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    Re: FW: A noon sight conundrum
    From: George Huxtable
    Date: 2003 Nov 24, 20:23 +0000

    In a mailing earlier today I said-
    
    "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.) "
    
    This was sloppy, because I didn't state the units of measurement of the
    time-correction, which should have been seconds of time. Sorry about that.
    
    I added-
    
    "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."
    
    I should have pointed out again that in applying the above formula to a
    vessel speed of (say) 20 knots Northerly, it's the DAILY rate around noon
    that is required, all of 240 miles per day.
    
    ===========================
    
    Zorbec Legras said-
    
    "There is a formula to correct the problem of observing the sun by a
    mouving observer:
    T0 = ((T 1 + T2) /2) + correction
    correction = 15,28 * ( motion in Lat  - motion in dec )*(tan Lat 1 - tan dec 1)"
    
    ===================
    
    George comments-
    
    In this expression, I guess that T1 and T2 represent the times of two
    equal-altitude observations, so that (T1 + T2)/2 represents the moment of
    maximum altitude.
    
    What Zorbec doesn't make clear however, is that his "motion in Lat" and
    "motion in Dec" refer to the (Northerly) rate of change in these quantities
    PER HOUR, which is why his multiplying constant is just a factor of 24
    greater than mine. Then, his correction will, like mine, be in units of
    seconds of time, and his formula and mine agree. The remaining puzzle, to
    me, is what "Lat 1" and "Dec 1" refer to, and whether they differ from lat
    and dec.
    
    ==================
    
    Bill Arden, no doubt tongue-in-cheek, asked-
    
    Gee, why do we bother trying to take time measurements to the second when
    we're taking sights?  
    
    Well, any attempt to determine longitude, by chronometer or otherwise,
    involves measuring time. As longitude changes with time by 15 degrees per
    hour, or 15 minutes of arc per minute of time, then to arrive at a
    longitude to within an arc-minute requires a knowledge of time to better
    than 4 seconds.
    
    George.
    
    ================================================================
    contact George Huxtable by email at george---.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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