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    Re: Longitude via lunar altitudes, simplified
    From: Gary LaPook
    Date: 2007 Feb 02, 17:09 -0800

    Well, what a disappointment because I thought that I was the first one
    to think of this method, I have been playing with it for years. I
    conceptualized itthis way. Any two or three star fix will be fixed at
    the correct latitude and at the correct SHA and can be plotted on a
    chart labeled with SHA as opposed to longitude. This fix rotates
    around the world every 23 hours 56 minutes and 3.9 seconds always
    maintaining the correct latitude and a constant SHA. What then ties
    this fix in SHA to longitude is GHA aries which varies with time.
    Since the moon marches to the beat of a different drummer its position
    does not move in conjunction with the fix SHA when you vary your
    assumed time. So by iterating time you move the moon line till in
    coincides with the stellar fix and so determine the time and by that
    the GHA aries and so the longitude.
    
    The Starpath example used two planets but using stars is better
    because the moon moves slightly more rapidly in relationship to the
    stars than it does in relationship to the planets so you have a larger
    difference to work with.
    
    BTW this is the way GPS works. The onboard clock is not accurate
    enough to determine the time accurately enough to determine the
    orbital positions of the satellites which is necessary to determine
    the propagation delay of the GPS signal from the satellite to the
    observer. This is why you need a minimum of three satellites in view
    for the GPS to work. The system uses the same methodology, it adjusts
    the time base in steps until the third gps position line coincides
    with the two LOP fix derived from the other two satellites.
    
    
    
    
    
    On Jan 30, 6:46 pm, "Peter Fogg"  wrote:
    > 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 N47� 45�, W123� 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     25� 04.9�       223.5�      T18.2
    >
    > Saturn   17     50      00       52  37.5         154.5         A3.3
    >
    > Fix at    17h     50 m        N47� 39.0�, W123� 35.1�
    >
    > Moon (LL) Observation at   17h     50 m   00 s     Altitude 19� 30.2�
    >
    > *Moon Observation and Intercept Calculations *
    >
    >  at 17 50m 00.0s, Latitude N47� 39.0�,
    >
    >  Sextant   Altitude   19� 30.2�.
    >
    >   Watch Correction     Longitude           Intercept
    > Slow (+)10m(WS)      W126� 05.1�(LS)   T6.3(IS)
    >                 0  (WF)      W123  35.1(L0)     T2.1(IF)
    >
    > Note: 10m  =  2� 30�
    >
    >            Azimuth of the Moon not required
    >
    >             LS  = W123� 35.1�+ 2� 30� =  W126� 05.1�
    >
    >                                     IS                   6.3
    >
    >                       F   =   ---   =  --
    >
    >                                 IS   - IF               4.2
    >
    > WS - WF   =  10m      LS   -  LF    =  2� 30�
    >
    > *Required Watch Correction*
    >
    > **
    >
    > WP   =   10m - F x 10m =   *- 5m 00s (Fast)*
    >
    > *Required Longitude*
    >
    > **
    >
    >        LP    =  W126�  05.1� - F x 2� 30�  =  *W122� 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       W122� 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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