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    Re: Averaging
    From: Bill B
    Date: 2004 Oct 22, 16:28 -0500

    >> 1. The body is very likely to be changing
    >> altitude in a nonlinear fashion.
    >
    > Just vice versa: very UNLIKELY.
    > Namely: ONLY when near the meridian on high altitude.
    > In all other cases it is linear for all practical purposes.
    
    I find myself constantly reevaluating my thinking.  For example I was
    attempting to apply a ratio of rate of change of Hc to a predetermined error
    due to non-linearity.  Bigger the rate of change, bigger the error.  I now
    see that concept is flawed.
    
    I am having trouble with the concept that non-linearity increases as the
    body approaches the meridian in all cases.
    
    In the case of the being on the equator at an equinox, the rate of change
    throughout the day would be an almost uniform 1d per 4 minutes.  Same at LAN
    as at sunrise or sunset.  However, the path of the Sun would close to
    perfectly linear.  Insignificant error due to non-linearity.
    
    If very near the PN at summer solstice, rate of change of HC would remain
    almost constant throughout the day and would be very close to 0. Yet here we
    could compute systematic error due to non-linearity.
    
    Perhaps this was made clear in the equations set forth, but the computer I
    use most for cel nav, the one between my ears, was not programmed to
    visualize the outcome of a string variables.
    
    I did note the formula provided by Alex included declination.
    
    sinA=sinDsinL+cosDcosLcost
    
    Einstein stated, "Everything should be made as simple as possible, but not
    simpler."  Perhaps the above formula is as simple as it can be while still
    covering all possible combinations, therefor the rules of thumb only operate
    within limits, but not in all situations.
    
    Feedback?
    
    Bill
    
    
    

       
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