heavens-above Moon transit anomaly

From: FrankEReed@aol.com
Date: Fri Apr 19 2002 - 03:13:46 EDT

  • Next message: Chris Peat: "RE: heavens-above Moon transit anomaly"

    Rob wrote:
    "Plugging in the coordinates of your four sites, they're all a
    bit west of the transit centerline, suggesting that either
    a different elset was used, or perhaps there is a systematic
    error in the lunar location." and
    "While the errors only average about 0.12 degrees in longitude
    (about 6 1/2 miles), this is more than enough for the track to
    miss the moon."
    
    I believe I've figured out what the problem is. It appears that
    the Moon position on the pass charts on heavens-above are 
    geocentric. They do not take into the account horizontal parallax, 
    IF I've figured this out correctly. 
    
    Your 6.5 mile difference eastward is just about what would have 
    been required for the pass in question to lower the altitude of 
    the ISS by about two-thirds of a degree. And since the Moon was 
    roughly 45 degrees high for that pass, its parallax would be 
    just about two-thirds of a degree lower in the sky.
    
    I also tried running some satellite passes for points along the 
    same longitude with latitudes of +60 and then -30. I found a pair
    of passes that occurred at the same zone time to make sure that
    they would be calculating the Moon's position at the same UT.
    And sure enough, the Moon was mapped on the pass chart at what
    seemed to be *exactly* the same position despite a 90 degree
    difference in latitude. Obervers that far apart, comparing 
    simultaneous observations of the Moon would normally be expected
    to see the Moon at positions against background stars that are 
    about a degree apart due to horizontal parallax.
    
    IF this turns out to be a correct analysis, it would be relatively
    easy for heavens-above.com to fix the problem, which should then
    make that site a fun way to find lunar transits. 
    
    In the meantime, you can apply a good, approximate correction by 
    peforming a simple calculation:
    
      d_away = r_sat / [60 * tan(h)]
    
    where r_sat is the approximate satellite range, tan(h) is the
    tangent of the satellite altitude, and the result d_away is the
    distance that you should "step back" in order to get the satellite
    lower in the sky to compensate for parallax. So, as a numerical 
    example, if the Moon is 25 degrees high in the southwest, and 
    heavens-above shows that ISS, or some other satellite, at a 
    range of 1200km will pass in front of the Moon as seen from 
    a specified location, you would correct the location by moving 
    43km towards the northeast ("away" from the direction of the Moon
    in the sky). Note that for a high pass of the ISS the effect of 
    horizontal parallax is much smaller. If r_sat is 450km and h is 
    75 degrees, the correction is only 2 kilometers.
    
    Please note the big "IF" above...
    
    -Frank E. Reed
    www.clockwk.com/fer
    Chicago, IL
    
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