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    Re: Exercise #16 High Altitude Sights near Noon
    From: Jeremy C
    Date: 2008 Jul 21, 17:13 EDT
    The problem is as follows:
    "On 13 November 1981, your 1030 ZT DR position is Lat 19 deg 03'S,
    Long 6 deg 34'E.  You are on course 164 deg T, speed 12 knots.  You
    take the following observations of the Sun:
    Zone Time    GHA        Declination    Observed Altitude (Ho)
    1112        351 deg 55.4'    S 18 deg 00.4'    88 deg 08.0'
    1121        354 deg 10.4'    S 18 deg 00.5    88 deg 33.9'

    What is the 1200 position?"

    A)    Lat 19 deg 22.3'S, Long 6 deg 37.8'E
    B)    Lat 19 deg 20.1'S, Long 6 deg 41.4'E
    C)    Lat 19 deg 17.6'S, Long 6 deg 39.2'E
    D)    Lat 19 deg 15.8'S, Long 6 deg 36.8'E
    The correct answer is "A"
    This is generally a plotting exercise; where we are plotting circles of equal altitudes and where the two circles intercept, we can determine position.  The trouble is that the circles will intersect in two places, so we need to pick the point closest to our DR.
    The first thing to do is plot the Geographic Position of the sun at the given times.  Since this is a plotting exercise, we are given GHA and the Declination.  Declination will equal Latitude, but unfortunately we are in the Eastern Hemisphere so we need to convert the given GHA to Longitude, which is 360-GHA.  Once these Longitudes we plot the two points on our plotting sheet along with the DR position.
    This problem asks for a 1200 LT position so that means we need to advance the GP's and the DR to 1200 before we scribe the circles.  This is the same way that radar LOP's are advanced in terrestrial navigation.
    Now that we have the GP's advanced to 1200, we can scribe our circles.  To find the radius of the circle, we find the zenith distance of the sun at each time.  This is equal to 90-Ho.  Since Ho is given it is a simple matter of arithmetic.  We do need to convert degrees to minutes in order to get the radius in nautical miles.  Once we have the radius, we carefully scribe the circles and determine where they intersect near the DR.  This will yield the position.
    One note, it is actually better to have between 30 and 100 minutes of zenith distance to reduce the ambiguity of which intersection is the position.  If you are within 10 miles of the GP of the body for one of the sights, which has happened to me twice, you run into a bit of trouble determining which point is the true position. 

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