SAROSIUM

Solar & Lunar Eclipse Tracker · 2000–2100

Data & methods

Everything on this page is computed in your browser, from the sources and with the methods below. The code is plain, unminified JavaScript served with the page (eclipse-core.js, ephem.js); open your browser's developer tools to read it, or press the button in the Validation section to recompute the comparison figures yourself.

Selected eclipse

Select an eclipse.

Ephemerides

JPL DE441 geocentric state vectors of the Moon (301) and Sun (10) from the NASA/JPL Horizons API: CENTER=500@399, REF_PLANE=FRAME (ICRF), VEC_CORR=NONE, VEC_TABLE=2, KM-S, hourly for ±6.5 h around every eclipse, times in TDB (treated as TT; |TDB−TT| < 2 ms). 458 windows, served with the page as ephem.js.
Between samples: cubic Hermite interpolation on position and velocity. Checked against an off-grid Horizons astrometric sample (2027-08-02 10:06 TT): Moon 0.020″ and 2 m, Sun 0.014″.
Outside those windows (only the globe lighting and the LIVE clock ever go there): astronomy-engine, whose Moon sits about 1″ from DE441 in the 2020s and 2″ by the 2090s.
Eclipse discovery (which dates, which type) still uses astronomy-engine's search; every quantity shown is then recomputed from the JPL positions with the model below. The library has no hybrid class; the model classifies seven hybrids in 2000–2100, the same seven as NASA's catalog.

Frames and corrections

Solar eclipses are worked in the geocentric frame at the instant of observation: the Sun as seen, S − v_Sτ_S (light-time plus annual aberration, i.e. the apparent Sun), and the Moon where it was when the light passed it, M − v_Mτ_M (τ_M ≈ 1.28 s). This is the same set of events as the barycentric line through the retarded Sun and Moon; the ground point is identical.
Lunar eclipses: Earth's shadow axis runs from the astrometric Sun through Earth's position τ_M earlier, which in the present geocentric frame puts the Moon at M + v_Eτ_M. Equivalent to the classical "both apparent" convention to 0.7″.
ICRF → true equator and equinox of date via astronomy-engine (IAU 2006 precession, IAU 2000B nutation). Earth rotation from its sidereal time (GAST); polar motion ignored (< 0.3″ ≈ 10 m).
Earth is the WGS84 ellipsoid (a = 6378.137 km, 1/f = 298.257223563). Observers are geodetic (latitude, longitude, height); the centre line is the shadow axis meeting the ellipsoid at height 0.
Time: JavaScript UTC is taken as UT1 (DUT1 < 0.9 s ignored, ≤ 0.5 km along track). TT = UT + ΔT.

Constants and conventions (NASA / Espenak canon)

Sun radius	696,000 km
Moon radius, umbral and central contacts	k = 0.272281 × 6378.137 km (allows for the mean limb profile)
Moon radius, penumbral contacts, obscuration, sky view	k = 0.2725076 × 6378.137 km
Earth's shadow at the Moon (Danjon rule)	R_p = 1.01 π_M + s_S + π_S, R_u = 1.01 π_M − s_S + π_S (equatorial horizontal parallaxes and Sun semidiameter, geocentric)
Umbral / penumbral magnitude	(R + r_M − sep) / 2 r_M
Obscuration	Fraction of the Sun's disc area covered (circle-intersection formula), topocentric
Central phase	Topocentric separation ≤ \|r_M − r_S\| with the umbral k; total if r_M ≥ r_S, else annular
Sun altitude	Geometric altitude plus astronomy-engine’s "normal" refraction (Sæmundsson’s formula, Meeus 16.4)
ΔT	USNO observed 1 January values 2000–2026 (63.83 → 69.11 s), linear interpolation; then a straight ramp to the Espenak–Meeus polynomial at 2050 (93.0 s); the polynomial beyond. The ramp gives 70.7 s in mid-2027 where NASA's 2027 page used 71.7 s.

