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    Re: Lewis and Clark lunars: more 1803 Almanac data
    From: George Huxtable
    Date: 2004 Apr 17, 00:04 +0100

    Ken Muldrew made the perceptive comment-
    >On 16 Apr 2004 at 17:33, George Huxtable wrote:
    >>  Maybe they have misidentified some other star
    >> as Aldebaran. Rigel gives a much closer answer, but still not close
    >> enough. I have eliminated any of the four planets, which weren't near
    >> the right place at that time.
    >If we consider the two series with Aldebaran (A and C in your
    >original message) as one series, then a least-squares fit gives an
    >apparent motion of the moon of 0.239?/hr. The almanac data shows that
    >the moon had an apparent motion with respect to Aldebaran of
    >0.534?/hr during that interval. So it would seem that the star Lewis
    >and Clark were observing was about 36? off the moon's path. Rigel
    >would be pretty close, moreso than Capella. There don't seem to be
    >any other obvious candidates. Is there any mention of whether it was
    >partly overcast? It's pretty hard to misidentify either Aldebaran or
    Ken is right, or nearly so.
    What the almanac shows, however, is the changing of the TRUE lunar distance
    with time. But  as the Moon and star altitudes change with time, there's a
    changing effect on the APPARENT lunar distance, mainly because of the
    changing Moon parallax, but also because of refraction. The net effect is
    nearly always to slow the apparent motion of the Moon across the sky,
    compared with the true motion predicted in the almanac. This is
    "parallactic retardation", and can have a big effect on the Moon's apparent
    speed. It is taken into account, and compensated for, in the "clearing"
    process. So that, in itself, can explain part of the reduction in the
    apparent speed. But not all of it.
    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.
    Ken asks whether there was any mention of it being partly overcast. The
    answer is "no", although, at other times, when it was partly overcast for
    an observation, they usually appeared to say so. We have to presume, then,
    that it was a clear night.
    This was their first lunar, and the first time they needed to identify a
    star from its name. Perhaps they just weren't good at it. Rigel would be
    the likeliest alternative, but would still give a bad result, though better
    than Aldebaran. Capella would be far too close to the Moon.
    Perhaps, if enough brains can tease away at this interesting, but difficult
    problem, as Ken has done, we may come to a conclusion. Keep on trying, do.
    contact George Huxtable by email at george@huxtable.u-net.com, by phone at
    01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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