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    Re: Old style lunar (in expert hands)
    From: Alexandre Eremenko
    Date: 2004 Dec 10, 20:22 -0500

    On Sat, 25 Dec 2004, Kieran Kelly wrote:
    
    > Eg I own a Wild T1a theodolite.
    > The  Zeiss Yachtsman sextant
    > and case which I use on expeditions weighs 2.8kgs.
    >
    > sextants have survived being bucked right off the back
    > of a pack horse and
    > on a recent expedition one travelled 750km on the back of a camel
    
    May I ask you what sort of expeditions are you participating in?
    750 km with horses, camels and sextant?
    I did not know that such things still happen in XXI century?
    Just for fun? Or this sort of surveying still exists?
    
    > Also the role of theodolites and sextants
    > should not be confused. A
    > theodolite is an instrument of surveying,
    > a sextant an instrument of
    > exploration and navigation.
    
    Well, I afraid this is based on tradition only:-)
    It is like Norie's advise for taking lunars:
    "have a good sextant to measure distances andf a good quadrant
    to take altitudes":-)
    
    You can certainly to all tasks with any of these instruments.
    
    > And don't underestimate the accuracy of a
    > sextant in the hands of an expert.
    
    I don't. The best marine sextants allow you READING the scale
    to 0.1'. I think this is more or less ultimate level of accuracy,
    even if you average long series.
    I don't know mych about theodolites, but some allow you to read
    to a single second, don't they?
    
    > "And you can certainly measure lunar or any other
    > distances with it."
    
    Let me make a disclaimer first: I have never held a theodolite
    in my hands. Only saw them in pictures. I assume your theodolite
    permits taking altitudes and measuring horizontal angles.
    Here is how you can measure a lunar distance.
    Set it firmly on a tripod on any other appropriate platform.
    Using the levels, insure that the asymuth ring is horizontal.
    Orientation with respect to the meridian is not essential.
    Now measure the altutudes of both bodies, and the difference
    in their azymuths in a quick sequence.
    Solving the resulting spherical
    triangle
    gives you the distance.
    
    Remarks.
    1. If you don't want to use a calculator, ordinary sight reduction
    tables can be used to solve the triangle.
    If someone is really interested I can write the formulas or
    an algorithm to do it with HO 229 sight reduction tables.
    
    2. That the measurements are not done simultaneously is going to
    cause a problem, but this difficulty can be overcome
    (see the Nonlinearity discussion in October for math
    justification of the procedure). I recommend the
    following sequence:
    (point at the first body) read alt1 azymuth1
    (turn the scope, point at the second body) read azymuth2 alt2
    (turn the scope, point on the first body)  and so on.
    Then take the average of 5-10 azymuths and altitudes,
    and solve ONE triangle with these average data.
    To take the averages accurately,
    you have to TIME the moments when the
    bodies
    are on the crossing of your wires, and all measurements have
    to be reduced to the SAME time.
    
    If you can do, say one cycle per minute (both azymuths and both
    altitudes, once each, in a minute) then averaging 5 observations
    spread over 5 minutes will surely give you better accuracy than
    measuring with a sextant. It is very helpful to have an assistant
    who will read the scales while you point the device.
    
    The reduction  of such sight is somewhat different from
    the sextant sight reduction. Different in the way the semidiameters
    are taken into account. But I can work all details if desirable.
    
    Very briefly, the justification is the following:
    on a 5 min interval, all quantities (altitudes, azymuths
    and the distance) change as linear functions of time,
    to VERY high degree of accuracy.
    So by averaging such sequence of sights you can obtain
    both altitudes and the difference of azymuths at the average time,
    as if they were measured simultaneously.
    
    If you are using some electronic reduction aids, you can even do
    quadratic interpolation which will kill the remaining small
    non-linearity error.
    
    Alex.
    
    
    

       
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