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    Re: Differential lunars
    From: Frank Reed
    Date: 2013 Jul 31, 11:55 -0700

    Stan Klein asked:
    "Is this the method discussed in the Navigator's Newsletter Issue 4?"

    Same name, 'differential lunars', but quite different. The article in that old issue of the Navigator's Newsletter is fairly typical of the pre-Internet era in discussions of celestial navigation. There were small numbers of people each working in isolation with little opportunity to communicate (the newsletter was thus much more useful in its heyday). Ideas were recycled, re-invented, and inaccurate claims were repeated again and again. Read the issues of the newsletter with great care.

    The method described with such enthusiasm in the NN (a couple of sentences in ALL CAPS!) has been re-discovered many times. There was a remarkably similar letter published by the Royal Astronomical Society from Lt. E.D. Ashe of the Royal Navy. He described the exact same procedure, and he also believed that it was something new. He had noted that in his twenty years at sea, he had encountered no one who had shot a lunar. Like the author in issue 4 of the NN, he had had a eureka moment over this discovery. Oh, and Ashe's article was published in 1849. By that date, so long ago, it was already "ancient history". The technique had been known as early as the late 18th century (apparently independently discovered several times), but it is inferior in accuracy to "real lunars" and requires special circumstances. And since "real lunars" are only slightly more difficult than time sight comparisons, the latter were considered an un-necessary distraction. I actually disagree with this judgement. There are circumstances where these altitude comparisons are easier and more readily available than traditional lunars. It's a tool that can work, so why not know it?

    As Peter Monta has already noted, this method of time sight comparisons is nearly identical to the method proposed by Chichester and also John Letcher (who also detailed traditional "real" lunars in his book in the 1970s). The only difference is that the latter authors used the language of LOPs. It's very easy to understand in those terms. Take sights of several stars and also several of the Moon at some "assumed" GMT (whatever you think to be the correct GMT). Plot the LOPs. The star sight LOPs will all cross in a nice fix, as tight as the accuracy of your observations dictate. If the GMT is wrong, the fix will merely be shifted east or west in the usual proportion: one minute of longitude for every four seconds error in GMT. But the Moon LOPs may not cross the tangle of LOPs from the star sights. This is because the Moon is moving on the celestial sphere relative to the stars. The Moon LOPs will move east or west at a slightly different rate. If you plot the sights again with a modified GMT, you would find that the separation between the Moon LOPs and the other LOPs changes. By simple linear interpolation (or extrapolation) you can figure out the GMT that makes all of the LOPs cross in a tight fix. In order for this to work, the Moon should be bearing roughly east or west (obvious enough if you think about shifting an LOP east or west) and most importantly the Moon's horns should be more or less parallel to the horizon, within 30° of horizontal is fine but certainly within 45°. This guarantees that the Moon's motion on the celestial sphere has a significant effect on the Moon's altitude since when the horns are horizontal, the Moon's motion on the celestial sphere is near to locally vertical. This method could only be used if the GMT from the chronometer was suspect by more than a couple of minutes. This is unlikely to happen ever again except in contrived semi-historical experiments.


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