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    Lunars without calculator
    From: Herbert Prinz
    Date: 2001 Jul 10, 10:15 AM

    nigel_gardner wrote:
    
    > In the absence of tabulated LD's, is it possible to establish longitude by
    > means of currently available ephemeris (Nautical or Astronomical Almanacs),
    > log. tables and a sextant? And of course without the use of calculators or
    > computers.
    
    Dear Nigel,
    
    It was not fair of you to send us on a wild goose chase looking for all kinds
    of algorithms, when what you really wanted was a procedure without calculator.
    To most of us, this restriction is not so "of course" as it appears to be to
    you.
    
    But, OF COURSE, there is a way of finding longitude at sea without tabulated
    lunar distances and without calculator. All you need is the regular tables,
    plotting tools, etc. that you normally use when working your favorite flavor
    of  intercept method.
    
    Latitude, longitude and time can be found simultaneously from the observation
    of  3 bodies, one of them being the moon. In order to avoid the need for lunar
    distance tables, we confine ourselves to altitude observations. One should be
    aware though that this works best when the moon changes altitude the fastest.
    I.e. the moon should be near the prime vertical and it should rise vertically,
    such as is the case in low latitudes. Even then the method is inherently less
    accurate than the lunar distance method, because an observation error in the
    altitude of the moon caused by abnormal refraction will have full impact on the
    result (unlike the LD method, where the detrimental effect of abnormal
    refraction is subtler, but certainly not non-existent, as was claimed
    elsewhere).
    
    The principal method is described in Chauvenet (see R. van Ghents earlier
    reference), pp382-386, including a worked example. It goes without saying that
    the method requires no calculator or computer, since Chauvenet wrote the book
    in 1863.
    
    It was Sir Francis Chichester's merit to find an elegant way of solving the
    same problem with the tools that every sailor has on his boat. It is documented
    in Francis Chichester, Along the Clipper Way, New York, 1967 (There may be an
    earlier English edition). I am quoting from  pp.170-171:
    
    "Make a simultaneous observation of moon and sun [...]. Compute a sun-moon fix
    in the ordinary way, using a guessed-at GMT. Now compute a second fix from the
    same observation but using a GMT which differs from the first by half anhour or
    an hour. Now establish the latitude by meridian altitude of the sun [or any
    other way]. [...] Join the two sun-moon fixes and the point where the line
    joining them, produced if necessary, cuts the known latitude must be the
    correct longitude at the time of the observation. Knowing the longitude enables
    you also to know what the correct GMT was at the time of the sun-moon fix."
    
    I don't recommend the exercise in an unsettled sea. Your plotting has to be
    rather accurate...
    
    Herbert Prinz (from 1368950/-4603950/4182550 ECEF)
    

       
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