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    Re: Lunar eclipses and other things
    From: Herbert Prinz
    Date: 2004 Oct 29, 16:22 -0400

    Alexandre Eremenko wrote:
    > > Why was any lunar theory
    > > (whether that of Hipparchus or anybody else) required to interpret the
    > > dates?
    > I have to dig the literature for more precise info.
    > But Lunar eclipses (and other historical records of astronomical
    > observations) are frequently used by historians to establish
    > the real dates of the past events.
    Astronomical events are indeed used for chronology to establish dates,
    confirm, refute or correct dates, or to correlate dates given in different
    systems. Neither of these cases apply here. The dates of the observations
    are explicitly given. As they are the basis of the lunar theory, the latter
    cannot confirm them. This would be tautological.
    > Do we have their [the Chaldeans'] own records or only mentioning in
    > secondary
    > sources? I would be grateful if you provide more precise info about them,
    > or references.
    We have their own records and they have been deciphered at the end of the
    19th cy. by Epping and Strassmaier.
    Kugler, Die Babylonische Mondrechnung.
    Neugebauer, A History of Ancient Mathematical Astronomy, Part One, Book II.
    Swerdlow, The Babylonian Theory of the Planets.
    > > people collected their knowledge of longitudinal distances
    > > through travelling.
    > My impression was that this was much less precise.
    > For example, in Erathosphenes measurement of the Earth
    > radius, the main technical problem was how to measure
    > the distance on the land, not the angle in the sky.
    > And it is the error in this land distance that limited
    > the presision of his method.
    But doesn't the detailed example with numbers from Ptolemy's Geography that
    I quoted show that the error in the astronomical measurement matched that of
    the land distance measurement? The eclipse reports were scarce and
    > And how indeed would you measure
    > a distance when traveling? I mean in those ancient times.
    > In "days of the travel".
    > And how do you insure that you travel on a straight line?
    Ptolemy was aware of these problems and pointed them out to the reader, but
    he had nothing better available to him.
    > > He used one lunar eclipse mainly to frighten the poor Red
    > > Indians.
    > Really? I thought he was really very concerned about his longitude.
    Of course, he was concerned. I explicitly said that. I was merely
    reinforcing your own statement that he was not successful. The only real use
    he got out of the one eclipse was to frighten the Read Indians. Please read
    how the original conversation went:
    You > This was the only method Columbus could use ...
    I>       But in fact, he used dead reckoning. He tried to confirm it twice
    with an eclipse.
    You > ... (Though he was not very successfull with this,
    I>       Indeed.  He used one lunar eclipse mainly to frighten the poor Red
    > > Lunar eclipses never played any role in map making before Mayer. The
    > > method was too crude.
    > I doubt about both statements. But cannot refute the first
    > at this moment; this would require a history research.
    One and a half millennia after Ptolemy, the Connoissance for 1790 has this
    to say on lunar eclipses: "L'observation des Eclipses de Lune, n'est pas
    susceptible d'une tres-grande precision, parce que les bords de l'ombre de
    la Terre qui sont diffus & mal termines, laissent de l'incertitude sur le
    vrai moment des phases." Then they proceed to suggest the use of Mayer's
    method that I described in the last message.
    > About the second statement, I think we can easily
    > decide by giving specific numbers.
    > Unfortunately the sky is obscured today so I cannot observe
    > the eclipse myself:-( But what do you think the precision of the
    > method would be with observation tools of 1000-2000 years ago?
    No need to guess. I presented a specific example, in fact the ONLY one that
    Ptolemy mentions in the Geography. (Ptolemy complains bitterly about the
    crudeness of older reports because "it was not yet understood how useful the
    more mathematical mode of investigation is")
    > > 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.
    > When I was talking of "Hipparchus lunar theory" I did not separate
    > it from Ptolemy's. I simply don't know how do do it: Hipparchus original
    > work did not survive, and it is known to us mainly through Ptolemy.
    Ptolemy makes the separation. Book 4 of the Almagest describes Hipparchus'
    lunar theory. Book V, his own.
    > > Kepler hit on the "annual equation" around the same time as Brahe.
    > At the time when he was Brahe's assistant?
    No, he was still in Graz. By the way, neither Kepler's explanation nor that
    of Brahe (actually, of his assistant Longomontanus) was correct. But
    Kepler's fit into heliocentrism, whereas Brahe's didn't.
    Alex, there is a mailing list dedicated to the history of astronomy. It
    seems you might be interested to join it. Over there, you will meet again
    several members of the navigation mailing list. Subjects not directly
    related to navigation are probably better discussed there. On the one hand,
    there is probably only a limited interest in astronomy or its history
    amongst the members of the navigation-l; on the other hand, on hastro-l, we
    can enjoy the input of many professional astronomers and historians.
    Herbert Prinz

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