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    Re: Lewis and Clark lunars: more 1803 Almanac data
    From: Ken Muldrew
    Date: 2004 Apr 16, 23:10 -0600

    > >On 16 Apr 2004 at 17:33, George Huxtable wrote:
    > Another part of the cause of the slowing of speed between Moon and
    > star can be caused by a sort of misalignment, due to the star not
    > being directly in line with the path of the Moon across the sky.
    > That's the effect that Ken was considering. It should have been taken
    > into account in the Moon-star true-distance predictions in the
    > Almanac. But if the star turned out to be a different star from the
    > one the predictions were for, and further away from the Moon's path,
    > then we would not only expect the lunar-distance predictions to be
    > wrong, but also to be changing more slowly too. That, I think, is what
    > Ken was getting at. I can't quite see, yet, how he arrives at that
    > misalignment of about 36deg from the numbers he quotes: perhaps he
    > will explain further.
    That is exactly right. In the few lunars that I've done (I'm a complete
    beginner at this), the moon's apparent motion with respect to the ecliptic
    stars/planets has always been around 27"/min. I know that this can
    change due to refraction and parallax, even for a star or planet that's
    right on the moon's path, but I don't know what the limits of this change
    are. I assumed that the apparent motion would remain pretty close to the
    true motion. So for a first order approximation (perhaps zeroeth order
    would be more appropriate, despite my numbers with 3 figures!), the
    departure of the apparent motion from the true motion along the ecliptic
    (since Aldebaran is pretty close to the ecliptic) could tell us how far off
    the ecliptic the star being used really was. When you do plot both sets of
    readings and fit a line through them, it does appear that confidence can
    be put in the slope of this line. With the measured motion of the moon
    with respect to the mystery star, and the almanac motion of the moon
    with respect to aldebaran (almost as far away, but along the moon's
    path) we can construct a simple, Euclidean triangle (this is the zeroeth
    order part) and get the angle of divergence. That's where I got my "about
    36?" angle off the moon's path. I think if the problem is treated properly
    (taking refraction, parallax, and spherical geometry), we may get a much
    better estimate of the actual angle. But then again, I may be well wide of
    the mark. Nevertheless, I'll take a stab at this tomorrow. Hopefully the
    experts here will also give it a try if there's any sense in doing so.
    Ken Muldrew.

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