Ecliptic Limit

FIGURE A-11. A grazing eclipse of the Sun (S) would result in the situation depicted here. We know the angle at which the Moon (M) crosses the ecliptic at its node; this is the inclination, about 5.15 degrees. Then it is a simple geometrical matter to calculate the ecliptic limit, the maximum separation in longitude between the Sun and the node that will result in an eclipse of some stipulated type.

above parameters, if L is below 15.35 degrees then at least a partial solar eclipse is certain; if L is less than 9.92 degrees then a total or annular solar eclipse is certain. If L were below respective limits of 18.52 and 11.83 degrees, then such eclipses are possible but not certain.

The precise limits are not important. The significant factor to note is that they are all much greater than the step of 0.48 degrees that occurs from one saros to the next. This means that once the Moon gets into an orientation such that it passes a node within the ecliptic limits, for many following saronic cycles it will continue to produce eclipses.

Consider first the most stringent limit above, the range of 9.92 degrees certain to produce a total or annular eclipse. This is a permissible range for each side of the Sun, so that the total range in nodal longitude is almost 20 degrees. It will take 41 or 42 steps of 0.48 degrees to cross that distance, meaning that there will be a sequence of at least 40 total solar eclipses, each spaced by 18.03 years, the sequence lasting for perhaps 750 years.

This is the minimum sequence duration. For total eclipses the greater limit of 11.83 degrees might apply, producing a sequence persisting for maybe 900 years. If one allowed any solar eclipse to count, including the partial obscurations, then a sequence may continue for over 1,400 years and contain in excess of 80 events. Certainly saros (meaning "repetition," remember) is an apt name!

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