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Subject: Re: Still on LOP's
WSMurdoch@XXX.XXX
Date: Mon May 06 2002 - 16:56:07 EDT
In a message dated 5/4/02 6:24:07 PM Eastern Daylight Time,
george@XXX.XXX writes:
> Bill Noyce made a perceptive contribution a few days ago, about systematic
> errors in celestial observations that can increase the probability of the
> true position lying within the cocked hat. This happens because those
> errors expand the cocked hats to surround the true position.
>
I am not sure that is correct. A three body fix using celestial navigation
puts three small circles on the surface of the earth. If all were perfect,
the three would intercept at one point. Because all is not perfect they
intercept making a triangle. Draw three circles intercepting to form a
triangle in the middle. If you are like me, you drew three circles of about
the same size intercepting in a total of six places with a small triangle in
the middle with all three sides bulging outward. You pointed at the small
triangle in the middle, the one with three convex sides, and said, "I am
here." That is true if all three LOPs are away from their bodies.
Surrounding that triangle are three more triangles with two convex sides and
one convex side. You would be in one of them if two of the LOPs were away
and the third was toward. To see the other two cases, you have to redraw the
circles moving the centers around to leave triangles with either three
concave sides or two concave sides and one convex side.
If the usual systematic error is to tilt the sextant and record an
erroneously large reading, the circles will be too large. In some cases that
will make the triangle larger. In other cases it will make the triangle
smaller.
Bill Murdoch
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