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    Re: Photo sextant sights
    From: Paul Hirose
    Date: 2008 Jul 31, 14:42 -0700

    George Huxtable wrote:
    > Wolfgang Köberer is right to question that example of an intended lunar 
    > distance measurement by camera, in Navigator's Newsletter 99. Andres Ruiz 
    > has provided the relevant link in-
    > http://www.starpath.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=31;t=000040
    
    That's a conventional altitude shot for a LOP. Also, the location is at 
    opposite corner of the U.S. from Florida.
    
    This page seems to be the right one:
    http://www.starpath.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=31;t=000017
    
    
    > Now look at the spacing between the Moon and Jupiter, that's being measured 
    > in the photo in an attempt to determine the Moon's position along its track. 
    > You can see that it's nowhere near that optimum direction; in fact, it's not 
    > far short of being at right-angles to it. The Moon isn't travelling towards 
    > or away from Jupiter, it's simply going past it.
    
    My lunar program confirms the bad geometry. As the output (below) shows,
    the lunar distance rate of change at the observer is only about 1" per
    minute! However, the geocentric rate is 14" per minute due to the
    different point of view.
    
    I came up with the idea of "velocity efficiency" as a figure of merit
    for the geometry between the bodies. It's the rate of change of lunar
    distance, divided by the total angular velocity of the bodies. If
    they're moving directly toward or away from each other, velocity
    efficiency is 100%. But it's only 4% in the photo.
    
    Checking the computed position angles vs. the image shows that it seems
    to preserve the original orientation you would have seen that night.
    That is, it hasn't been rotated so it could be cropped for display.
    
    The observed lunar distance reported by the program is a little
    different from the value on the web page. That's because I repeated the
    pixel computations but rounded the result to a higher precision, and
    added Jupiter's refracted semidiameter to simulate an observation from
    the Moon's near limb to Jupiter's far limb.
    
    That latter correction is necessary the program has no provision for a
    center to (Moon) limb observation, unless the other body has zero
    semidiameter. From the relative orientations of the bodies and the
    direction of the Sun, the correct limbs to observe are determined. If
    the actual observation was different, the measured angle has to be
    adjusted. In this case, I believe the center of Jupiter was measured
    rather than its limb. The difference is only a couple pixels, though.
    
    It's interesting that if the web page computation is repeated, but with
    the refracted Moon diameter from my program instead of the USNO value,
    the measured lunar distance is only 22" different from the prediction!
    This shows the difficulty of determining image scale from such a small
    object. In fact, I think they have the cart before the horse. It would
    be better to first use lunar distance photos to determine the scale and
    distortion of the camera. Then see how well you can measure an unknown 
    angle.
    
    
    Program Lunar1.
    
    2006-03-19T05:38:23.00  UTC (Gregorian)
                  + 0:00.28  delta UT (UT1-UTC)
    2453813.735743  JD (TT)
    2006-03-19T05:39:28.19  TT (Gregorian)
               +00:01:04.90  delta T (TT-UT1)
    2006-03-19T05:38:23.28  UT1 (Gregorian)
               -05:20:53.60  LMT-UT1
    2006-03-19T00:17:29.68  LMT (Gregorian)
                  -07:52.71  equation of time
    2006-03-19T05:30:30.57  GAT (Gregorian)
    2006-03-19T00:09:36.97  LAT (Gregorian)
    
    Moon, apparent geocentric (true equinox)
    14h48m52.97s  -19°54'57.2"  RA, dec
    55'33.9"  15'08.1"  HP, SD
    
    Jupiter, apparent geocentric (true equinox)
    15h05m47.63s  -16°05'53.1"  RA, dec
      0'01.9"   0'20.8"  HP, SD
    
    geocentric separation angle:
        5°32'37.3"  (center to center)
    
    geocentric angular rate, velocity efficiency:
    -13.7" per minute
    44% of total angular velocity is utilized
    
    observer position:
    +27°12'12.0" - 80°13'24.0"  north lat, east lon
    - 80°29'40.2"  ephemeris east lon
    0 meters above ellipsoid
    
    atmosphere at observer:
    20°C  68°F  temperature
    1010.0 mb  29.83" Hg  altimeter setting
    1010.0 mb  29.83" Hg  station pressure
    
    Moon illumination:
    48°  phase angle (0 = full Moon)
    152°  position angle to Sun (0 = 12 o'clock)
    5°  -63°  Sun az, alt
    
    Jupiter illumination:
    8°  phase angle (0 = full)
    151°  Sun position angle (0 = 12 o'clock from Jupiter)
    
    position angles:
    80°  Moon to Jupiter
    263°  Jupiter to Moon
    
    topocentric unrefracted angles:
        5°37'05.9"  center to center
        5°22'11.7"  Moon near limb to target far limb
    
    topocentric angular rate, velocity efficiency:
    -1.1" per minute
    4% of total angular velocity is utilized
    
    topocentric refracted angles:
    15'14.8"  moon SD (refracted)
      0'20.8"  target SD (refracted)
        5°37'00.0"  center to center
        5°22'06.0"  Moon near limb to target far limb
    
        5°23'55.7"  observed lunar distance
        0°01'49.7"  error (observed - predicted)
    
    -- 
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