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    Re: Lunar eclipses and other things
    From: Herbert Prinz
    Date: 2004 Oct 27, 07:28 -0400

    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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