“Official” Spring

Posted by jns on March 20, 2007

Speaking of the Vernal Equinox, many people were — speaking of it — yesterday but occasionally with some imprecision, saying that spring “officially” arrived at about 2007 EDT. They would be better off saying “astronomically” arrived, since there’s nothing “official” about it: no international committee meets to set the time of the arrival of springtime. Instead, we have chosen to relate the change of seasons to clearly and precisely defined events related to the apparent motion of the sun, events that have been noted since antiquity.

Because of the tilt of the Earth’s axis of rotation (about 23.5°) relative to the plane of its orbit around the Sun, the zenith of the Sun (i.e., it’s largest angle above the horizon each day) changes with the seasons; it’s higher in the sky during summer and lower during winter.^* In other words, the Sun appears to move not only along a path across the sky (the “ecliptic”), but that path appears to move higher and lower as the year progresses.

Now, imagine a line from the center of the Earth to the Sun; where the line passes through the surface of the Earth is the point at which the Sun, at that moment, can be said to be directly overhead. Let’s call this line the “Sun Chord” — so far as I know it has no generally recognized name, and this name sounds harmonious.

As the days of the year pass, the apparent motion of the sun in the sky — or the intersection of the Sun Chord with the Earth’s surface — traces out a squished figure-eight (the “analemma“);^# the exact shape of the analemma depends on the location of the observer.

As the Sun executes its stately analemmic dance, there are fixed extremes to its motion. When the Sun appears at its northern-most point, the Sun Chord passes through the “Tropic of Cancer”, which is at a latitude of about 23.5°N; similarly, when the Sun appears at its Southern-most point, the Sun Chord passes through the “Tropic of Capricorn”, is at a latitude of about 23.5°S. It is not a coincidence that these latitudes have the same angles as the tilt of the Earth’s axis; it is a consequence of geometry. The Sun’s passing through these extreme points is called a “solstice”. In the northern hemisphere we often call the solstice that occurs in June the “summer solstice”, and the solstice in December the “winter solstice”.

Also during the year there are two times — very nearly 6 months apart and 3 months separated from each solstice — when the Sun Chord passes through the Earth’s equator, i.e., when the sun is directly overhead at the equator. When the Sun appears to be moving in a northerly direction this point is the “vernal equinox” (or “spring equinox”); when the Sun is moving in a southerly direction this point is the “autumnal equinox”. “Equinox”, of course, means “equal night”, a name given because the amount of daylight and nighttime are [roughly] equal everywhere on the Earth (except extremely near the poles, which are singular points in this geometrical picture).

And now to the point of this essay. Equinox and solstice times are mathematical concepts describing astronomical events. They occur at well-defined times that can be determined with as much precision as one would care to take. We can calculate to any number of decimal places the exact moment when the Sun Chord intersects the equator, making it possible to say that the vernal equinox occurred at seven minutes past eight (EDT) last evening.

Now, whether spring “officially” started then is another matter entirely, a matter of convention and history, but not a geometric necessity.

[After I'd started writing this piece, Isaac sent me a link to an essay on the vernal equinox in the New York Times by Natalie Angier, "The Tilted Earth at Its ‘Equal Night of Spring’ ", which adds some cultural considerations to the topic. The illustration is kind of cute, too, although it does suggest something more along the lines of a "martini equinox".]
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^*This statement is true in both northern and southern hemispheres, but the seasons are reversed, which should become clear with a moment’s reflection.

^#Yes, this is true at the equator as well: the apparent motion of the sun describes an analemma. It is a common misconception that the sun at the equator is always overhead; what is true is that day and night at the equator are always equal, but there is apparent motion of the sun by about 23.5^° to both sides of vertical.