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    Re: Working a lunar - a PS
    From: George Huxtable
    Date: 2009 Aug 7, 01:02 +0100

    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" 
    To: 
    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  wrote:
    
    From: Brad Morris 
    Subject: [NavList 9392] Re: Working a lunar - a PS
    To: "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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