Besselian elements

Besselian elements

[bə′sel·yən ¦el·ə·mənts]
(astronomy)
Data on a solar eclipse, giving, for selected times, the coordinates of the axis of the moon's shadow with respect to the fundamental plane, and the radii of umbra and penumbra in that plane; the data allow one to derive local circumstances of the eclipse at any point on the earth's surface.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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However, in their calculation of the Besselian elements, HM Nautical Almanac Office have adopted a larger, IAU-recommended value of k, the ratio of the Moon's radius to the Earth's equatorial radius.
The mathematical models for each eclipse (the Besselian elements) are based on extremely accurate measurements of the motions of the Sun, Earth, and Moon.
For comparison, the Table gives the speed of the shadow at the instants tabulated in the original paper, calculated by the method just described from the Besselian elements presented in the relevant NASA Solar Eclipse Bulletins.
A requirement to calculate anything about a given solar eclipse (such as local circumstances or points on the northern and southern limits of totality) is having the so-called Besselian elements. Since these values had already been accurately calculated for all eclipses from 2000 B.C.
The remaining Besselian elements are the vertex half-angle f2 of the umbra and f1 of the penumbra, together with the radii of the umbra (L2) and penumbra (L1) in the fundamental plane.
Those [xi], [eta], [zeta] have to be computed from the observer's geographical latitude and longitude as well as the Besselian elements [micro] and [delta].
Now this geodetic equation needs to be transformed to the (x, y, z) axes of the Besselian elements. The transformation is described by the linear equations:
For our purpose this quadratic equation expresses the unknown distance z as a function of the Besselian elements x, y and 8, in other words the z-coordinate of the spot on the Earth's surface hit by the lunar shadow axis.
3, 6 and 7 make use of Besselian elements with up to third order polynomials, aiming at the highest precision eclipse contact times and geographic coordinates of the umbral path limits and central line.
Select one from the list and the program calculates its Besselian elements. Now you're down to business.
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