Short-term solar eclipse predictions using Euclidean geometry and dynamical systems
Alin-Doru Aluas, Valerian-Alin Fodor, Virgilius-Aurelian Minuta
Abstract
We propose a computationally inexpensive algorithm to determine whether an opaque spherical body eclipses a luminous one, using only classical geometrical tools. We apply this method to the Sun-Earth-Moon system and predict solar eclipses, including their type, beginning, and duration, using the three-body problem. For predictions over a one-year period, the resulting errors are in the order of minutes.
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