Algorithms

Greatest eclipse: instant of least distance between the shadow axis and the geocentre (golden-section search, ±2 h). Its ground point is the axis–ellipsoid intersection at that instant. Kind from the sign of the umbral cone radius at greatest eclipse and at both ends of the central track (hybrid when it changes).
Central line: axis–ellipsoid intersection every 90 s. Cone radius on the ground r_u = r_M − t (R_S − r_M) / |S − M| at the intersection distance t; footprint stretched by 1/cos z along the Sun's azimuth (display only).
Band edges: for each path sample, bisection across the track on the central-phase test at the local maximum, to ~25 m, in a web worker. The pin card uses the identical test, so a pin flips exactly at the drawn edge (sea level).
Local circumstances (pins): local maximum by golden-section search on topocentric separation within ±3.5 h; first/last contact and second/third contact by bisection to < 1 ms; durations shown to the second. Pins fetch ground elevation from Open-Meteo (Copernicus GLO-90 DEM) and observe from that height.
Longest duration: maximum over the central-line samples, refined by golden-section search in time between the neighbouring samples.
Lunar contacts: least separation from the shadow axis by golden-section search; P1/P4, U1/U4, U2/U3 by bisection where separation = R + r_M (penumbral, umbral) and R_u − r_M; the two sides are averaged into semidurations (they differ by a few seconds).
Shading (display only): solar, maximum obscuration on a 1° grid sampled every 5 min, spherical Earth, faded over the last 3° of Sun altitude, stepped to 20 %; lunar, share of the eclipse with the Moon up on a 1° grid, 10-min samples with interpolated rise/set, no refraction, stepped to 25 %.

Validation

Each figure below is compared with a published value. The "this browser" column is empty until you press the button; it then recomputes every figure here, from the same code and data this page runs on, so the comparison is yours, not ours.

Check	Published / expected	This browser
Interpolated JPL positions vs a Horizons sample off the hourly grid (2027-08-02 10:06 TT, astrometric ICRF)	Moon 132.00903°, +18.00501°, 0.00238896 au; Sun 131.97212°, +17.86320°	—
2027-08-02 centre line vs NASA's path table, at NASA's ΔT of 71.7 s (Espenak, ELP2000-85, coordinates to 0.1′)	Greatest eclipse 25°30.3′N 33°11.0′E at 10:06:37.7 UT; greatest duration 26°49′N 31°08′E at 10:00:21 UT	—
2027-08-02 central durations	382.6 s at greatest eclipse, 383.2 s longest (NASA)	—
Duration at greatest eclipse, 2024-04-08 total and 2027-02-06 annular	4m28s (268 s) and 7m51s (471 s) (NASA)	—
2025-03-14 total lunar eclipse contacts P1, U1, U2, U3, U4, P4 (NASA used ΔT = 75 s)	03:57:24, 05:09:33, 06:25:59, 07:31:23, 08:47:48, 10:00:01 UT; magnitudes 1.1784 / 2.2595	—
Hybrid solar eclipses 2000–2100	2005-04-08, 2013-11-03, 2023-04-20, 2031-11-14, 2049-11-25, 2050-05-20, 2067-12-06 (NASA catalog)	—
Drawn band edge vs the pin test (2024-04-08, across the track near 32.7°N)	The central-phase test should flip within 200 m of the edge	—

Known limits

ΔT after 2026 is a forecast; a 1 s error moves a shadow about 0.5 km along its track. Every published prediction shares this.
The Moon is a sphere of mean radius k; no limb profile (Watts/LRO), so contact times near the band edge carry ±1–2 s and the edge itself ±1 km, as in NASA's tables.
No atmospheric refraction in the shadow geometry (only in reported altitudes); the band is drawn at sea level while pins use their elevation.
Time zones from tz-lookup (coarse borders) and the browser's current DST rules for future dates.
Sources: NASA Eclipse Web Site (Espenak), shadow enlargement (Danjon), USNO ΔT, JPL DE441.

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COMPUTING EPHEMERIDES

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