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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2022 Aug 22, 09:59 -0700
Frank, Thanks to you for your very interesting recent article.
While I had, started addressing it some of its underlying ideas in this post, shortly afterwards Lars you wrote : " I have to admit that I have difficulties grasping the concept of a moving observer in this case. " .
I wish to attempt clarifying this concept through an example (see attachment) with a GDOP better than our most recent "A Lichtenstein Lunar" .
(1) Classical Lunars rely on 3 different angles : 1 Lunar Distance Distance and 2 heights.
In the vicinity of the solution of this specific Lunar Solution - which is here at Position 1 and for UT = T1 - it is possible to draw the locus of all points running westwards and for which Moon and Aldebaran heights remain constant. That's a line running almost due West, very slightly to the South because of the Moon changing Declination.
This "runnng line" is running at a speed close to 14.5° / h in Longitude, i.e. roughly the Sun speed in Longitude (15°h) minus the Moon angular speed among the Stars.
All blue sketches and indications pertain to the computations made around and about this running westward line.
If we are computing Lunars through the classical method, we are to consider this line, or at least keep it in mind as an "environment safeguard" because our Lunar solution lies somewhere on it:
- At position P0 for UT = 05:25:00.0, the constrained heights fullfil the observation but the LD is a bit too short.
- At position P2 for UT = 05:35:00.0 the unchanged constraint heights still fulfill the observation data, but the LD is a bit too big.
- At position P1, for UT = 05:30:00.0 we "solve" our LD.
In other words, whenever you are solving a Lunar through the classical method, you are to somewhat to consider a "running observer" moving on Earth at about 14.5° in Longitude. Most often, you do not tackle the Lunar this way, but you should remember that you implicitly should keep considering such a somewhat running observer.
For such a running observer, the actual LD rate of change as seen in the sextant (here 12.33 s / 0.1') is extremely close from the geocentric one (12.38 s / 0.1').
On the other hand we verify again that the topocentric rate for a fixed observer (here at 16.45s / 0.1') is less "favorable" than for a "running observer".
Hope it helps,
Antoine M. "Kermit" Couëtte
