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    Re: Working a lunar - a PS
    From: Hanno Ix
    Date: 2009 Aug 6, 16:38 -0700
    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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