Eclipse Calculator

Eclipses require two conditions at once: correct lunar phase and proximity to a node. The Moon's orbit is inclined about 5.145 degrees to the ecliptic, so most new moons pass above or below the Sun. An eclipse becomes possible only when the syzygy falls within the ecliptic limits, roughly 15.4 to 18.5 degrees of a node for solar eclipses and about 9.5 to 12.2 degrees for lunar ones. Because the line of nodes regresses westward and completes a circuit in 18.6 years, eclipse seasons recur every 173.31 days rather than every six calendar months. That spacing guarantees at least two solar eclipses each year and allows as many as five, with four to seven eclipses of both kinds in total. The Saros arises from a triple near-coincidence: 223 synodic months of 29.530589 days equal 6585.32 days, 242 draconic months of 27.212221 days equal 6585.36 days, and 239 anomalistic months of 27.554550 days equal 6585.54 days. The leftover 0.32 day shifts each repeat about 120 degrees west in longitude, so a given location sees the same series only every third Saros, or one Exeligmos of about 54 years. Whether a central eclipse is total or annular depends on lunar distance, which ranges from about 356,500 km at perigee to 406,700 km at apogee. Totality can last at most 7 minutes 32 seconds and the shadow path is at most about 267 km wide. This tool works from a tabulated eclipse list, so it gives dates and broad visibility regions rather than precise local contact times.

Systematic eclipse prediction begins with Babylonian scribes, whose cuneiform records from at least the seventh century BCE track lunar eclipse intervals and recognize the 223-month repetition. The word saros was actually a misapplication: Edmond Halley took it in 1691 from the Suda lexicon, which had garbled a term attributed to the Babylonian writer Berossus. Herodotus credited Thales of Miletus with predicting the solar eclipse that halted a battle between the Medes and Lydians in 585 BCE, though the basis for any such prediction is disputed. Ptolemy's Almagest, written around 150 CE, gave the first surviving geometric theory capable of computing eclipse circumstances. Modern eclipse computation rests on the method Friedrich Wilhelm Bessel devised in the 1820s, which reduces the shadow geometry to a small set of Besselian elements evaluated on a plane through Earth's center. Theodor von Oppolzer's Canon der Finsternisse of 1887 applied this to catalog 8,000 solar and over 5,200 lunar eclipses spanning 1208 BCE to 2161 CE. Fred Espenak and Jean Meeus extended the work at NASA Goddard with the Five Millennium Canon of Solar Eclipses published in 2006, covering 2000 BCE to 3000 CE. Eclipses also drove discovery directly: helium was identified in the solar spectrum during the 1868 eclipse, and Arthur Eddington's 1919 expedition measured the deflection of starlight predicted by general relativity.