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Subject: Re: Still on LOP's
WSMurdoch@XXX.XXX
Date: Tue May 21 2002 - 21:23:22 EDT
In a message dated 5/20/02 1:16:27 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.
> >>
>
This is the only part of the discussion that I have not worked my way
through. Let me explain my problem with it again in a different sort of way.
Let's say I take three sights equally spaced around the horizon. The three
sights put three circular LOPs on the earth's surface. If there are no
errors, they intersect in one spot which is my true position. If there are
errors, the LOPs intersect forming a triangle. The sides of the triangle are
either toward the sighted body or away. I could have several combinations of
sides; TTT (one kind), TTA (three kinds), TAA (three kinds), AAA (one kind).
The Ts happen because the circular LOP was too small in diameter, because the
zenith distance of the body was measured too small, because the altitude was
measured erroneously large. The As happen for the opposite reason. If my
systematic error is to measure angles erroneously large because I tilt my
sextant, my TTT triangles will be systematically erroneously large and my AAA
triangles systematically erroneously small. It seems to me that my
systematic error has one effect on one type of cocked hat and the opposite
effect on another. Systematic errors expand some cocked hats and contract
others.
Bill Murdoch
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