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    Re: Celestial Course
    From: Adrian P. Vrouwenvelder
    Date: 1998 Mar 18, 6:18 AM

    Ref:  Note from Ruth Summers  (attached)
    >  So, I'd really like to see something we all could work together on.
    >  I am currently working with another lady to figure out this celestial stuff.
    >  We have books, tables, more books, I just ordered some videos.
    >  For crying out loud, what makes this so damned hard !!
    >  -ha probably the *&^%$ math.
    The math is easy.  As Dan Hogan mentioned, it's add, subtract, multiply
    and divide (mostly just add and subtract if you use ho229 and all the
    neat tables).
    >  Although I can see after my minor investigation into this that I think the
    > angles of measurement is where the math is needed, ie-usually the boat is tilted
    >  but the GP is that line coming out of the earth and it's straight.
    Boat heel has no bearing on your navigation.  Forget about it.
    I've noticed that some books show _how_ to do celestial, but
    don't really do a good job of painting the "big picture" so you can
    keep everything in perspective.  Here's my attempt at a big picture.
      1. Given that you know your distance from three known positions on the
         planet, you can draw three circles of position.  The point at which
         all three circles intersect is your position.  (Two overlapped
         circles define two points of intersection; the third circle should
         intersect at or near one of those two points).
      2. If a star is directly overhead (i.e. exactly 90deg to the horizon),
         you are at its geographic position (GP) and your distance from it
         is zero (0).  If you can see a star at your horizon (corrected
         for dip, refraction and all) so that it measures 0deg to the
         horizon, you are 1/4 of the planet's circumference from its GP.
         Got that?  That amounts to 5400 nautical miles (because the
         there are 60 nautical miles at earths surface for every degree
         of arc).
         If the star measures 45deg, you're 2700 miles from its GP.
         And so on.  The point is, the angle you measure off the horizon
         to the star is directly convertible to your distance from its
         GP.  If you knew its GP, you could plot your circle of position.
      3. Sextants measure angles.  Period. However, the angle you measure
         with the sextant (Hs) must be corrected for dip, refraction of the
         atmosphere, index error, and some other factors. This is easy to
         do using the nautical almanac, which contains some easy-to-use
         tables facilitating this correction.  The result is Ho, for
         "Height observed."
      4. The Geographic Positions of celestial bodies are obtained from the
         Nautical Almanac, and will ultimately be expressed in terms of
         GHA (Greenwich Hour Angle) which expresses the star's position
         with respect to Greenwich, and Declination, which corresponds
         to the GP's "latitude."
         If you had a very large chart and could draw very large
         circles, you could stop here.  You would not need sight
         reduction.  However, you probably have a small chart spanning,
         say, 80x80 nautical miles, so charting the GPs of all of your
         celestial bodies is impractical.  Therefore, you need sight
      5. Sight reduction allows you to plot your celestial circle fragments
         of position on a small chart (using straight lines as
         approximations of those circle fragments).  Basically, since
         you don't know where you are, but have a pretty good idea (i.e.
         "somewhere on this chart"), you pick an arbitrary spot on the
         chart.  The sight reduction procedure then ultimately tells
         you how to draw your line of position (the line on which your
         vessel is) relative to the point you chose.  The procedure does
         this by giving you "Height computed" (Hc) an azimuth (Z, given
         as a true bearing), and a direction (away from or towards the
         celestial body along the azimuth).
         You take the difference of Hc and Ho to come up
         with a distance (remember there are 60 miles in a degree).
         When you've digested all of this, we can talk about how to
         plot your LOP using the Hc, Z, and direction.
    I used the word "star" a lot, but any celestial body (planets, the sun
    and the moon) will do. The principle remains the same, though the
    correction and reduction procedures do vary a bit.
    Adrian P. Vrouwenvelder
    Durham, NC.
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