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    Re: Working a lunar - a PS
    From: Hanno Ix
    Date: 2009 Aug 6, 17:30 -0700
    George:

    Re - inventing gives lots of satisfaction and is a great method of learning. You gentlemen over there have boatloads of literature on our topic, and if by raising the issue I can elicit pointers to it then I have achieved already something.

    Needless to say, I'd also like to try out these methods. You see, I have no boat and I get seasick easily, but there are vast desserts around here in CA where I can test my mettle!
    I think, I will search for an astronomical transit - that I can afford. Any suggestions?

    BTW: I am finding a copy of this book from 1874 on Google Books. I'll download it and see what Chauvenet has to teach us.

    I truly appreciate your interest.

    H






    --- On Thu, 8/6/09, George Huxtable <george@hux.me.uk> wrote:

    From: George Huxtable <george@hux.me.uk>
    Subject: [NavList 9394] Re: Working a lunar - a PS
    To: NavList@fer3.com
    Date: Thursday, August 6, 2009, 5:02 PM


    Hanno seems to be re-inventing the method, described by Chauvenet in
    "Spherical and Practical Astronomy", (1863), as his 4th method for finding
    the longitude (by moon culminations). Also relevant is his 5th method, by
    azimuths of the moon, or transits of the Moon and a star over the same
    vertical circle. Both highly accurate when observed from on land, but not
    possible otherwise.

    Used for determining the longitude in the ice of James Bay, an appendix of
    Hudson bay, accurately by Thomas James, who overwintered there in 1630-31.
    This was the first successful use (that I know of) of lunar methods for
    longitude determination.

    As opposed to William Baffin, who is often credited with the first use of
    such lunar measurements 40 years earlier, but actually got it hopelessly
    wrong.

    There may be more to be said, but it's time for bed.

    George.

    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message -----
    From: "Hanno Ix" <hannoix@sbcglobal.net>
    To: <NavList@fer3.com>
    Sent: Friday, August 07, 2009 12:38 AM
    Subject: [NavList 9393] Re: Working a lunar - a PS


    Brad:

    Thank you for the time and thoughts you spent on this.

    We both agree that - if it worked - this approach to find position/GMT by
    the difference between the times of culminations, i.e. DT, is only practical
    from land. But that itself would be rather desirable and probably quite
    within the technical means of a traveling ship.

    Frankly, I don't really know much about the kinematics of culminations of
    moving Heavenly Bodies. I suspect, though, that there might be significant
    deviations from a first order analysis. Even though these deviations might
    seem small for now, they might also end up a little cumbersome in practice
    because of the small size of the observed phenomenon itself - the movement
    of the moon.

    Nevertheless, the simplicity of the concept would make the approach
    attractive because it seems easy to understand and to remember. And applying
    some corrections is a common part of celestial navigation. So, it might
    perhaps end up useful - if it is correct!.

    So, let's submit this concept to further critique of the group members.

    Thanks again and regards

    H



    --- On Thu, 8/6/09, Brad Morris <bmorris@tactronics.com> wrote:

    From: Brad Morris <bmorris@tactronics.com>
    Subject: [NavList 9392] Re: Working a lunar - a PS
    To: "NavList@fer3.com" <NavList@fer3.com>
    Date: Thursday, August 6, 2009, 1:34 PM









    Hi Hanno

    I have been considering your statement “If I see things right, there must be
    a LOP which connects
    all those locations on Earth that have a given, fixed difference DT between
    the meridian passages of
    sun and moon”

    Just to be sure I understand your statement, I will re-write it. The first
    object crosses your meridian. Let us assume that it is the sun. While this
    is
    LAN, we don’t care about that, you merely start your timepiece stopwatch.
    Next we wait for the second object to cross your meridian. When it does, you
    stop your timepiece. We observe the delta time. From this one data point, we
    are expecting a LOP.

    This has nothing to do with the altitudes of the objects, just the Delta
    Time of the meridian crossing.

    One problem (not insurmountable) is that the two celestial objects have
    apparent diameters. As such, we must perform a few more measurements. That
    is, assuming
    you are using an older theodolite with 5 wires, you would record the 5
    times that the leading limb crosses each wire and the 5 times that the
    trailing limb crosses each wire, and then mathematically determine when the
    object was on your meridian.

    The next problem (not insurmountable) is to align the theodolite to your
    meridian. Even Bowditch in the 1800’s knew how to do this. However, the
    requirement
    to align the theodolite to the meridian precludes any use of this method
    whilst at sea.

    Now which LOP corresponds to the Delta Time (DT)? I suggest to you that it
    is your MERIDIAN. Anyone, at any other latitude, that is on your longitude
    will
    measure the same precise value that you do. Now there’s an interesting
    outcome! Sure, the altitudes will be different, but the DT will be the same.


    Can we tell which meridian? Considering that the moon essentially travels it’s
    diameter in an hour, we run right into the resolution problem, very similar
    to the Lunar lack of resolution. Since we will be measuring with a
    theodolite, we will have a very good measurement for the time of meridian
    crossings, assuming that the theodolite is aligned to the meridian to
    perfection. Assuming you measure precisely
    and accurately, then the answer is yes.

    Best Regards
    Brad






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