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    Re: Lunar longitudes, not by lunar distance.
    From: George Huxtable
    Date: 2009 Aug 9, 15:03 +0100

    Thanks to Geoffrey for some useful comments, paricularly about viewing high 
    objects in a theodolite, such as Polaris from Northern Europe.
    
    Although Polaris will be lower in San Diego, the Moon altitude will be 
    higher. Will that cause a difficulty?
    
    I've just had a chat with Clive Sutherland, Navlist member in the next 
    village to mine, who has theodolites, fiddles with and modifies them, and 
    knows a lot about them.
    
    An alternative to an expensive instrument with the light path bent through 
    90� where the axes intersect, such as the Wild, is to fit an eyepiece with a 
    reflecting prism, on the same lines as a star-diagonal as fitted to a 
    telescope, though this may obstruct some movements.
    
    I omitted to mention that a theodolite would be needed that possessed 
    illumination, not only for the scales, but the cross-wires also.
    
    Geoiffrey added-
    
    "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.
    
    "For azimuths, the correction is the semi-diameter divided by the cosine of 
    the altitude."
    
    Indeed, that would be the case, if we were measuring azimuths, but we're 
    simply timing the Moon as it passes a vertical line, so the correction is 
    constant in time, independent of altitude.
    
    I would expect a reasonable instrument on a firm base could be set to 
    vertical to rather better that 1 minute, but in this case it doesn't matter 
    much. As long as the reference star chosen is close to the altitude of the 
    Moon, the tilt matters little. It doesn't even matter much, for establishing 
    the time difference to deduce GMT, whether the telescope tilts exactly in 
    the plane of the meridian. For observing the reference star's time of 
    meridian passage, to get local time for determining longitude, then that 
    does matter.
    
    George.
    
    contact George Huxtable, at  george{at}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: "Geoffrey Kolbe" 
    To: 
    Sent: Sunday, August 09, 2009 11:08 AM
    Subject: [NavList 9431] Re: Lunar longitudes, not by lunar distance.
    
    
    
    
    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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