Repeating Eclipses

angle it will progressively cover most of the other disk before receding. Let us consider this in more detail.

Figure A-11 shows the trajectory that would give a grazing eclipse: the limb of the Moon just touches against the apparent edge of the Sun in the sky. Using quite simple geometry it is possible to calculate the value of the ecliptic limit, the longitude difference between the node and the Sun at which such a grazing eclipse would occur.

Actually there are distinct values for the ecliptic limit depending upon the specific conditions, because several varying parameters affect the calculations: the apparent sizes of both Sun and Moon depend upon our distances from those orbs, and also the inclination of the lunar orbit oscillates. Call the ecliptic limit L for shorthand purposes. Taking the most unfavorable values for the

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