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    Longitude via lunar altitudes, simplified
    From: Peter Fogg
    Date: 2007 Jan 31, 13:46 +1100

    Francis Chichester described a method of finding longitude and watch correction from lunar altitudes ("Longitude Without Time"; Journal of the Institute of Navigation , Vol. 19, 1966) that he apparently devised independently, although it is said to have been earlier described by John Letcher, best known for his work on self-steering systems.

     

    This method: longitude via lunar altitudes, has been discussed at least a couple of times on this and/or the earlier Nav List. It tends to be less accurate than the conventional method of lunar distances but has the advantage of using familiar sight reduction methods. It requires the moon's azimuth to be near to due east or west.  

     

    The Starpath site:

    http://www.starpath.com/catalog/accessories/starpilot/lun_alt.htm

    describes the method, with an example, using the StarPilot calculator (based on a Texas Instruments TI-86) and successive reiterations to achieve a result.

     

    George Bennett has devised what he claims to be: "a simple method of … calculating longitude from lunar altitudes that does not require a succession of approximations".

    This proposed method, with a worked example, has been published as: "Longitude from Lunar Altitudes Simplified" in the Journal of the Institute of Navigation , Vol. 53, No. 2, 2006.

     

     This article can be accessed by going to:

    http://gbennett.customer.netspace.net.au/

    and then choosing the last option on the left:

    Longitude from Lunar Altitudes Simplified

     
    The following example of finding longitude and watch correction from lunar altitudes contrasts the methods used by the Starpath site and that proposed by Bennett. The symbols and sign conventions are Bennett's; the time, DR and bodies used come from the Starpath example.

     

     

    Date 19th January 2000:     DR position N47º 45´, W123º 05´

    Time Zone 8h W:    Height of Eye 9 ft:    Sextant Index Correction 0

     
    Observations and Calculations

     

    Body      Watch Time      Obsd. Alt.    Azimuth     Int.

    Mars     17h    50 m  00 s     25º 04.9´       223.5º      T18.2

    Saturn   17     50      00       52  37.5         154.5         A3.3

    Fix at    17h     50 m        N47º 39.0´, W123º 35.1´

     

    Moon (LL) Observation at   17h     50 m   00 s     Altitude 19º 30.2´       

     

    Moon Observation and Intercept Calculations

     at 17 50m 00.0s, Latitude N47º 39.0´,

     Sextant   Altitude   19º 30.2´.

     

      Watch Correction     Longitude           Intercept 
    Slow (+)10m(WS)      W126º 05.1´(LS)   T6.3(IS)
                    0  (WF)      W123  35.1(L0)     T2.1(IF)
     
    Note: 10m  =  2º 30´

               Azimuth of the Moon not required

                LS  = W123º 35.1´+ 2º 30´ =  W126º 05.1´

     

                                        IS                   6.3

                          F   =   ———   =  ——

                                    IS   - IF               4.2   

     
    WS - WF   =  10m      LS   -  LF    =  2º 30´     

     

    Required Watch Correction

    WP   =   10m - F x 10m =   - 5m 00s (Fast)

                              

    Required Longitude

           LP    =  W126º  05.1´ - F x 2º 30´  =  W122º 20´

     

    Check: When the above watch correction and longitude is used with the original data the intercept should be zero.

     

    Starpath Values

    - 5m 12s (Fast)     and       W122º 17´

     

    In the context of lunar observations these differences are of no significance.

    The Starpath values, while similar, involve five pages of graphics.

     

     

     


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