NavList:

Frank,

Thanks for the simple explanation. It turns out I was suffering from mistaken terminology. I thought you were saying that at 90deg the lunar distance was insensitive to the moon altitude CORRECTIONS, when all along you were saying that it was insensitive to moon altitude measurement ERROR. I took the time to work out the equations and now I get the point. Of course the moon's altitude correction contributes since the parallax correction is dominant. The amusing thing is that in the 90deg case it is the sun's altitude that determines how much the moon's altitude correction contributes! In fact the moon's altitude does enter in a small way: it alone determines how much the refraction correction for the sun's altitude enters. It might be better to call this the "90deg anomaly" instead of the "90deg miracle".

I tried to visualize what is unique about the geometry of the 90deg lunar distance case. The only obvious feature I could see was that if you hold the sun's location constant, then the possible locations of the moon lie along a great circle. This apparently has the effect that the projection of the moon's altitude along the lunar distance has a cos(h_moon) term in the denominator, which exactly cancels the cos(h_moon) term in the moon's altitude correction. But this isn't a very profound observation.

George B
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