The Next Eclipse Solving

How It Is Solved

NASA publishes each solar eclipse as eight polynomials in time: the shadow axis's position on the fundamental plane (x, y), its direction (d, μ), the radii of the penumbral and umbral cones (l₁, l₂) and their angles (tan f₁, tan f₂). This page puts your place on the WGS84 ellipsoid, turns it into the same plane (ξ, η, ζ), and solves for the instants when the axis passes within the shadow's radius of you: Newton's method, each time iterated to 0.004 s. The method is Chauvenet's of 1863, as the Explanatory Supplement (2013, ch. 11) and Meeus (1989) set it out.

Lunar eclipses have no published elements, so they are solved from scratch: Meeus's full-Moon series picks the candidates, his Moon and the VSOP87 Sun place both bodies, and the Earth's shadow is enlarged by Danjon's rule, as NASA applies it.

What It Cannot Know

• The Moon's edge has mountains. NASA's elements and this page both use a smooth Moon, so second and third contact can land a second or two off near the edge of the path.
• Weather. A cloud deck removes an eclipse more completely than any rounding here.
• Refraction. Sun altitudes are geometric, as in NASA's tables, so near the horizon the Sun looks about half a degree higher than printed. Moon altitudes include standard refraction, and moonrise is timed for the Moon's centre, about a minute after an almanac's upper limb.
• Lunar times print to the minute: the shadow's edge is soft, and the abridged Moon is good to about 15 s.
• Heights come from GeoNames for listed cities and are sea level for typed coordinates.
• The century stops at 2100, where NASA's twenty-first-century elements stop.