A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
From: Frank Reed
Date: 2018 Apr 6, 19:10 -0700
Sean, you wrote:
"To be clear, I have never used this correction. I've always stuck to the method outlined on your "Easy Lunars" page (with great results). I only included it with the N.A. formulae because it was there."
Yes, sorry, I didn't mean to imply that you had made an error, rather that Luycks had made an error a generation ago, in 1997. It's not a big error either. The correct correction for the earth's oblateness (polar flattening/equatorial bulge) is quite small, and this incorrect correction is very small, too. Ed somehow misread the article by Luycks and thought it was a correction for the moon's own oblateness. Definitely not!
"Which leads me to wonder: If the N.A. oblateness correction affects the HP - and if the HP is used in the lunar clearing formula - then why is it not useful in that context ... even if oblateness affects the lunar distance in another way?"
Well, remember that the instructions in the N.A. are tailored for altitude observations, and those equations are excellent and accurate for altitudes. The problem is that the earth's oblateness also shifts the Moon's azimuth. Unlike refraction and parallax, this is not a purely vertical shift, and that's why we can't just fold it in along with the other altitude corrections when clearing a lunar. That's also why it was usually ignored historically --it was a rather large amount of extra effort for a trivial improvement in the complete process.
"In retrospect, I probably should not have included that particular formula in my response to Ed Popko. Especially considering the fact that I don't use it."
No, it's worth knowing those corrections for standard celestial altitude sights ...if you're trying for tenth of a minute of arc quality in the calculations.
And you wrote:
"But, I do remember you saying at some point that we are trying to squeeze as much accuracy as possible out of a lunar."
My philosophy on squeezing accuracy out of lunars is that you should always work to the maximum possible when creating computer and app solutions (but that's un-necessary with pencil-and-paper or historical approaches). No matter what your philosophy, you have to stop at some point and you need to be realistic about that limit. The largest correction ignored by my online clearing tool, for example, is the irregular figure of the Moon's disk. It's not "oblate" in any useful sense in the way the earth is oblate. It's just lumpy. If you look for online images of lunar limb profiles for total solar eclipses, you can get a sense of these undulations in the Moon's limb. They have a scale of a few seconds of arc. Since that correction is not included by anyone (that I am aware of), that's the limiting level for the whole process. What does that imply in terms of our determination of time by lunars? Well, there's a doubling rule in lunars: whatever inaccuracy or error you have in your angle in minutes and seconds yields just about twice as many minutes and seconds of time. That makes sense when you remember that the Moon moves across the celestial sphere by its own diameter, which is half a degree, in one hour of time, or in other words 30 minutes of arc in 60 minutes of time. So if we accept two seconds of arc error by ignoring the undulations of the lunar limb, then we are accepting roughly four seconds of arc error in the resulting Greenwich time. If we go for a crude approximate solution for lunars, maybe with an accuracy of 5 minutes of arc, then we should expect 10 minutes of time error in Greenwich time (which, as usual, implies 2.5° error in longitude).
"I would investigate it myself, but with my very limited math skills I wouldnt even know where to begin."
Take my word for it: it's no fun! :) This is one of those things where you can dig through the math three or four different ways, but when you're done you're not enlightened in that "aha" way that makes the effort worthwhile on good days. There's also nothing interestingly "teach-able" in it. It's just math.