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George H wrote:
"What has surprised me (and intrigued Frank) is that the above expression
continues to give a value for D in circumstances that are QUITE IMPOSSIBLE,
in that the lunar distance is such that there's no value of azimuth
(between 0 and 180) between Sun and Moon that can accomodate such a lunar
distance. In those circumstances, although any attempt to deduce that
azimuth would fail, the expression for D still seems to work, and gives
some sort of result."
Not only "some sort" of result, but the correct result. That's the fun thing.
And wrote:
"When the numbers input to the equation correspond to azimuths in range 0 to
180, then the result D has a simple physical meaning, the true lunar
distance D. In other situations, is there any physical meaning we can
attach to D?"
I think it's fine to say that D is still the cleared lunar distance. But the
intermediary Z, which should be a difference in azimuth, has left the real
number line in a case like this, and there's no way to "draw it" in a simple
diagram or interpret it as an azimuth. It's just a meaningless intermediate
quantity. Here's something to ponder: imagine what the reputation of lunars would
have been if navigators 200 years ago had learned that the difference in azimuth
might occasionally be partly an imaginary number but, not to worry, this is
normal, and it's a good thing! Maybe that's why this issue is not discussed in
the usual sources. They were afraid it might drive mariners mad... :-)
Frank R
[ ] Mystic, Connecticut
[X] Chicago, Illinois
