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    Longitude by Sunset
    From: Alexandre Eremenko
    Date: 2012 May 5, 15:06 -0700

    Jeremy,

    Due to your last message, I discovered the February 2010 thread
    about "Longitude by Sunrise". Accidentally I just recently tried
    to investigated this
    matter:-)

    I found this idea in the book of Marguet, Histoire generale de la navigation
    du XV au XX siecle (1931) where he mainly describes the longitude story
    from the French point of view.
    The method was proposed by Saint-Jaques de Silvabelle, before the 1-st quarter
    of XVIII, the exact date is not given.

    It looks indeed elegant and simple: you just time the DIFFERENCE
    (time elapsed) between
    sunset and moonset. Using a good watch. No chronometer is necessary,
    because you only need elapsed time, not GMT.
    If you know your latitude (for example from Sun at noon or Polaris),
    this time gives you your longitude.
    Mathematics is not very easy but I worked it.

    This is a version of Lunar distances, except that a watch is used to measure
    the distance instead of a sextant. A good watch was about the same accuracy
    as a good sextant, for time intervals less than 1 day.
    (Of course, good almanac is needed, and it
    was not available at the time of this proposal).
    I was even somewhat excited, and wanted to write to the list:-)

    But then I decided to check the details. Of course the major obstacle for
    the method is how accurately you can time a sunset or moonset.
    And what prevents you from doing this is refraction at the horizon, and
    the dip.

    My main source is the article "Refraction near the horizon" by
    B. Schaeffer and W. Liller, Publ. Astr. Soc. of the Pacific, 102(1990)796-805.
    The authors and their friends made massive observations trying to time
    sunsets with their watches. The conclusions are discouraging.

    However:

    1. In the introduction they cite other literature on the subject, and most
    authors assume that the uncertainty in refraction is 1' or so.
    (Their purpose is to refute this opinion. How come that everyone who investigated the question before was wrong by so much they do not explain).
    They claim that variation can be as large as 0.2 degree (!)

    2. They confirm this with many observations made in Hawaii, Chile and other places. However the observations were made on different dates, and they
    compare refraction at different places, and at one place several days
    apart.

    The question is how much can refraction change in LESS THAN 12
    at the same place, remains unaddressed. And I hope (and their data suggest)
    that it does not change much. And this is the only thing we need,
    because Sun and Moon have about the same diameter and will be equally
    affected with refraction:-)

    Do here is a little research project for an interested List member who
    has a luxury of having a sea horizon facing West.
    Time a Sunset and Moonset on the same day, as well as you can
    and do it for several days...

    I volunteer to reduce the data:-)
    And we will see, with what accuracy can longitude be derived from this.

    Perhaps neither a good sextant not chronometer is necessary for longitude
    after all:-)

    Alex.

    P.S. To me it seems evident that it is easier to time Sunset rather than
    Sunrise. The moment of disappearance of the Sun upper limb. And certainly Moonset is easier than Moonrise. But of course the correct limb of the moon must be timed.
    P.P.S. These guys record a Green Flash in about 15% of their observations...



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