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    Re: 1491 The year China discovered longitude
    From: George Huxtable
    Date: 2004 May 9, 13:13 +0100

    I seldom find anything to disagree with in Trevor's postings, but on this
    topic of timing lunar eclipses for longitude, I do.
    In his first posting, he responded to Kieran's quote from Menzies as follows-
    >> "When the astronomer returned from his voyage, he and his colleagues in
    >> Beijing compared their data. Using their time keeping device, calibrated
    >> from the gnomon, they timed the interval between the transits of the star
    >> observed in the new territory at the time of the eclipse and the star seen
    >> by the astronomers in Beijing at the same moment.
    >That seems a rather unnecessary step. All they needed was a star
    >catalogue, with angular measures equivalent to SHA or Right Ascension --
    >the sort of thing that the astronomers back home should have been
    >working on anyway.
    I think Trevor is wrong here. The longitude difference can be deduced from
    the difference in time (measured by star positions) of a common observed
    event (Moon eclipse). Without accurate predictions of the Moon's position,
    it was, presumably, impossible to predict the exact moment of the lunar
    eclipse. All that could be done was to go back to Beijing, after the event,
    and find out at what time (measured by those same stars) it had occurred
    there (hoping it had been a clear night). It wasn't the star-timings that
    were unpredictable, it was the Moon event.
    >George wrote:
    >> There is no way to time a lunar eclipse with "absolute precision", as
    >> anyone who has watched one will know. The whole event is fuzzy and
    >> indefinite. [snip] the moment of the Moon entering completely into full
    >> shadow is indeterminate
    >I have watched a number of lunar eclipses and what still surprises me is
    >that the umbra has a rather sharp edge -- not sufficient to satisfy
    >those who like to fuss over the precise moment that one of the moons of
    >Jupiter passes into the shadow of its parent but very much sharper than
    >if the penumbra shaded steadily into the umbra. Why this should be so, I
    >have never figured out. But it is.
    Well, yes and no. Seen from a man-in-the-Moon, the Sun is the same size
    (half-a degree) as it is to us, but the Earth that is gradually covering it
    is four times the sixe (2 degrees).
    The extent of the penumbra subtends about half-a-degree, just the width of
    the Moon itself. When the Moon is half-way in to being fully eclipsed, a
    Moon-man at its Western limb will still be in full sunlight, whereas
    another at the East is already in complete darkness.
    To a Moon-man, it's rather similar to a straight-edged blind being slowly
    drawn across the Sun's disc. And it's quite true, the last bit of that
    area-of-light does cut off rather suddenly. So I agree with Trevor that the
    edge of the umbra is a bit sharper than one might naively expect. Looking
    at a Moon eclipse; I have noticed that, just as he has.
    And yet, that edge is not the stuff of which "absolute precision" can be
    obtained (which was the phrase that Menzies used, that I was questioning),
    and I still doubt that either Trevor or I could do much better in timing
    the first or last moments of full-eclipse, than the "5 or 10 minutes" that
    I suggested.
    What's important, presumably, is that the field-observer makes his timings
    using the same test of brightness at the edge of the Moon as did the
    astronomers in Beijing. Only by comparing symmetrical events before and
    after eclipse, such as U2 and U3, and splitting the time difference to
    determine mid-eclipse, could they arrive at a result that was independent
    of their brightness-test (provided that they did the same in Beijing).
    Trevor continued-
    >George thereafter noted:
    >> Menzies tells us that the key event that had to be timed (with a star), was
    >> what he calls U3, at the first signs of emergence from full umbra. This
    >> seems surprising, as U2, the entry into full umbra, would have been equally
    >> useful, and the combination of the two more useful still.
    >I would suggest that the observer has no warning that U2 is coming until
    >it has arrived. It would be some little while, even a few minutes, after
    >U2 before anyone would know that it had been passed. U3, in contrast,
    >can be anticipated as the patch of umbra visible on the Moon's disc
    >becomes smaller and smaller.
    I really can't understand what Trevor is saying here. Menzies defined U2
    and U3 as follows-
    >U2 - second
    >contact, when the moon has just fully entered the umbra and is totally
    >covered; U3 - third contact, when the moon first starts to emerge;
    So U2 happens at the end of a period when the observer has watched the
    umbra spreading across the Moon until the final moment when the Moon's disc
    becomes completely dark. How can Trevor possibly claim that the observer
    "has no warning"?
    It's U3 of which the observer "has no warning". From the Moon being
    completely dark, the first sliver of light is seen, at one edge.
    Either Trevor's picture of this is wrong, or mine is. Which?
    contact George Huxtable by email at george---.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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