A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2017 Sep 5, 11:29 -0700
Francis, the author of that article, in the section you quoted, was talking about a motionless observer, which is a trivial case, and it is most unfortunate that the author chose to be-labor such a trivial case since it would surely lead to confusion. You say that you "always got the correct answer" and "it seems to work for me". But face it, Francis, that is the problem with many of your testimonials about your experiments in celestial navigation: you like them all. You never met or a tool or a method that you didn't fall in love with! Don't get me wrong: these equations do exactly what they do, and they are not "without interest". But they are no panacea, and you will get a dangerously incorrect position from them if the observer is on a moving platform (e.g. a boat) and any significant time has elapsed.
From the article, in the next couple of paragraphs after the one you quoted, the author, Gery, has some comments on dealing with the motion of the observer. Unfortunately his analysis is muddled by his infatuation with the idea of advancing a circle of position along a loxodromic curve, which obsessed and confounded many navigational calculators (of the human sort) for a couple of decades starting in the 1990s.
So why don't we regularly use equations for a "direct fix" like the ones in Karl's book or the equations in Gery's article from 1996? The problem with correcting for the motion of the observer is significant. Equally important is the fact that this solves a two-body problem and only a two-body problem. But beyond these technical concerns, there's the basic issue of need. We really don't need this methodology for anything practical. Equations like these solve a fantasy problem. It's a type of problem that confounds armchair hyper-nerds (and yes, if you spend a lot of time playing with a slide rule or programming a programmable calculator, then you are one giant leap beyond nerd... you are hyper-nerd! [insert slightly off-key trumpet blast here]). "What do I do if I have no idea where I am?!", asks the armchair hyper-nerd. A real navigator would never face this scenario. In real-world navigation, there is never a case where we need this sort of solution. There are no reality tv shows where contestants are dropped on deserted islands in the middle of an unknown ocean with only sextant, almanac, chronometer, and programmable calculator for their tools (well, to be fair... there are no such shows yet!). And real practical navigators are never lost (except in a case where they have been kidnapped, like the doomed passengers on Malaysian Airlines Flight 370, and kidnapping victims would not have the luxury of the tools of celestial navigation in any conceivable case). Even student navigators, beginners trying to understand the concept of circles of position, can do quite well just by plotting the circles on a ball marked up as a globe as suggested by several people in a recent thread. Using a calculator would offer no benefit and would deny them the value of seeing the actual circles of position on the globe. These equations are not "without interest" but that's about the best you can say.