R.A. = 76.8083121939399    [ 22 41' 44" ]
      Decl = 22.695574042851273  [  5h  7m 14s ]
    
      distanceAu = 0.28888191990789386
      angular size = 57.7604178704807"
    
    Venus ECI position (in Earth radii)
      x = 1429.290544670262
      y = 6097.790361173431
      z = 2619.326244595597
      r = 6788.725117835505
    
    
    Sun
      R.A. = 76.9076004175049
      Decl = 22.89281392398576
    
    Sun ECI position (in Earth radii)
      x =  4903.9779087427905
      y = 21086.260086381702
      z =  9141.69766728416
    
    
    TLE / ISS ECI state
    
    1 25544U 98067A   04159.51929753  .00020000  00000-0  20000-3 0  9009
    2 25544  51.6330  15.0298 0005537 207.1571 152.9300 15.68796178 36803
    
       epochMinutes = 1301.49489013334
    
        x = 1784.4122498587008 km
        y = 4271.0884941226495
        z = 4894.862266108481
      alt = 358.7782847503186
    
      Vx = -7.337916601663112 km/s
      Vy =  0.46692168049684957
      Vz =  2.2584063182316476
       V =  7.691777103303874
    
      latitude  =  46.7814346067128
      longitude =  17.870979197597443
      altitude  = 370.09222138123096 km
    
    
    ISS "Venus shadow" at level of (WGS72) ellipsoid
    
      ECI position
        x = 1697.6844643740644 km
        y = 3901.049452456747
        z = 4735.939877289497
    
      IssRange = 411.9550057955607 km
    
      latitude  = 48.25687973456843
      longitude = 17.027567063918482
    
      altitude angle = 1.1022170167806276 radians
      azimuth angle  = 2.7643204894311206
    
      Unit vector from sea-level transit spot to ISS
        x = 0.21055189532539664
        y = 0.8981908522338168
        z = 0.3859029571516306
    
    ISS "Venus shadow" 208 meters above the (WGS72) ellipsoid
    
      ECI position
        x = 1697.733541452813  (0.266180203974 Earth radii)
        y = 3901.2588097893804 (0.611661276867 E.r.)
        z = 4736.029826562042  (0.742541367347 E.r.)
        r = 6366.482388008189
    
      IssRange = 411.59912894205052586
    
      latitude  = 48.25599880506202
      longitude = 17.028086079902213
      altitude  = 0.20791908736009646 km
    
      topographic coordinates of the elevation-corrected transit position
        x = 2522.8149851761577 miles
        y =  772.6544107227356
        z = 2956.7930603304003
        r = 3962.8544623108087 (6376.2328298580912 km)
    
      refracted altitude angle = 1.1022335211230583 radians
      azimuth angle            = 2.7643204894311206 radians
    
    
    Check; subtract the transit vector from the vector to Venus (in earth-radii), to
    give the vector from the transit to Venus
    
      x = 1429.024364466288
      y = 6097.178699896564
      z = 2618.58370322825
      r = 6787.833184715370
    
    The vector from the transit spot to the ISS should then be
    
      x = (1429.024364466288 / 6787.833184715370) * 411.59912894205052586
        =  86.652863681999204109623436791623
      y = 369.71937488571075701381737721299
      z = 158.78510004305470312259209597198
    
    Adding this to the vector to the transit spot should the give us back the
    position of the ISS:
    
      x = 1784.3864051348122
      y = 4270.9781846750912
      z = 4894.8149266050967
      r = 6736.8021094965031
    
    However, compared with the SGP4 computation for the position of the ISS
    (repeated below), in each case, the numbers are too small by some number of
    meters (possibly because my computation of the range is a little too small):
    
      x = 1784.4122498587008 km
      y = 4271.0884941226495
      z = 4894.862266108481
      r = 6736.9132847503185
    
    If I scale them, so that they represent the same range, I get:
    
      x = 1784.41585228321752
      y = 4271.04866723877701
      z = 4894.89570414360828
    
    There appears to remain about a 50 meter positional discrepancy in these
    numbers, though the 73 meter width of the ISS's solar panels puts that in
    perspective.
    
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