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    Using star-star distances
    From: George Huxtable
    Date: 2008 Sep 22, 22:58 +0100

    Andres Ruiz wrote in [6290],
    "I am writing an article about "Index error by a star-star distance".
    Unfortunately there is not much information about this subject, or I can't 
    found it. Anybody has any source of information; old books, papers, ... ? "
    I think Andres has misnamed his project. Measuring star-star distances 
    allows the calibration, not of index error, but of sextant scale error, at 
    various angles that correspond to the separation of each star-pair. As Gary 
    LaPook says, all you need to determine index error is a single star, not a 
    Hewitt Schlereth wrote, in [6292] "John Karl's book "Celestial Navigation in 
    the GPS Age" has star-distance tables in the back, and some discussion of 
    how they are done on page 194."
    Those pages and tables need to be taken with a pinch of salt, however.
    Karl provides star-star distance tables, which have been corrected for 
    refraction; 12 star-pairs, at well spaced angles covering the whole range of 
    a sextant. But they have been over simplified.
    Take, for example, the table on page 247, for the pair Betelgeuse and 
    Regulus. The angular distance between them, always near to 25 degrees, is 
    tabulated, corrected for refraction, as seen from different latitudes for 
    various observed altitudes of Betelgeuse, .
    This was based on the false assumption that from a certain latitude, a 
    defined altitude of Betelgeuse defines also what the altitude of Regulus 
    must be. However, this isn't so. There are two distinct sidereal times when 
    Betelgeuse has a certain altitude; when it's passing through that altitude 
    when rising, and also when it's passing through that altitude and falling. 
    The refraction of Betelgeuse is, of course, the same in both cases, but the 
    configuration of the sky will be quite different at those times, and the 
    altitude (and therefore refraction) of Regulus will be different. The table 
    on page 247 caters for only the situation when Betelgeuse is rising, BEFORE 
    culmination. Really, that limitation should have been noted on the table; 
    each such table should have been accompanied by a counterpart table, showing 
    the relevant star-star distances when observed AFTER Betelgeuse had 
    There's another problem. The angular distance between two stars is not 
    affected by precession, nor by the Earth's nutation. Aberration, on the 
    other hand, does have a different effect on different stars, depending on 
    the star's direction with respect to the Earth's velocity around the solar 
    system, something that reverses after six months. This can cause a 
    worst-case difference of about 0.7 �, between a star-star distance and its 
    value six months later.  John Karl has tabulated his star-star distance to 
    0.1 �, but the numbers can not be relied on to anywhere near that precision.
    John Karl is now aware of those difficulties, which will be addressed in any 
    later edition.
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