A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2010 Nov 10, 23:02 -0800
Antoine, you wrote:
"Certainly this very special planetary configuration should prevent from treating it as a "conventional lunar" and I am sure that you have already addressed this a few times earlier Frank, but I am certainly surprised to see that in this very special case - which might be so easily overlooked and treated as a casual case - your longitude error ratio is so far off from reality, by a factor of 30."
Sorry you haven't seen the explanation before, Antoine. The "approx longitude error" given in that online tool is nothing more than the error in the observed lunar multiplied by a factor of 30. It's a pedagogical value --designed to answer the simple question "how am I doing?" that so many navigation students and enthusiasts want answered as quickly as possible after they shoot a sight (that "instant gratification" that Hewitt was talking about). They shoot a lunar, without necessarily picking the correct geometry for a longitude (GMT) analysis, and they want to know how far off they were. Naturally, being able to say "three tenths of a minute of arc" is helpful but then they frequently ask, "ok, so what would that mean if I was using this to get a longitude?" Now, it has been MY experience, having ACTUALLY TAUGHT lunars to many people, that these folks are really interested in knowing how this observational error would have impacted their estimation of longitude in a TYPICAL case, not in the specific case of the lunar that they are shooting in the instance, which was probably chosen for no other reason than the convenience of the moment. And in the typical case, the error in longitude is approximately equal to the error in the observed lunar distance multiplied by 30.
Now, when someone posts data on a lunar like this one, where the other body is nearly in line with the horns of the Moon, I usually point out at some point down the road that this observation could not have been used historically for getting GMT (since the Moon's motion is nearly perpendicular to the arc to the other body) but that doesn't mean that it's not useful in some other way. As for providing "no clue" that they've taken a lunar that can't be used for GMT, that's a good point, and I've considered adding a little warning that says something like "other body too far from the axis of the Moon's motion for determining longitude accurately" but anyone with even a trivial understanding of taking lunars for longitude would know this anyway, and furthermore, they would SEE that the conditions are wrong simply by looking at the Moon in the sky that the sight couldn't be used for longitude.
For reference, here's the observational rule to use: look at the Moon in the sky and draw a line through its horns (or nearly the same thing, through its north and south poles, which anyone familiar with the Moon's face should be able to do just based on the bright and dark features, maria, etc.). Now draw an arc across the sky, in your imagination, perpendicular to that line through the horns. This arc represents the path of the Moon's motion relative to the background of the stars. Next draw an arc to the selected "other body" whether a star or planet (it's never an issue for the Sun). The angle between those two arcs should be smaller than 45 degrees IF the sight is intended to be used to determine GMT and from that find longitude --the smaller the better. If the angle is small, then the other body is "lined up" with the Moon's motion through the heavens and the rate of change of the lunar distance will be very close to the average value which is about a tenth of a minute of arc for every twelve seconds of time. That is, if we cane resolve the lunar arc to the nearest tenth of a minute of arc, then we can resolve GMT to the nearest twelve seconds. If the angle is as much as 20 degrees out of line, the resolution of GMT is reduced to thirteen seconds of time (hardly any difference, so clearly we don't need to be obsessive about this). When the angle is as high as 45 degrees, the error in GMT has risen to 17 seconds for a tenth of a minute error in the observed distance, still not a big reduction in quality but it's a very reasonable cut-off point and it appears to be near the cut-off point that was used historically in the almanacs were predicted lunar distance tables were published. If we go to higher angles, the ability to determine GMT accurately, and hence determine longitude accurately, drops off rapidly.
Also, please note that if you read Greg's message in context, nothing about this "camera trial" was designed to determine longitude in any way. He simply wanted to know how good he could estimate this "lunar distance" angle using photography. And since he used a fairly basic, ad hoc system for calibrating his camera for angles, the results were not great. The "longitude" numbers were completely irrelevant to his purpose here, so I didn't go into it further.
PS: You wrote: "TT-UT=67seconds of time". As noted many times, this information has nothing to do with the analysis of a lunar. There's no reason to post these values. You might as well post the obliquity of the ecliptic! That's also something that enters these calculations that has nothing specifically to do with the analysis of a lunar.
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