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    Re: FW: A noon sight conundrum
    From: George Huxtable
    Date: 2003 Nov 24, 19:10 +0000

    Kieran Kelly said-
    
    >We have just lost the Rugby World Cup so the
    >sun may never shine in Australia again.
    
    George responds-
    
    Citizens of other nations may not appreciate the seriousness of this event
    to the Australians, and indeed, to the English (who won it).
    
    On a more trivial level, he asked-
    
    >Firstly how can the Azimuth of the sun move from 0d to 360d as it passes the
    >local meridian. I have checked my two compasses - a Francis  Barker
    >prismatic and a modern Silva baseplate and neither exhibits 0d. Isn't zero
    >degrees the absence of degrees? And aren't there 360d in a circle therefore
    >the sun bears 360d at local noon. By definition it doesn't move from 0d
    >to 360d.
    
    I don't see Kieran's problem here. I happen to have two steering-compasses
    at home. One marks North with 360, the other marks it with 0. For most
    purposes, these angles are identical, just as 1 deg and 361 deg are
    identical, and also -1 deg and 359 deg. For a few purposes, it's important
    to know how many whole turns have been made, as well as the direction you
    end up pointing. For example, when at double-anchor in a tideway, the whole
    number of turns that were made in azimuth tells you how many twists you
    must remove from the anchor cables before you can get them in. In that
    case, 0 deg is as valid an angle as any other. Zero degrees doesn't mean
    the absence of degrees.
    
    As for his question about the changing azimuth around noon, that's been
    answered by Herbert Prinz.
    
    Which leaves us with his three definitions of local noon-
    
    >(1) When the centre of the sun crosses the observers meridian and
    >
    >(2) When the centre of the sun is due north of the observer i.e. its Zn is
    >360d true and
    >
    >(3) When the centre of the sun reaches its highest altitude
    
    To be mildly pedantic, (2) is over-restrictive, applying only to Kieran's
    hemisphere, as it excludes cases when the Sun is South of the observer, and
    its Zn is 180d true. Otherwise, it corresponds with (1).
    
    However, (3) is incorrect, except at the times of summer and winter
    solstice. It is only approximately true, even for a stationary observer,
    because the Sun's declination is steadily changing, moving North or South
    at approximately one knot around the equinoxes. This change superimposes on
    the daily rise-and-fall of the Sun. When the Sun's declination is moving
    toward the observer's latitude, then the moment of maximum altitude is
    delayed slightly after local noon, and vice versa. The amount of this delay
    is calculated by taking the daily rate of Northerly increase of declination
    for that date (from the almanac, perhaps), and multiplying by
    0.637(tan lat - tan dec),
    where lat and dec are taken to be positive-North. (This is adapted from
    Cotter, "History of Nautical Astronomy, page 265.)
    
    In general, for temperate latitudes, the correction won't exceed 30 seconds
    or so, and the altitude, because it changes so slowly around noon, won't be
    affected by being taken at max. altitude rather than meridian altitude.
    However, if some form of time-sight is being taken, which determines the
    moment of max. altitude, such as an equal-altitude observation, then the
    time-correction referred to above becomes an important matter.
    
    What we have considered is the effect on a land-explorer, who remains
    stationary while determining maximum altitude. At sea, the effect can be
    much greater. The Sun's midday altitude changes according to the rate of
    Northerly or Southerly motion of the vessel with respect to the Sun's
    declination, combined with the rate of change of declination. The
    North/South component of a vessel's speed can be 20 knots or sometimes
    more. In which case the adjustment between maximum and meridian altitude
    can become a very important matter.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ================================================================
    
    
    

       
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