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    Re: Lunar longitudes, not by lunar distance.
    From: Geoffrey Kolbe
    Date: 2009 Aug 09, 11:08 +0100

    George wrote [NavList 9430]
    >All he needs to do, once it's been placed firmly on a well-set tripod, is to
    >set up his instrument so that its vertical axis is truly vertical, for which
    >the built-in levels should be quite adequate. Then to set it so that its
    >telescope swings in a near-meridian plane. One way to do this is to
    >establish North (in the Northern hemisphere), by bisecting the most-Eastern
    >and most-Western azimuth swings of Polaris. However, that's only possible at
    >certain times of year; at others, two different stars may have to be used,
    >but this presents no problem now that stars have been catalogued so
    >precisely. Then swing by 180� to look Southwards.
    A couple of practical points are worth noting 
    (again, as Hanno is new to the list) in the use 
    of transit theodolites for measuring azimuth.
    First is that for altitudes greater than about 50 
    degrees, it is usually not possible to get your 
    eyeball behind the telescope using a standard 
    transit theodolite. I think Hanno says he lives 
    in San Diego, whose latitude is low enough that 
    he will be able to see Polaris without difficulty 
    using a standard transit theodolite. Here in 
    Northern Europe, it would not be possible to do so.
    There are so called 'broken' theodolites, where 
    the viewing is done along the axis about which 
    the telescope and vertical scales rotate. There 
    is a 45 degree mirror which redirects the view up 
    the telescope. There is no limit to the altitude 
    one can view using such a theodolite, the most 
    famous example of which is the Wild T4 - but you 
    won't find one of those on ebay! What you do find 
    quite commonly on ebay are theodolites for 
    tracking weather balloons. These are 'broken' 
    theodolites and would be excellent for CN alt/az 
    measurements - except that their scales are quite 
    coarse, usually in degrees only I think, judging 
    by what I can see from the ebay pictures.
    Second, is that the error in azimuth goes as the 
    tangent of the error in vertical alignment of the 
    theodolite. So, if the theodolite is 1 minute off 
    vertical and you are looking at an object at an 
    altitude of 45 degrees, the error in azimuth 
    could be up to 1 minute. Luckily, standard 
    transit theodolites are self limiting in this 
    regard - see my first point above.
    Third and final point. As George mentioned, when 
    doing measurements on the sun or moon, it is 
    usual to take a measurement as the edge of the 
    body (top of bottom for altitudes, sides for 
    azimuth) touches the appropriate cross hair and 
    then make a correction to get the centre of the 
    body. For altitudes, the correction (to first 
    order) is simply the semi-diameter of the body. 
    For azimuths, the correction is the semi-diameter 
    divided by the cosine of the altitude.
    With both these last two points, it can be seen 
    that it is advantageous to observe bodies of low 
    altitude to avoid significant errors in azimuth.
    Geoffrey Kolbe
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