Re: accuracy of ISS / Venus transit track

From: Thomas Fly (tfly@alumni.caltech.edu)
Date: Thu Jun 03 2004 - 22:20:02 EDT

  • Next message: Steve Newcomb: "Clear night obs"

    > Thus, the apparent position of the ISS relative to the Sun/Venus would be
    identical, even if the earth had no atmosphere.
    
    I respectfully disagree.  I don't really compute refraction, since there are
    simple algorithms for that in Meeus, for example (although when I compute
    ray-bending, ultimately it's a computation of refraction).
    
    If you had a switch that allowed you to switch the atmosphere's refraction on
    and off, you'd see Venus (following the example at hand) pop up and down by some
    amount, depending on its elevation angle.  However, it'd be a different ray of
    light your eyes would see in each case.
    
    You could imagine a demon on Venus shining red and green lasers in your
    direction ("leading" the Earth appropriately, to account for the light delay).
    With atmospheric refraction, the red laser is aimed precisely so as to end up in
    your eyes.  With refraction switched off, however, the red laser beam passes
    over your head, and the green laser beam (traveling in a straight line) now
    enters your eyes (at a lower elevation angle than the red laser beam).
    
    Computing a transit is similar, in that it's not a question of just any old
    light ray being as good as the next, but it's a particular light ray that you're
    concerned with.  If, at precisely noon, the ISS were passing thru the red laser
    beam, then you'd see the ISS silhouetted against Venus, despite the fact that
    the ISS is not precisely between you and Venus!
    
    This would be made obvious by switching the Earth's atmospheric refraction off,
    and allowing the green laser beam to travel straight from Venus into your eyes-
    the ISS would no longer appear silhouetted against Venus (because it's
    illuminated by the red laser beam, and not the green beam).
    
    Admittedly, it's a very small effect, amounting to maybe 4' of arc for the ISS
    at the horizon.  For satellites in geosynchrous orbit, the effect would be
    corresponding smaller.
    
    The code is in Refraction.java:
    http://sourceforge.net/project/showfiles.php?group_id=70993
    
    Basically, I compute the angle at which a light of ray (i.e., the "transit laser
    beam") would intersect the WGS84 ellipsoid, at a height of MAUNA_KEA + whatever
    altitude a light ray at an elevation angle of 0 would pass over Mauna Kea, were
    refraction switched off (I don't expect anybody to be trying to observe transits
    from higher than the peak of Mauna Kea).
    
    I then look up the nearest entry to that angle in a look-up table, previously
    computed by ray-bending code in Refraction.java; the index of that entry is
    simply the amount of ray-bending, in meters, that the light ray would undergo
    were it to travel to the Earth's surface (at sea-level).
    
    By climbing a tower that high, and switching off atmospheric refraction, I
    observe the same red laser beam (with the ISS silhouetted) as I did on the
    ground, with the atmosphere bending the laser beam down to my eyes.  On top of
    the tower, however, the ISS is indeed directly between me and Venus, whereas
    it's not, when I'm on the ground!
    
    It's a subtlety that took me a while to appreciate.
    
    > By far the greatest source of uncertainty in the ISS transit calculation is
    the accuracy of the TLE itself.
    
    You're absolutely right on that point!
    
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