A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Lars Bergman
Date: 2018 Nov 9, 04:48 -0800
I do not pretend to be "more knowledgeable" than anyone else (which I obviously revealed in my reply to Frank), but regarding your question about the effect of small differences in the slope, I think they matter quite a lot. Suppose your observations actually has a slope of say 42" per minute of time, and the geocentric slope is 33"/min (from your graph, at 17 hrs). The difference is only 9", but during a say ten minute observation period this builds up to 1.5', which is clearly seen if you draw the slopes on a paper. This may lead to an erroneous choise of "best fit point", if using the geocentric slope.
"Sliding the line with the right slope up and down (only one free parameter)", as advocated by Frank, is, in my opinion, not a good method at all. The reason is that whatever pre-determined slope you use, that line will always pass through the point of the observation's mean time and mean distance, when the "least sum square" occurs. This is a mathematical fact. So, if you want to utilize the information in all your observations, just use the mean of times and the mean of distances.
Why, then, was I interested in finding a simple method to determine the expected slope of the apparent distances? Well, that slope may, perhaps, facilitate identification of outliers in some cases. But I am not sure about that!