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    Re: An instant value vs an integrated one?
    From: Peter Monta
    Date: 2021 Oct 10, 05:21 +0000
    Hi Tony,


    Is it always enough to simply delay the sampling by the half-duration of the integration interval to present it as the reference to compare with integrator's result?


    For all practical purposes, probably the answer is yes for integration times of a few minutes and to sextant accuracy.  Some numerical experiments would tell the tale (and sorry for this handwaving post without any numbers).  Any plot of altitude with time will have some curvature, so the midpoint will be an underestimate or overestimate (usually the latter, though a circumpolar star at lower culmination would be an example of the former).

    One extreme case would be celestial bodies near the zenith.  Their altitude plots will have an inverted-V shape with high curvature at maximum altitude.  There the midpoint could be substantially different from the integral.

    Cheers,
    Peter

       
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