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Re: ? ? ? Question on Lunars
From: Bruce Stark
Date: 2004 Oct 25, 20:09 EDT
From: Bruce Stark
Date: 2004 Oct 25, 20:09 EDT
Alex,
There were two reasons short lunar distances were avoided. First, the Almanac gave predicted distances at three hour intervals. Unless the star is exactly on the moon's orbital path, as seen from the center of the earth, the rate of change in the distance slows down as the moon nears the star, then speeds up as she recedes. As you know, that causes a second difference problem, and second differences are proportional to the square of the interval.
But even if a shorter interval had been used, there would have been a problem in clearing short distances. Most, if not all, of the popular methods of clearing were what we call "approximate." That is, they calculated a set of corrections to apply to the apparent distances. The calculations were based on some not-exactly-true assumptions. A final correction took care of this. When the distance got short, this final correction got a bit wild.
In the 1877 Norie I'm looking at, that correction is in table XXXV and titled "To correct . . . for the Effects of Parallax and Refraction," (although that isn't really what it's for). Probably XXXV in the 1828 Norie also. Notice how fast values change toward the bottom of the table, where the r&p correction to the distance was large.
Bruce
There were two reasons short lunar distances were avoided. First, the Almanac gave predicted distances at three hour intervals. Unless the star is exactly on the moon's orbital path, as seen from the center of the earth, the rate of change in the distance slows down as the moon nears the star, then speeds up as she recedes. As you know, that causes a second difference problem, and second differences are proportional to the square of the interval.
But even if a shorter interval had been used, there would have been a problem in clearing short distances. Most, if not all, of the popular methods of clearing were what we call "approximate." That is, they calculated a set of corrections to apply to the apparent distances. The calculations were based on some not-exactly-true assumptions. A final correction took care of this. When the distance got short, this final correction got a bit wild.
In the 1877 Norie I'm looking at, that correction is in table XXXV and titled "To correct . . . for the Effects of Parallax and Refraction," (although that isn't really what it's for). Probably XXXV in the 1828 Norie also. Notice how fast values change toward the bottom of the table, where the r&p correction to the distance was large.
Bruce
