The Frequency of Solar Eclipses for a Given Place: A New Approach to a Classic Question

TL;DR

This paper revisits the frequency of solar eclipses at specific locations using modern computational methods, providing more precise estimates and insights into geographic and long-term cyclical patterns.

Contribution

It introduces a new computational approach to accurately estimate eclipse frequencies and explores geographic and long-term variations, improving upon previous statistical methods.

Findings

Total eclipse occurs approximately every 373 years

Annular eclipse occurs approximately every 226 years

Partial eclipse occurs approximately every 2.59 years

Abstract

In a classic 1982 paper in this journal, Jean Meeus used a statistical approach for finding the mean frequency of a total and an annular eclipse of the Sun at a given place on the surface of the Earth. In this current paper we tackle the problem again, taking advantage of the much greater computing power now available. We obtain narrower estimates of once every 373 $\pm$ 7 years for a total eclipse, and once every 226 $\pm$ 4 years for an annular eclipse. In addition, we obtain a result of once every 2.59 $\pm$ 0.02 years for a partial eclipse. We provide further insights into the "latitude effect", showing that solar eclipses occur most frequently around the Arctic and Antarctic Circles. We also show how the gradual shift of aphelion and perihelion with respect to the seasons produces a $\sim$21,000-year cycle in the frequency of eclipses in the Northern and Southern Hemispheres.