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Re: Lewis and Clark lunars: more 1803 Almanac data
From: Ken Muldrew
Date: 2004 Apr 16, 23:10 -0600
From: Ken Muldrew
Date: 2004 Apr 16, 23:10 -0600
> >On 16 Apr 2004 at 17:33, George Huxtable wrote: > Another part of the cause of the slowing of speed between Moon and > star can be caused by a sort of misalignment, due to the star not > being directly in line with the path of the Moon across the sky. > That's the effect that Ken was considering. It should have been taken > into account in the Moon-star true-distance predictions in the > Almanac. But if the star turned out to be a different star from the > one the predictions were for, and further away from the Moon's path, > then we would not only expect the lunar-distance predictions to be > wrong, but also to be changing more slowly too. That, I think, is what > Ken was getting at. I can't quite see, yet, how he arrives at that > misalignment of about 36deg from the numbers he quotes: perhaps he > will explain further. That is exactly right. In the few lunars that I've done (I'm a complete beginner at this), the moon's apparent motion with respect to the ecliptic stars/planets has always been around 27"/min. I know that this can change due to refraction and parallax, even for a star or planet that's right on the moon's path, but I don't know what the limits of this change are. I assumed that the apparent motion would remain pretty close to the true motion. So for a first order approximation (perhaps zeroeth order would be more appropriate, despite my numbers with 3 figures!), the departure of the apparent motion from the true motion along the ecliptic (since Aldebaran is pretty close to the ecliptic) could tell us how far off the ecliptic the star being used really was. When you do plot both sets of readings and fit a line through them, it does appear that confidence can be put in the slope of this line. With the measured motion of the moon with respect to the mystery star, and the almanac motion of the moon with respect to aldebaran (almost as far away, but along the moon's path) we can construct a simple, Euclidean triangle (this is the zeroeth order part) and get the angle of divergence. That's where I got my "about 36?" angle off the moon's path. I think if the problem is treated properly (taking refraction, parallax, and spherical geometry), we may get a much better estimate of the actual angle. But then again, I may be well wide of the mark. Nevertheless, I'll take a stab at this tomorrow. Hopefully the experts here will also give it a try if there's any sense in doing so. Ken Muldrew.