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Hello and Seasons Greetings!

In the recent topic of "no plotting sheet required" Mike Freeman has asked me to explain the correction for the movement of an observer. A seemingly simple question but can be a mind-twisting thing if thought about from wrong perspective.

I can explain why it is valid to advance (or retire) a LoP (a Line of Position) by drawing another line parallel to the LoP, separated by the gap equal to the product of the distance covered between the sights (let's call it the Sailing) and the cosine of the angle between the TC and Azimuth (i.e., the cosine of the relative bearing).

It is valid to do so because the initial LoP represents all the points where I could have been at the instant of the first sight, and from any of those points some portion of the Sailing I have travelled will be perpendicular to the initial LoP, which (the portion) is exactly the Sailing times the cosine of the relative bearing. Thus the advanced LoP and the initial LoP have a gap between them of the certain width. If I was Sailing along the Azimuth (either towards or away from the body observed), then 100% of the Sailing will go in the gap, if I was Sailing across the Azimuth - the gap will be nill.

I hope this is the correct interpretation of the "LoP advance|retire" procedure.

Now to the mind-twisting perspective. :)

I have unsurpassable problem explaining the procedure in terms of altitude change pretending I was stationary but the celestial sphere moved during the time between the sights. It did indeed move! Whether I am moving or not - the sky always rotates. It is only the relative speed (and direction) that matters. How can I bring the two non-simultaneously-observed altitudes to the common instant in time? Especially if altitudes were taken from different places! I must not think that the advanced LoP represents the altitude of the first body seen as if taken simultaneously with the second altitude. The sky has rotated somewhat. Clearly this is the wrong approach...

Please comment and let me out of this puzzle! :)

Warm regards,
Tony
60°N 30°E