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    Re: Photo sextant sights
    From: George Huxtable
    Date: 2008 Jul 30, 17:00 +0100

    Wolfgang K�berer 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
    
    Wolfgang wrote-
    
    "Yesterday I received "The Navigator's Newsletter" issue 97 - 99. The last
    issue contains an article by David Burch (from his book "Emergency
    navigation") about "Photo sextant sights". As this had been discussed on the
    list not too long ago I read the article right away. It relates the example
    of a "Photo sextant sight" taken in Florida at 27deg 12,2 min N, 80 deg 13,4
    min W.
    ...
    The article sums up: "had we not known time or
    longitude, we would have found our longitude this way to within 53 min ".
    This would mean a possible error of about 47 miles - which is probably
    acceptable.
    
     Then I did a quick "Sumner": I varied the input to see what happens to the
    result. On the assumption that there is no error in latitude (having bent my
    sextant only after taking the height of Polaris or a star on the meridian)
    and that my time is correct, I varied my assumed longitude and got a
    perplexing result: Using Frank's program and assuming I am about 150 miles
    out in the Atlantic (= assumed longitude 77deg 10 min W) I got the following
    result:
    
    "Error in Lunar: 0 min
    
    Approximate Error in Longitude: 0 deg 00.4 min"
    
    which - following David Burch � I interpret as saying I am almost at my
    assumed position. As the "Photo Sextant Sight" supposedly was taken 3
    degrees further west something doesn't fit. What did I get wrong? It's not
    the input, I checked it several times."
    
    ============================
    
    I haven't checked out those details, but suspect that Wolfgang did nothing 
    wrong. It's simply that this was a completely inappropriate geometry for 
    measuring a lunar distance, as a glance at the photo will show.
    
    Look at the way the gibbous Moon is illuminated. Draw a diameter across the 
    Moon, which divides it so that the lighting on each side of that diameter is 
    symmetrical. That line (which is at right-angles to the line joining the 
    Moon's rather-blunt "horns") shows the direction from which light is falling 
    on the Moon from the Sun. That direction is the great-circle joining the 
    Moon to the Sun.. Very closely, it's also the direction in which the Moon is 
    moving against the star background, because the Moon never strays more than 
    5� from the plane of the ecliptic. And that motion, in that direction, is 
    what a lunar distance is attempting to measure. So always, a lunar distance 
    is the spacing measured between the Moon and another body that is on, or 
    near, that line of symmetry.
    
    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. And so the measured spacing 
    is almost completely insensitive, as a measure of longitude.
    
    Frank's lunar calculater estimates the error in longitude simply by 
    multiplying the error in lunar distance by a factor of 30, taking a typical 
    value for Moon's motion, but, crucially, assumes that the measured distance 
    is always in or near the correct direction. In the example shown, the 
    misalignment is so great that the error could easily be 5 or 10 times 
    greater than that.
    
    A Moon-Jupiter lunar is usually highly recommended, because Jupiter is 
    always close to the ecliptic in its path, so what has gone wrong in this 
    case? It seems to be a consequence of trying to use a camera, rather than a 
    proper angle-instrument, to make the measurement. To keep distortions low in 
    the camera optics, it's desirable to keep subtended angles small. But in 
    traditional lunar-distance measurement, the measured angles are kept to 25� 
    or more, so the two bodies are well spaced around the ecliptic, and smaller 
    angles than that wouldn't even be shown in the lunar tables. You would never 
    even consider measuring with a sextant lunar distances of 5� and-a-bit, as 
    was being attempted here. And so the bodies were not at all spread around 
    the ecliptic; instead, it was damn-near a conjunction between the Moon and 
    Jupiter, exactly the wrong moment to try a lunar distance.
    
    I'm a bit sad that this example has now shown up in Navigator's Newsletter, 
    because its editor, David Burch, asked my opinion about it, and I explained, 
    back in late 2006, the drawbacks of that particular camera-shot.
    
    There are other drawbacks in making celestial observations by camera rather 
    than by instrument, but that will do to be going on with.
    
    George.
    
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 
    
    
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