Autumn equinox 秋分

陰陽相半也，故晝夜分而寒暑平

By definition：

the instance of the autumnal equinox in the northern hemisphere corresponds to the moment when the apparent geocentric longitude of the center of the Sun is equal to 180 degrees.

At this moment, the right ascension is not exactly equal to 12 h and the declination of the center of the Sun is not zero, because the apparent latitude of the center of the Sun is not zero, but these last two values ​​are close to zero. The direction of the center of the Sun is then very close to the direction opposite the gamma point, intersection of the ecliptic and the celestial equator. The definition of this direction is therefore unique on the celestial sphere.

The direction of the autumn equinox, which is unique, should not be confused with the fact that the Sun passes through this direction. Thus, in the northern hemisphere, the beginning of autumn corresponds to the passage of the Sun in the direction of the autumn equinox, while this same phenomenon represents the beginning of spring in the southern hemisphere.

Our calendar (the Gregorian calendar) is constructed in such a way as to avoid drift in the dates of seasonal changes by maintaining a quasi-fixed date for the start of each season.

2024:

The date of the autumn equinox is, in 2024, Sunday, September 22 at 12:43:40.82 UTC, or 14:43:40.82 in French legal time (UTC + 2 h). At this moment the geocentric latitude of the center of the Sun is 0.56″, its right ascension is 12 h 0 min 0.015 s and its declination is 0.52″. As can be seen, the declination and latitude are very close to zero and the right ascension is very close to 12 h. This is why it is often said that the Sun is in the opposite direction to the gamma point, which is partly correct since the apparent diameter of the Sun is of the order of thirty arc minutes.

However, for a calculation to the nearest second of time, the choice of definition is important. Indeed, the declination of the center of the Sun is zero at 12:44:12.69 UTC and the right ascension of the center of the Sun is equal to 12:00 at 12:43:34.85 UTC.

2 factors why not equal day and night:

- Sun is a disk, not a point 

- Atmospheric refraction

Reference 

IMCCE 

Earthsky