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    Lunar eclipse report
    From: Alexandre Eremenko
    Date: 2004 Oct 28, 00:38 -0500

    Contrary to my expectation, the weather
    in West Lafayette IN, USA was good: the clouds cleared just
    before the eclipse.
    I wanted to try "Hipparchus/Ptolemy/Columbus style"
    observation for the longitude and here are the results.
    The times are GMT reduced from my wristwatch (just added 5 hours):
    Beginning:        1:13:30
    Full phase begun: 2:22:25
    Full phase end:   missed
    End of eclipse:   4:52:45
    Because I knew the time in advance (from the almanach
    up to 1 min) I invited my (Russian-speaking)
    friends who did not know the
    time of the eclipse, and asked for their best
    estimate of the beginning
    of the eclipse, and the beginning of the full phase.
    The first two lines is from these friends judgement
    (naked eye). Then we had a drink with those friends,
    and the result was missing the end of the full phase:-(
    After that the friends left, and I tried to time the end
    using my 8x40 binoculars. I also asked another friend of mine,
    who was not with us this evening, to time with her wristwatch
    as precisely as she coold, while walking her dog in the evening.
    It is too late now but I expect her report tomorrow.
    Now let me try to reduce these sights:-)
    I know GMT from the almanac (up to 1 min, maybe the lunars
    experts can tell me more precise times?)
    According to the almanac the times were:
    begin:             1:14,
    begin ful phase:   2:23,
    end full phase:    3:45,
    end:               4:54.
    The average error was 1 min 5 sec, which gives approx 16'
    of longitude.
    One problem is of course, to what precision could
    Hipparchus-Ptolemy-Columbus measure their local time
    (with an astrolabe, I suppose).
    Another problem was the precision of their almanacs.
    (Columbus used "Regiomontan(us) tables". What Ptolemy used,
    I don't know, not speaking of Hipparchus).
    Anyway, it seems that timing of the eclipse itself
    was not the main problem limiting precision.
    On Wed, 27 Oct 2004, Herbert Prinz wrote:
    > Alexandre Eremenko wrote:
    > > Hypparchus own astronomical observations, referred by
    > > Ptolemy permit to establish the time when Hipparchus lived,
    > > by applying the Lunar theory of Hipparchus backwards in time:-)
    > >
    > > (So he built a good memorial for himself, did not he?:-)
    > Can you tell us more about this? The observations are given as
    > straightforward dates in terms of Kallippic Cycles, converted to
    > Egyptian years. This is pure arithmetic based on the Metonic cycle (1
    > Kallippic cycle =  4 Metonic cycles - 1 day).  Why was any lunar theory
    > (whether that of Hipparchus or anybody else) required to interpret the
    > dates?
    > > 90% of our knowledge about Moon motion was known to Hypparchus.
    > > (part of it is apparently due to "Chaldeans" of whom we know
    > > nothing).
    > We know nothing about the Chaldeans ???
    > > Most of this theory was derived by Hypparchus by careful
    > > reduction of the eclipse observations of Chaldeans and of
    > > hismelf.
    > >
    > > The method of finding longitude by the eclipses of the Moon
    > > (and Sun) remained the ONLY method of finding longitude for
    > > almost 20 centuries!
    > To be sure, it remained the only ASTRONOMICAL method, but in practical
    > terms, people collected their knowledge of longitudinal distances
    > through travelling.
    > > This was the only method Columbus could use.
    > But in fact, he used dead reckoning. He tried to confirm it twice with
    > an eclipse.
    > > (Though he was not very successfull with this,
    > Indeed.  He used one lunar eclipse mainly to frighten the poor Red
    > Indians.
    > > due to the general collapse of knowledge and educcation,
    > > which came soon after
    > > Ptolemy and lasted for about 1500 years).
    > Let us not sweep eight centuries of Arab science under the rug ....
    > > This was also the only practiceable method on land,
    > > to make geographic maps. (The direct measurements of distances
    > > on land was VERY imprecise).
    > Lunar eclipses never played any role in map making before Mayer. The
    > method was too crude.
    > For all we know, Ptolemy had ONE useful record of a simultaneous eclipse
    > observation, which he worked into his "Geography" (Carthage-Arbela, 331
    > BC). His main source were travel reports (itineraria), mostly indirectly
    > through the work of Marinos. It is illuminating what Berggreen and
    > Jones, Ptolemy's Geography, 2000, have to say on the subject of the use
    > of eclipses (esp. pp 29-30). Ptolemy assumes 3 hours difference between
    > the respective observations, the actual time was about 2 1/4 hours.
    > Apparently the resulting longitudinal difference of 45 deg between
    > Carthage and Arbella (correct: 34 deg) fits in with his other data,
    > because his value for one degree expressed in stades is too small by
    > 18%. (A mis-estimate from which Columbus and/or his sponsors were later
    > to suffer.)
    > The first systematic effort to apply astronomical methods to the
    > longitude problem in map making was by Cassini, who observed eclipses of
    > Jupiter satellites. Later, he was followed by Mayer, whose interest in
    > the moon was rooted in cartography. He improved on the technique of
    > observing star occultations by measuring the small distances between
    > star and limb shortly before immersion and after emersion with a
    > micrometer (averaging!). He also realized that lunar eclipses would only
    > be useful if the features of the Moon were accurately mapped. Given such
    > a map, two observers could time the moment when the earth's shadow
    > passes over a certain feature. Hence Mayer's engagement in selenography.
    > This lead to the next problem that he needed to study: Libration.
    > I am not sure that even after these efforts eclipse observations ever
    > played the role in cartography that Mayer envisaged. If our Mayer expert
    > is listening, would he care to comment on this?
    > > Hipparchus theory of the Moon motion was not superceeded
    > > until Tycho Brahe (XVI cent AD), who added a correction term
    > > of 40' amplitude.
    > Hipparchus' theory of the moon was very simple. It lasted for 300 years,
    > until Ptolemy arrived on the stage. Hipparchus himself realized that his
    > theory worked in the syzygies and not in quadratur with the sun. There
    > was a second anomaly that could amount up to 2? 39'. Ptolemy took care
    > of this by introducing the concept of evection into the model. It was
    > thus Ptolemy's lunar theory that lasted - but only as far as longitude
    > is concerned - without a major modification until Brahe added the term
    > for variation.
    > > Neither Copernicus, nor Kepler added much to the Lunar theory
    > > in the sense of prediction of the Moon motion.
    > That depends on what you consider "much". Most people will be totally
    > puzzled when you tell them that Copernicus' biggest success was in lunar
    > theory. While his rearrangement of the orbits of the planets - as
    > "pleasing to the mind" as it may have been - did not do much for the
    > predictive capability of the model, his revamping of the lunar model
    > removed a headache that had long been troubling astronomers: Ptolemy's
    > model did not adequately account for the distance of the moon. That is,
    > it gave absurdly wrong results for semidiameter and parallax. The model
    > of Copernicus, employing Arab technology, did much better in this
    > respect.
    > Kepler hit on the "annual equation" around the same time as Brahe. This
    > is not much, as you say, but in fact it is the next largest term after
    > variation.
    > Herbert Prinz

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