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Re: Still on LOP's
From: Bill Murdoch
Date: 2002 May 21, 21:23 EDT
From: Bill Murdoch
Date: 2002 May 21, 21:23 EDT
In a message dated 5/20/02 1:16:27 PM Eastern Daylight Time, george@HUXTABLE.U-NET.COM writes:
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
>> 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
