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    Re: Testing sextant arc error
    From: Paul Hirose
    Date: 2017 Jan 19, 14:28 -0800

    On 2017-01-17 10:58, Brad Morris wrote:
    > Further, you really cannot limit yourself to the 57 navigational stars.
    > That will not provide sufficient coverage of angles, unless you were to hop
    > about the globe.  What does provide a sufficient number of stars is to use
    > the Astronomical Almanac's "Bright Stars" list.
    That table is complete to magnitude 5.5 (I think) and its precision is
    one arcsecond. Furthermore, it's online so you don't have to buy the
    rather expensive book.
    But there are complications. According to the Astronomical Almanac, "the
    positional data in Section H are mean places, i.e., barycentric ...
    referred to the mean equator and equinox of J2016.5 [this passage is
    from the 2016 Almanac]." Thus you have to apply annual aberration and
    refraction to obtain the apparent separation angles.
    Star coordinates in the Nautical Almanac include aberration, so only
    refraction need be applied. But the precision of the coordinates is not
    quite what I'd like for sextant testing. Unrefracted separation angle
    must be calculated from four almanac values: two SHAs and two
    declinations. Each is rounded to the nearest tenth minute, and so you
    have a "calibration standard" which isn't comfortably superior to the
    device under test.
    Regarding published tables of separation angles, over the years I've
    seen several criticisms of their accuracy. It is claimed that
    differential aberration will cause the distances to vary significantly
    during the year. I may even have said that myself. But I've never seen
    it demonstrated in an example. An ounce of data is worth a pound of
    theory. For someone who owns a book with such a table (I don't), there's
    an opportunity to confirm or rebut the critics.
    Windows users are welcome to try my free program, Lunar4. It was
    specifically designed for separation angle calculations with the Sun,
    Moon, planets, and stars. (Contrary what the URL implies, the current
    release is at the site.)
    One of its helpful outputs is the position angle of each body with
    respect to the other. For example, if the position angle from the Moon
    to a star is 0°, the star is directly above the Moon and the sextant is
    upright to make the observation. If PA = 270°, the star is at the 3
    o'clock direction from the Moon, so you lay the sextant on its side.
    With the sextant preset to the expected separation angle and oriented to
    the PA, it's much easier to get both bodies in the scope. Also, you can
    plan observations to avoid awkward sextant positions.
    Tests have confirmed Lunar4's unrefracted topocentric coordinates are as
    accurate as the USNO MICA and JPL HORIZONS programs. The practical
    accuracy is really limited by the refraction computation. I use the
    Cassini model. This choice is explained near the bottom of the page at
    my site.
    For observers well above sea level, the air pressure correction is
    significant. Even at 2000 feet refraction is .1′ less than standard at
    30°. At 3000 feet the difference is .2′. Many cities in the western US
    are even higher. The Salt Lake City area is 4000 feet above sea level,
    Albuquerque is at 5500 feet, and of course there's Denver.
    The refraction correction for air pressure needs the actual pressure
    ("station pressure") at the observer. However, the only readily
    available pressure data (in the US, at least) are aviation altimeter
    settings. These are almost always called "barometric pressure" (except
    in aviation) but there's a difference. Lunar4 expects height above sea
    level and altimeter setting, and recovers the corresponding station
    That value is displayed, as are azimuth and unrefracted altitude of both
    bodies. So, if you prefer to apply your own refraction model, the
    necessary data are at hand. Of course in that case you have to do the
    separation angle calculation yourself.
    (Along with altimeter setting, the honest to God barometric pressure
    adjusted to sea level is part of the hourly weather observation at
    airports. However, the definition of the latter makes it inconvenient to
    reverse the computation and derive station pressure. It's much easier to
    use altimeter setting.)
    The default Lunar4 angle display format is DM.m at .01 minute precision,
    but the user can modify the precision or change the format to D.d or DMS.s.
    One negative aspect of Lunar4 is that it's useless without a JPL
    ephemeris for the time period of interest, and I don't supply one. It's
    my stubborn belief that you should know how to create your own
    ephemerides. The necessary ASCII files are online at JPL. After they're
    downloaded to your machine, Lunar4 can convert them to the binary format
    it needs to compute positions.
    Apparently the instructions at my site are not adequate, however.
    Recently I had to walk a new user through the steps. The process is much
    easier after you do it once.
    A positive aspect of Lunar4 is the minimal impact to your system. My
    stuff does not mess with your stuff any more than absolutely necessary.
    It always makes me a little uneasy to grant system administrator
    privileges to a software installer, so Lunar4 has no installer. Simply
    request to extract all files from the .zip. The folder that contains the
    .zip will get a new sub-folder which contains the Lunar4 installation.
    That's all! You don't even get a desktop shortcut to the .exe. If you
    want one, do it yourself.
    Based on my limited experience, lunar distances are easier to shoot that
    star to star distances. For the latter, I thought it difficult to see
    when the stars were in static coincidence. I got better results by
    holding the star in direct vision stationary and swinging the reflected
    star through it, in the manner of rocking the sextant during an altitude
    Optimum lunar geometry for sextant error testing is the opposite of what
    you want for a time determination: the lunar distance should be changing
    as slowly as possible. Lunar4 displays this rate as angle per minute and
    also as a percentage of the Moon's angular velocity. E.g., 100% means
    the center of the Moon is moving exactly toward or away from the body.

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