Equinox and Solstice Times

Definitions

An equinox occurs when the geocentric apparent ecliptic longitude of the Sun is zero (vernal equinox) or 180° (autumnal equinox) per the Astronomical Almanac glossary. That seems equivalent to the notion that the Sun is exactly on the equator at an equinox, since the intersections of the ecliptic and celestial equator are the zero and 180° points on both circles. However, the Sun oscillates a few tenths of an arc second north and south of the ecliptic on a monthly cycle, so its center doesn't pass exactly through those intersections. Consequently it's at zero longitude, zero declination, and zero right ascension at three different times.

Zero geodetic latitude occurs at still another time because the geodetic pole doesn't coincide with the rotation axis. (The latter is the basis of declination.) The point where the rotation axis emerges from the crust moves continuously in a quasi circular path about 20 feet in diameter. Moreover, the geodetic pole is a quarter second of arc outside the circle. Therefore, the geodetic and celestial equators are out of coincidence by several tenths of an arc second.

All these complications mean there are four different "equinoxes". For example, here are the times (UTC) on 2017 September 22. Geodetic latitude is calculated with polar motion values from IERS Bulletin B: x = 230.274 mas (milli arc seconds), y = 320.857 mas. The second line is the correct equinox.

The situation at solstice is a little simpler since the circle of 90/270 degrees longitude is also the circle of 6/18 hours right ascension. On the other hand, the Sun's declination and geodetic latitude change very slowly near the solstices, so the times of maxima are not well defined and the discrepancy between the celestial and geodetic equators has a large effect. For instance, geodetic latitude is constant within 1 mas for 18 minutes near the 2017 June 21 solstice. Maximum latitude occurs at 0437 UTC. Declination is constant within 1 mas for 26 minutes, and maximum at 0421. The true solstice time, computed with ecliptic longitude, is 0424.

For simplicity in the calculation above I used polar motion angles x = 130.474 mas, y = 454.980, which are valid at the nearest UTC midnight. In reality the pole can move more than one mas per day.

Another problem is that polar motion has a random component and thus the extremes of the Sun's geodetic latitude are not precisely predictable in the long term. Clearly, neither latitude nor declination is suitable for the precise definition of a solstice. The choice between right ascension and ecliptic longitude is not so clear. Both have an average rate of 360° per year. Right ascension is simpler to calculate but longitude has a more constant rate throughout the year. In a cursory check I saw ±5% variation from the mean, vs. ±10% for right ascension. I think both are constant enough, since solving for equinox and solstice times requires iteration anyway, but the formally correct angle is ecliptic longitude with respect to the true equator (i.e., affected by nutation). If nutation is neglected, the computed times can be several minutes different from the Astronomical Almanac.

Ecliptic coordinates are probably too much for a non-technical person, so I don't see any harm if the public believes equinoxes and solstices are calculated from the geographic latitude of the Sun.

Short Term Table (UTC)

This table extends as far into the future as I can confidently predict leap seconds.

Long Term Table (TAI)

UTC is easy to convert to civil tme, but it's problematic for long term equinox and solstice predictions due to the step adjustments (leap seconds). These are not predictable several years in advance. If you estimate future leap seconds wrong, your times are in error the same amount. UT1 gives similar trouble, except that its error is a real number which depends on the accuracy of your delta T estimate. Therefore, I give long term predictions in TAI.

In reality, the computation is performed in TT (Terrestrial Time), since that's the time scale of the solar system ephemeris and the precession / nutation model. But TT would make extra work for the table user, since you must first subtract a constant 32.184 seconds to obtain TAI, then subtract the (non-constant) TAI-UTC value to obtain UTC.

In the table below, times are TAI to eliminate the subtraction of 32.184. You need only subtract a whole number of seconds to get UTC. For example, UTC is 37 seconds behind TAI in 2025, so the March equinox occurs at 09:02:06 TAI or 09:01:29 UTC. The difference TAI-UTC increases one second after each leap second. The current value is easy to find online, for example, at the International Earth Rotation Service site. (TAI-UTC will remain 37 seconds throughout 2025.) If leap seconds are discontinued, TAI-UTC becomes constant and the table is still accurate.

Tables were computed with the JPL DE431 or DE441 ephemeris, IAU 2006 precession model, and 2000B nutation. Sun geocentric apparent ecliptic longitude with respect to the true equinox is 0 (March equinox), 90° (June solstice), 180° (September equinox), or 270° (December solstice).

Accuracy

I believe future improvements will not change my times more than two seconds. The tools of the late 1990s (JPL DE406 ephemeris, IAU 1976 precession model, and 1980 nutation model) generate almost identical results. Most of the difference is due to a known problem in the 1976 precession model. In 2020 its pole is about 100 mas in error, whereas the 2006/00B model is within 1 mas of the true pole. But even with a flawed precession model the above tables are duplicated within two seconds.

The solar system ephemeris has little effect. DE406 (1997) and DE431 (2013) give identical results in 2030 and 2031.

Calculation Example

Begin with UTC. Convert to Terrestrial Time, the scale of the ephemeris and precession / nutation model. Delta T doesn't matter because Earth rotation has no effect on the calculation.

2026-06-21 08:24:30.0 UTC
2026-06-21 08:25:39.2 TT

The JPL DE441 ephemeris gives barycentric Earth and Sun positions with respect to the ICRS.

-0.0082026 -0.9175173 -0.3976112 unit vector (Earth)
1.528243e+008 distance (km)
-0.3312812 -0.8730533 -0.3578138 unit vector (Sun)
8.499729e+005 distance (km)

Subtract Earth from Sun to get Sun geocentric geometric place.

0.0063938 0.9174876 0.3977130 unit vector
1.520204e+008 geometric distance (km)
 89.60073° +23.43529° Sun geometric RA, dec (ICRS)

That's where the Sun is. Where it was, when it emitted the light that reaches us now, is its astrometric place. The difference is invisible at this precision.

 89.60073° +23.43529° Sun astrometric RA, dec (ICRS)

Next, correct for aberration due to Earth's velocity. Get velocity from the JPL ephemeris, apply it to astrometric place to obtain apparent place.

0.9999519 -0.0090081 -0.0038809 Earth velocity unit vector
2.533241e+006 km/day
 89.59462° +23.43527° Sun apparent RA, dec (ICRS)

That's the geocontric apparent place of the Sun in the ICRS. Transform coordinates to the true equator and equinox system with the IAU 2006 precession model and 2000A nutation model.

 90.00000° +23.43793° Sun apparent RA, dec (true equator of date)

X-rotate the coordinate frame by the true obliquity (23.43798°) to obtain geocentric apparent ecliptical coordinates. This last step is not necessary to calculate a solstice because the circle of 90°/270° longitude is also the circle of 90°/270° (6/18 hours) right ascension.

 90.00000°  -0.00004° Sun ecliptical lon, lat

Longitude is 90°, so this is the 2026 June solstice. Of course normally time is unknown, so begin with an approximate time and correct it by iteration until longitude is the desired value. This is easy since the Sun longitude rate is an almost constant 1° per day.

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(Last revision 2026-05-24)