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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: October Lunar
From: Frank Reed
Date: 2008 Oct 06, 20:23 -0400
From: Frank Reed
Date: 2008 Oct 06, 20:23 -0400
George wrote: "If all points on a sextant calibration are out by 1', that's not so much an error in the overall scale as an index error of some sort." That's true, but it's probably too early to conclude that yet. If all angles up and down the arc are out by 1' then, yes, it's a simple error in IC. And it's worth repeating here that everything depends on the IC. It's worth spending extra time determining the index error, and it's worth trying other non-standard methods for measuring it. And: "And this takes us into rather deeper waters. The discrepancy that Jeremy reports, though consistent, is only a small angle, of 1'." Through a sight tube or a low-power scope, that would be a fair statement, but with a 7x scope, which Jeremy has, an angular difference of a minute of arc is plainly visible. And: "To measure a planet against the Moon's limb calls for a bit of judgment, because the image of the star is not a precise point, and the image of the limb is not an infinitely-sharp boundary." Yes, and because the plains and mountain ranges on the Moon vary the outline (at average sextant scope resolutions) by anywhere from one to two seconds of arc, that is the absolute limit on any historical lunars (a modern computation could include limb effects). And: "The eye does its best with them, but it's beset with the problem of "irradiation" " This is irrelevant to this Moon-Venus lunar. Except under extreme circumstances, irradiation is a minor issue. And George concluded: "Whenever we near the limits of what we can perceive, some such degree of personal judgment comes in. It sets a limit to the inherent accuracy available in an observation, and being systematic rather than random, repetition and averaging aren't going to help." That's a good point in general terms. It's fine rhetoric. But it does not apply here. The "limits" of what we can perceive are well-known. The resolution of the human visual system is about one minute of arc for standard optical resolution tests at unit magnification (with corrective lenses or adjusted focus as necessary --in other words, when wearing eyeglasses or contacts-- and assuming no exotic uncorrected eye defects). The famous phrase "20-20 vision" by definition means one minute of arc resolution. NOW, when you look through a 7x scope on a sextant, the limit in the visual field remains the same, but the limit of angles measured on the celestial sphere improves by that same factor of seven. That's what optical magnification means. In other words, the "limits of what we perceive," to use your phrasing, are approximately 0.14 minutes of arc. An angle of ONE minute of arc, when seen through a 7x scope, is well-above the limits of what we perceive. And let's not limit ourselves to theoretical discussion. If you have a 7x sextant scope, you can test this. You don't even need to go outside. For a simple indoor test, load up your favorite graphics software on your computer and place a few white dots on a black background. Make a couple of them just a few pixels apart and measure the distance between them (in inches, e.g.). Now walk away from the monitor... How far away can you get before the dots seem to merge? Divide the distance between the dots by the distance to your observing point and then multiply by 3438 to get your angular resolution in minutes of arc. If you want to make the observation more comparable to a lunar observation, you could animate a white dot passing a bright round edge (simulating the lunar limb) at some short distance. After you've found the limiting distance without optical aid (except eyeglasses or contacts, as necessary), try it with your sextant scope. A nice way to make this experiment more realistic would be to allow some random distance between the observed bodies. Then the observer has fewer opportunities to bias the results. It has been my experience that observers with well-adjusted sextants equipped with 7x scopes, with reasonably good conditions (on land, no clouds, no haze) can observe lunar distances with an accuracy of about 0.25 minutes of arc (standard deviation) on each individual sight, and when four are averaged, the results are generally twice as good (0.13' s.d.). These are typical results for Sun and planet lunars. My results with stars have been worse and seemingly directly dependent on the magnitude of the star. Your mileage may vary. -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---