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    Re: Lunars: Jupiter's BIG.
    From: Fred Hebard
    Date: 2003 Dec 20, 17:44 -0500

    Thanks Herbert,
    It is very easy to shoot guns at these sparrows due to my computer
    software, where the fit and plotting of the line is but one button push
    away.  Plotting distance versus time would still be my preferred method
    for getting a feel for the quality of the data, then drawing in a line
    by hand or letting the computer do it.  I was pointing this out as
    being a lousy method for then picking an observation to clear because
    it was close to the method being advocated earlier this year.
    What exactly would you be regressing to minimize clock error?  A
    numerical example would help me understand this.  It seems blindingly
    obvious now you point it out.
    On Dec 20, 2003, at 4:57 PM, Herbert Prinz wrote:
    > Fred,
    > It would seem that you are applying the least square fit incorrectly.
    > To apply
    > it to the plot of distance versus time is to shoot with guns at
    > sparrows. You
    > can have this cheaper by averaging the time, averaging the distances,
    > and then
    > proceed as if the averaged values where the actual observation - just
    > as you
    > are suggesting. This is what was normally done, and what is feasible
    > to the
    > navigator without electronic tools. To use this technique does not
    > prevent you
    > from plotting the distances versus time to find outlyers. As long as
    > you have
    > the individual distances, that is, because from repeating instruments
    > (such as
    > the Borda circle), one does not get them.
    > However, if you really must apply a least square fit to the given
    > data, (and I
    > could not argue with you if you claim that this is the only rigorous
    > treatment
    > of any set of more than 2 observations), the only correct method is to
    > solve
    > for the watch error for which the sum of the square of the distance
    > residuals
    > becomes a minimum. Besides from being correct, it has the additional
    > benefit
    > that you can combine observations to different objects, in particular
    > observations on either side of the moon, which helps to cancel certain
    > instrument and observation errors.
    > It goes without saying that this has no practical value on the boat.
    > But it
    > could have been used this way in surveying, right before the telegraph
    > was
    > introduced.
    > Herbert Prinz
    > Fred Hebard wrote:
    >> Interestingly, I usually plot the raw distance against the time of
    >> observation and use the least squares fit to pick out a point for
    >> reduction.
    >> I think perhaps the old method of using the mean of the observations
    >> would be better than using a line of best fit, although plotting the
    >> data instantly tells one how good they are.  Using the mean, the time
    >> would have been out by 8 seconds, about 2 minutes of longitude.

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