# 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

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

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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