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Re: ? ? ? Mendoza's method for clearing lunars.
From: Bruce Stark
Date: 2004 Aug 2, 13:55 EDT
From: Bruce Stark
Date: 2004 Aug 2, 13:55 EDT
George,
You are right. That particular method of Captain Mendoza del Rios' (sometimes called "Norie's fourth method") is an approximate one. It's similar to Bowditch's original method, before that was improved by special tables, and looks to me to be a simplification and improvement of it. A special feature of both is that, unlike other approximate methods, the rules don't depend on which body is highest or whether or not the distance is over 90 degrees.
Norie's old Table XXXV was three pages long. The title, "To correct the Apparent Distance of the Moon from the Sun, a Star, &c, for the Effects of Parallax and Refraction," isn't exactly a fit. What it does is adjust for the error caused by treating the moon's corner as if it were a plane right triangle, with the moon's altitude correction as the hypotenuse.
Two sides of this little triangle are always straight lines. That is, they are sections of great circles. The side opposite the angle at the moon is seldom part of a great circle, so is curved. Table XXXV adjusts for the error caused by the curve.
Bruce
You are right. That particular method of Captain Mendoza del Rios' (sometimes called "Norie's fourth method") is an approximate one. It's similar to Bowditch's original method, before that was improved by special tables, and looks to me to be a simplification and improvement of it. A special feature of both is that, unlike other approximate methods, the rules don't depend on which body is highest or whether or not the distance is over 90 degrees.
Norie's old Table XXXV was three pages long. The title, "To correct the Apparent Distance of the Moon from the Sun, a Star, &c, for the Effects of Parallax and Refraction," isn't exactly a fit. What it does is adjust for the error caused by treating the moon's corner as if it were a plane right triangle, with the moon's altitude correction as the hypotenuse.
Two sides of this little triangle are always straight lines. That is, they are sections of great circles. The side opposite the angle at the moon is seldom part of a great circle, so is curved. Table XXXV adjusts for the error caused by the curve.
Bruce
