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I'll take a shot at answering some of Bill's questions...

The "magic number" 0.2724 isn't an angle, it's simply the ratio
   moon_radius / earth_radius
SD is the angular distance of the moon's radius as seen from the
earth, and similarly HP=SD/0.2724 is the angular distance of the
earth's radius as seen from the moon, which is another way of
describing the parallax of the moon at the horizon.  When we're on the
line from the center of the earth to the moon, parallax is zero (and
Ho=90 degrees).  For intermediate cases, cos(Ho) represents how far
from that centerline we are, and thus how much of the HP to include.

Augmentation reaches a maximum of about 0.3' and is caused simply by
being closer to the moon when it's overhead because the earth is a
sphere.  The ideal formula would involve tangents, and the ratio of
the earth's radius to the moon's orbital distance, but this ratio is
so small we can approximate tan(x)=x (when x is in radians).  sin(Ho)
represents how much closer to the moon we are than the center of the
earth is; it's zero when the moon is on the horizon, and 1 when it's
overhead.  So the formula ends up something like
  aug = tiny_number*sin(Ho)*SD, where tiny_number is something like 0.005
For most practical purposes, you can cut a lot of corners, and simply say
  Ho(degrees)   augmentation
     <10 . . . . . . 0.0'
    10-30  . . . . . 0.1'
    30-56  . . . . . 0.2'
    56-90  . . . . . 0.3'
This neglects the fact that augmentation will be slightly more when SD
is greater, or less when SD is less.  I believe that this kind of
"constant augmentation" is built into the "moon correction" tables in
the NA.

I'm pretty sure the NA doesn't try to account for the effect of
oblateness.  It would affect parallax a tiny bit, and augmentation an
entirely negligible amount, I believe.

    -- Bill N.

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