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    Re: October Lunar
    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 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.
    "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).
    "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
    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.
    Navigation List archive: www.fer3.com/arc
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