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    Re: Patrick O'Brian characters discuss time and longitude
    From: Peter Monta
    Date: 2016 Jun 26, 23:59 -0700
    Hi Herbert,



    - the duration of ingress / egress depends on which satelite we are talking about. It's minutes, not seconds.

    For the full time from first to last contact, yes, but I meant the span of time over which the brightness noticeably varies.  I've seen a couple of eclipses of Io through a small telescope, and not much happens right at the start of the event---it's only near the time of full eclipse that the brightness changes perceptibly.  It's about three minutes end-to-end, but all the action is in the last 10 or 20 seconds.  Ideally one would want the time at which the brightness falls to half, but that's not possible with the naked eye.  (My events were all immersions.)
     
    - The theory of of the Jupiter satelites was more elusive than that of the moon because of the resonances that were not immediately understood. Wargentin's method was more or less to empirically fit orbital parameters to the observed data without using much analytical theory. Almanac error at Cook's time was in the order of half a minute of time. I can't say at the moment how much that had improved in the few decades until the Napoleonic Wars.

    I didn't know the almanac errors were that high.  Has someone already looked at the errors of the NA eclipse predictions?  Were they straightforward tabulations of this Wargentin theory?

    In sum, the timing of Jupiter moon events was most useful when used with reference to control observations with calibrated instruments at known locations. No ship's captain set his chronometer by them.

    It sounds like Jupiter events were part of the equation for Cook, though, in conjunction with lunars.  Maybe there was a standard correction applied for size of telescope---a larger telescope will prolong visibility of the faint moon until it falls below the visual threshold.

    Cheers,
    Peter

       
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