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    Re: Halley's lunar knowledge.
    From: Frank Reed
    Date: 2007 Nov 25, 02:53 -0500

    Regarding Halley's calculational method for determining the Moon's true
    position... In fact, he didn't need one as long as he had a diligent
    astronomer back home willing to measure the Moon's position as frequently as
    possible. For mapping and surveying, where the position determined by
    observations can wait to be calculated when we get home (as opposed to live
    navigation where we want the position on the spot), we don't need any lunar
    theory at all. Imagine an alternate history where the reflecting sextant or
    a similar instrument was invented 2500 years ago. If some king or emperor
    with money to burn had decreed it necessary, astronomers could have been
    sent to the far corners of the known world. They could have determined
    longitudes as accurately as any late 18th century lunarian. A team of
    astronomers in the imperial capital would measure lunar distances every hour
    of every night, and travelling observers would measure the same distances
    whenever they could in distant lands. Then, upon returning home, with some
    clearing calculations (which would have been possible given the state of
    mathematics though definitely challenging) those observations made in
    distant lands could have been compared with the reference observations made
    at home and as easily as that the world would have been mapped --to an
    accuracy as good as world maps in 1800 (in the real world). Of course they
    would need to understand lunar parallax (Hipparchus probably did) and they
    would have needed a basic refraction table (which would have been discovered
    almost immediately after the invention of the double-reflecting sextant). Of
    course, an accurate map like that is nearly useless economically unless you
    have a 'live' navigation method to go along with it.
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