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    Re: Graphs of Lunar Distances.
    From: Frank Reed
    Date: 2010 Oct 23, 21:47 -0700

    Douglas Denny, you wrote:
    "The programming error was, as you said would most likely be, a very simple and small slip... Very annoying once found; it took some considerable time to discover, as one keeps looking at it without seeing it."

    The catch with software engineering: where there's one bug, there may be two.

    This business about our expectations can be really pernicious. If we're expecting a certain level of accuracy from these observations and when we clear them, if they fall within that range, we stop looking for errors.

    You say you now see an error of "only" 1m 29s in time for the mean of your eleven Jupiter observations. Yet you should be seeing just 22 seconds error in the time (plus or minus a couple of seconds for small differences in assumptions) or FOUR TIMES better than your calculations are showing. I must emphasize that seven out of eleven of your Jupiter lunars were observed with errors in the observed distance smaller than 0.25' of arc (equivalently smaller than 15" of arc) which would correspond to less than 30 seconds error in GMT on each and every one of those seven sights. Your standard deviation on these eleven sights rights now is somewhat larger, at around 0.4', because you had a couple of real outliers, but with just a little more practice, or perhaps some checks on your sextant, you should be getting the same quarter of an arc minute accuracy (at the 1 s.d. level) that I have described. That would still be roughly 7 out of 11 within 0.25', as you've already achieved, but you would simply see fewer outliers. For example, if we drop just the last two of your Jupiter lunars out of this set of eleven, the s.d. drops to 0.30 with a mean error of only 0.07 minutes of arc (FOUR arcseconds!). There's no legitimate reason a priori to drop those two. They don't stand out. I'm just demonstrating that an improvement in consistency would bring your results into a range that I think you can expect to see.

    As for fixing your calculations, maybe we should go through one in really excruciating detail. Other folks might enjoy that, too, yes? We could work through your arithmetic mean Jupiter lunar, or we could work through one of the individual lunars. If the latter, I nominate your fourth sight from that set of eleven where the distance was 34d 9.4' since it has almost no error (at least by my calculations).

    PS: Sorry for the delay in replying. I got busy with a project. Now I have a lot of catching up to do.

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