During the equinoxes, the Earth's axis of rotation is exactly perpendicular to the direction of the sun's rays, and therefore the length of the day is the same as the length of the night. Obviously, the September equinox marks the beginning of fall in the Northern Hemisphere, while it marks the beginning of spring in the Southern Hemisphere. The reverse is true for the March equinox.
The Solstices
Literally, the solstice is the time when the Sun reaches the point of maximum or minimum declination in its apparent motion along the ecliptic. This means that the summer and winter solstices are the longest and shortest days of the year, respectively. Like the equinox, the solstice is due to the tilt of the Earth's axis of rotation relative to the ecliptic (the apparent path the Sun takes during the year relative to the background of the celestial sphere). The term solstice is derived from the Latin solstitium, meaning "the sun stands still," because on solstice days the sun stops rising (or falling) relative to the celestial equator and appears to stand still. The Sun reaches its maximum value of positive declination in June (marking the beginning of boreal summer and austral winter) and its maximum value of negative declination in December (marking the beginning of boreal winter and austral summer).
Precession of the equinoxes
The precession of the equinoxes is one of the motions of the Earth that causes the orientation of the Earth's axis of rotation to change with respect to the fixed stars. The Earth's axis precesses (similar to a spinning top) due to two factors: the shape of the Earth (flattened spheroid, protruding at the equator) and the gravitational forces of the Moon and Sun. The precessional motion makes one complete revolution about every 25,772 years: in 12,000 years, the pole star will be Vega.
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