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    Re: Longitude via lunar altitudes, simplified
    From: Peter Fogg
    Date: 2007 Feb 21, 14:42 +1100

    On 2/14/07, dw <waldendand@yahoo.com> wrote:

    I would suggest Letcher's Feb 1964 article in Yachting is the earliest
    "modern" rediscovery of the longitude by lunar altitude methods.

    As Frank points out, such methods were well known more than a hundred
    of years ago.  The Ashe discussion is from: Monthly Notices of the
    Royal Asronomical Society, Vol XII, nov 1851-june 1852, page 179.
    (Available from Google books.)  Many of the astronomy and navigation
    texts from the 1800's (and there are quite a large number on google
    books) have references to longitude by lunar altitudes.  Since this
    was before LOP, most discuss only longitude assuming latitude by one
    of a number of other methods.  See for example, New Methods of finding
    the Longitude at sea or on shore, by Yarrow and Lynn, 1826, also on
    google books.

    Below is an example using one of these methods with the data from
    Bennett's recent "Longitude from Lunar Altitudes Simplified".

    On 15 Feb (local time!) Dan Walden sent an example using "one of these methods"
    (which one? and why?)
    to establish longitude / time via lunar altitude.

    It seems quite a bit more complex than the method proposed by Bennett. 

    In Chichester's article, latitude was observed prior to a Sun/Moon observation. Position fixes were calculated at some convenient time interval before and after the Sun/Moon fix – he chose half an hour. This required a plot to be made covering about fifteen degrees of longitude to find where the line joining the two fixes would intersect the previously determined latitude. Using the principles shown in the Bennett article in the Journal of Navigation, this process can be simplified by using a numerical technique. The following is an illustration of this:

    Date: 4th March 1990. DR: Lat N40º, Lon W20º. H.E. 6 ft.  Index  Correction +3.5'.

    Observed latitude: N39º 52.6'  


    Lat N40º.  Watch Time 16h 02m 17.0s.                                                                                                                             

    Body            Watch Error    Lon       Altitude                     Lat             Lon

    Sun LL                 0            W20º     31º 58.7'    Fix       N39º 48.8'   W19º59.5'

    Moon UL             0            W20º     40º 53.3'


    Sun LL        Slow 20m       W25º    31º 58.7'     Fix       N39º 39.1'   W24º46.7' 

    Moon UL    Slow 20m       W25º    40º 53.3'                                                     .

                                                                               Diff.                9.7         4º47.2'


    Let A =  N39º 52.6' - N39º 48.8' = 3.8


    Longitude:      W19º59.5' – A/9.7 x  4º47.2'=  W18º 07.0' 


    Watch Correction:     A/9.7x20m = Fast 7m 50s



    While a simplification, this calculation technique is considered inferior to the method shown by Bennett in the Journal of the Institute of Navigation article.



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