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    Lunar vs. Occult software test
    From: Paul Hirose
    Date: 2023 May 12, 22:47 -0700

    I compared my Lunar software to the Occult program to test the effect of
    the lunar limb profile. Occult takes that into account. Lunar does not.
    I used occultations by the Moon in the near future:
    Gam Vir (Porrima), sig Sco (al Niyat), and del Sco (Dschubba) were
    excluded because they are double. (A close double is OK.) The choice of
    observer sites was random. Sometimes a site was selected because it was
    near the top of the list (Abu Dhabi) or because it was interesting
    (Easter Island). If I were doing this again, I would pick sites to get
    an approximately uniform occultation distribution on the Moon limb.
    The test method was to compute immersion and emersion times with Occult.
    For those times I calculated lunar distances with Lunar 4.4. In most
    cases the star was below the magnitude 3.0 cutoff in the Lunar catalog,
    so I got its data from the SIMBAD site.
    I assumed any failure to get zero lunar distance was entirely due to my
    software. The standard error (root of the mean squared error) was 1.07″
    for the 10 events (5 occultations, immersion and emersion for each).
    The Moon position from Lunar is the position of its center of gravity.
    However, that point is a little different from the mean limb center of
    figure. In the Astronomical Almanac eclipse predictions, corrections in
    ecliptic latitude and longitude are applied to adjust for the
    difference. See page A79:
    The main window of Lunar has a "solar eclipse corrections" check box to
    apply the corrections. In theory they should also improve occultation
    computations. In my test the standard error decreased a little, from
    1.07″ to 0.87″.
    However, a lunar distance observation with a sextant is much different
    from an occultation. The observer oscillates the body and makes its
    motion tangent to the limb. A low power telescope in the hand cannot
    resolve limb irregularities that are obvious in an occultation.
    In lunar distance calculations I believe a typical limb error from my
    Lunar program is about 0.5″. That's a mix of calculation, observation of
    the limb profile display in Occult, and guess. First, how large is the
    arc that affects the perception of the limb in a sextant observation? I
    guessed 8°, that is, 4° either side of the true tangent point. Such an
    arc is 2.2′ in great circle measure and departs 2.3″ from a straight line.
    I analyzed the limb display in Occult for each of the 10 occultations in
    my test. At each occultation, I obtained the height of the visible limb
    with respect to the mean (circular) limb at five points: at the contact
    point, and 2 and 4 degrees (position angle) either side of contact. I
    computed the sample standard deviation of the five values. That gave a
    value for limb irregularity in the vicinity of each immersion or
    emersion. The 10 values were averaged (root mean square). Result was
    0.50″ for the typical semidiameter variation in an 8° arc of the limb.
    It soon became obvious there was a great deal of luck in what limb
    details were sampled. Often I measured a limb height close beside a
    narrow peak or valley which would have made a large difference. But such
    small details would not be visible in a sextant.
    I have in mind a second test with more occultations and a more uniform
    distribution on the limb.
    Paul Hirose

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