About

The autumnal equinox marks the astronomical instant when the Sun crosses the celestial equator heading southward, placing its ecliptic longitude at exactly 180°. At this moment, day and night are approximately equal in duration at every latitude. Approximate equality, not exact: atmospheric refraction, the Sun's angular diameter (~0.53°), and the observer's latitude introduce deviations of 1 - 8 minutes from a perfect 12h/12h split. The September equinox drifts across a ~53-hour window within the Gregorian calendar, primarily falling on September 22 or 23 (UTC), but reaching September 21 or 24 in edge years near century boundaries. Getting the exact instant wrong matters for agricultural scheduling, satellite thermal modeling, and legal definitions of seasons in some jurisdictions.

This tool computes the equinox instant using Jean Meeus' algorithm with 24 periodic correction terms derived from planetary perturbation theory. The Julian Ephemeris Day JDE₀ is first estimated from a quartic polynomial, then refined by summing sinusoidal corrections keyed to solar mean anomaly M, lunar node longitude Ω, and lunar mean anomaly F. Results are converted from Terrestrial Time to UTC via an approximate ΔT model. Accuracy is within ±1 minute for the period 1900 - 2100. Outside that window, the ΔT extrapolation degrades and results should be treated as estimates.

Formulas

The autumnal equinox Julian Ephemeris Day is computed in two stages. First, a baseline JDE₀ is estimated from the year Y:

JDE₀ = 2451810.21715 + 365242.01767 ⋅ T − 0.11575 ⋅ T² + 0.00337 ⋅ T³ + 0.00078 ⋅ T⁴

where T = (Y − 2000) ÷ 1000. The correction S is then computed from 24 periodic terms:

S = 23∑i=0 A_i ⋅ cos(B_i + C_i ⋅ T)

The final equinox instant in Julian Ephemeris Day:

JDE = JDE₀ + 0.00001 ⋅ SΔλ

where Δλ = 1 + 0.0334 ⋅ cos(166.79° + 35999.373° ⋅ T) − 0.0007 ⋅ cos(74.6° + 35999.36° ⋅ T). Conversion from Terrestrial Time to UTC subtracts ΔT, estimated via polynomial models from the IERS.

Where: JDE₀ = initial Julian Ephemeris Day estimate, T = time in Julian millennia from epoch J2000.0, A_i, B_i, C_i = tabulated coefficients for periodic solar/lunar terms, Δλ = lambda correction factor from solar mean anomaly, ΔT = difference between Terrestrial Time and Universal Time in seconds.

Reference Data

Year	Equinox Date (UTC)	Time (UTC)	Day of Week	Julian Day
2015	Sep 23	08:21	Wednesday	2457289.85
2016	Sep 22	14:21	Thursday	2457654.10
2017	Sep 22	20:02	Friday	2458018.33
2018	Sep 23	01:54	Sunday	2458382.58
2019	Sep 23	07:50	Monday	2458746.83
2020	Sep 22	13:31	Tuesday	2459111.06
2021	Sep 22	19:21	Wednesday	2459475.31
2022	Sep 23	01:04	Friday	2459839.54
2023	Sep 23	06:50	Saturday	2460203.78
2024	Sep 22	12:44	Sunday	2460568.03
2025	Sep 22	18:19	Monday	2460932.26
2026	Sep 23	00:05	Wednesday	2461296.50
2027	Sep 23	06:02	Thursday	2461660.75
2028	Sep 22	11:45	Friday	2462024.99
2029	Sep 22	17:38	Saturday	2462389.23
2030	Sep 22	23:27	Sunday	2462753.48
2031	Sep 23	05:15	Tuesday	2463117.72
2032	Sep 22	11:11	Wednesday	2463481.97
2033	Sep 22	16:51	Thursday	2463846.20
2034	Sep 22	22:39	Friday	2464210.44
2035	Sep 23	04:39	Sunday	2464574.69
2036	Sep 22	10:23	Monday	2464938.93
2037	Sep 22	16:13	Tuesday	2465303.18
2038	Sep 22	22:02	Wednesday	2465667.42
2039	Sep 23	03:49	Friday	2466031.66
2040	Sep 22	09:44	Saturday	2466395.91

Frequently Asked Questions

The tropical year is approximately 365.2422 days, not exactly 365.25. The Gregorian leap-year rule corrects most drift, but a residual ~53-hour window remains within which the equinox instant can fall. Century years not divisible by 400 skip the leap day, causing the equinox to shift earlier in the calendar over multi-decade spans, then snap back after a century correction.

For years between 1900 and 2100, the algorithm matches USNO/IERS published equinox times to within ±1 minute. The dominant source of error is the ΔT approximation, which converts Terrestrial Time (the uniform timescale used in orbital mechanics) to UTC. Beyond 2100, ΔT extrapolation becomes speculative, and errors may grow to several minutes.

No. Atmospheric refraction bends sunlight around the horizon by approximately 0.57°, making the Sun visible when it is geometrically below the horizon. Combined with the Sun's angular diameter of ~0.53°, sunrise occurs ~2-3 minutes early and sunset ~2-3 minutes late. At mid-latitudes, the day of equal day/night (the equilux) typically occurs 3-4 days before the September equinox.

Yes. The equinox is a single astronomical instant defined by the Sun's ecliptic longitude reaching exactly 180°. It occurs at the same UTC moment globally. However, local clock times differ by time zone, so the calendar date may differ: an equinox at 23:50 UTC on September 22 is already September 23 in Tokyo (JST = UTC+9).

The Earth's orbit is not a perfect ellipse. Gravitational perturbations from the Moon, Jupiter, Venus, and other planets introduce oscillations in Earth's orbital velocity and axial precession rate. Each of the 24 terms captures a specific harmonic of these perturbations. The largest term (A = 485, driven by solar mean anomaly) accounts for the eccentricity of Earth's orbit. Omitting the corrections would introduce errors of up to 15 minutes.

The September equinox is the autumnal equinox for the Northern Hemisphere and the vernal (spring) equinox for the Southern Hemisphere. The astronomical instant is identical; only the seasonal label differs. This tool labels it "autumnal" following Northern Hemisphere convention but the computed date/time applies globally.

Axial precession shifts the equinox point westward along the ecliptic at ~50.3 arcseconds per year (one full cycle in ~25,772 years). This changes which constellation the Sun appears in at equinox but does not significantly change the calendar date, because the tropical year (equinox-to-equinox) is the basis of the Gregorian calendar. Precession does affect sidereal calculations and star-chart epoch references.