Always More to Learn — Years
#AMTL rises from its year of silence to prowl the earth once more. And what better way to celebrate the anniversary of its hiatus than by exploring the concept of the year.
The common knowledge about years includes two major contradictions. First, a year is measure the duration of the cycle of the seasons but also the duration of the orbit of the Earth around the Sun. Second, a year is 12 months long and 365 days long (except on leap years, when they’re 366 days). In both pairs of facts, both cannot be true at once. “How long is a day?” could be a #AMTL episode of its own, but for the sake of simplicity all mentions of days will be assumed to be ideal days — exactly 24 hours × 60 minutes per hour × 60 seconds per minute = 86,400 seconds. “What is a month?” and “What year is it?” could, too, but I’ll leave them out for now.
So what is a year? One cycle of the seasons? One orbit of the Earth around the sun? On trip through the calendar?12 months? 365 days? 365.25 days (because of leap year)? It turns out that all of these answers are correct in some circumstances and incorrect in others. Rather than picking one “right answer,” humanity has instead given each of them separate names.
Perhaps the most well-known definition of the year, especially historically, is the cycle of the seasons, called the tropical year. Most calendars (that is, those known as solar calendars) try to match the tropical calendar, because knowing from the date where we are in the cycle of the seasons benefits all sorts of people; farmers, park rangers, sportsmen, environmental activists, statisticians who need to seasonally adjust things, etc. The tropical year gets its name from the angle at which sunlight strikes the Earth. During the summer solstice, sunlight strikes the Earth from straight above the Tropic of Cancer — the furthest north the sun ever rises in the sky. During the winter solstice, sunlight strikes the Earth from straight above the Tropic of Capricorn, its furthest southern reach. This cycle of the angle of the sun gives the year of seasons its name, and is the reason the regions between Cancer and Capricorn are called The Tropics. The two tropic circles get their names from the constellations behind and around the Sun, the same constellations that give the Zodiac signs their names. The tropical year averages 365.24219 days long (365d 5:48:45).
The orbit of the Earth around the sun is the definition most popular with science types (myself included). The relative location of the Earth through its orbit is measured against the so-called “fixed stars,” stars so far away that they don’t perceptibly move across the sky at all. The Latin name for such stars sidera, which gives this type of year the name sidereal. A sidereal year is 365.256363 days (365d 06:09:10), about 20m 25s longer than a tropical year. They drift relative to each other by about one day every 70 years.
Why judge the orbit of the Earth relative to the fixed stars? The measure the cycle of the Earth orbit from its shortest distance from the sun (called perihelion) to the furthest distance and back close again is called the anomalistic year. Anomaly, the word after which this year is named, is a term for what point on an elliptical orbit a celestial body (like our planet) currently occupies. The cycle through all possible anomalies and back to the beginning point takes our Earth 365.259636 days (365d 6:13:53). That means it drifts relative to the sidereal year by about 1 day every 307 years, and relative to the tropical year by about one day every 57 years. (Side note: The tropical year and the anomalistic year are almost exactly reversed from each other. The sun is closest to the Earth on the winter/southern solstice and furthest in the summer/northern solstice, which contributes to the southern hemisphere having slightly more extreme weather than the northern hemisphere. )
The eclipse year relates to the apparent relative positions of the sun and moon as is relevant for predicting eclipses. Specifically, it relates to when the moon’s orbit passes very near to the plane on which the Earth orbits the Sun (which scientists call the ecliptic). There is a roughly two month period twice each eclipse year when the moon is close enough to the ecliptic that eclipses are possible. These eclipse seasons are the only times when either solar or lunar eclipses are possible. This cycle is a bit further out of sync with the previous two types of years, lasting roughly 346.62 days (346d 14:52:54). It drifts more than 18 days per year relative to any of the above definitions.
There are other types of astronomical definitions of a year, but they get increasingly out of sync with our common customary definition from there. The lunar year (12 lunar cycles) is 354.37 days. The Full Moon Cycle (from largest full moon to smallest and back to largest) is 411.78 days. Et cetera. But let’s get away from observable cycles and on to human definitions.
Calendar years are ways of associating an integer number of days and an integer number of months even though the observable phenomena these terms represent never have integer relationships to each other. We like to say this year is 365 days long or 12 months, but that’s never exactly true. We humans love to design up calendars to make it true for convenience sake, using tricks called intercalation — calendar rules that define some days, months, or years differently than others. In the most popular calendar system in the world, the Gregorian calender you probably know and love, intercalation is handled by leap years and leap days. The rule is that any year that is evenly divisible by 4 (such as 2004 or 2016) is a leap year and, thus, is 366 days long instead of 365. An exception to that rule exists for years that are also evenly divisible by 100 (such as 2100 or 1900), which are not leap years. That exception itself has an exception, wherein years that are evenly divisible by 400 (such as the year 2000 that you may remember) are leap years after all. These complex rules make for a very accurate calendar; the Gregorian year is 365.2425 days long, which is only 3 days every 10,000 years different than the tropical year. By then, the length of the day will have increased due to the natural slowing of the Earth’s spin, so the length of the year in days won’t be the same anyway.
Scientists often need to precisely measure long periods of time, and need a very simple definition of a very uniform year for that purpose. To do that, they use Julian Years. The Julian calendar was the most common in the world before the Gregorian calendar was adopted, and the two are very similar. The only difference is that the Julian calendar had simpler leap year rules — one leap year every four years. Thus, the Julian year is exactly 365.25 days long. It’s very convenient as a scientific unit of measure.
These are both solar years — that is, they attempt to match the tropical year (the cycle of the seasons) as closely as possible. The Julian and Gregorian calendars were both adopted by the Catholic church with the intent of preserving the celebration of Easter as closely as possible as it relates to the seasons; the Gregorian just did a better job of it. But other calendars — the Muslim, Jewish, and Chinese calendars, most famously — find it more important to accurately track the phases of the moon than the cycles of the seasons. They track years that are exactly 12 months (lunar cycles) long, which means their holidays and anniversaries move around relative to the seasons. Most lunar calendars have a “leap month” once every three years to minimize that cycle through the seasons. Such calendars are called lunisolar, since they try to track both the months and the seasons but have emphasis on the former. The Muslim calendar notably does not have leap months. Their true lunar calendar means their holidays roam through the seasons making a complete cycle every 30 years or so.
Perhaps you’ve heard the phrase “once in a blue moon.” What is a “blue moon” and how often does it occur? The term refers to when you see the full moon two different, non-consecutive days in the same calendar month. This can only only happen in solar calendars, as a consequence of them not being tied tightly to the lunar cycle. A blue moon happens roughly once every 3 years, the same frequency as leap months in lunisolar calendars and for the same reason. Ya gotta do something with that extra lunar cycle.
I could go on to talk about fiscal years, school years, the great year (the time it takes for the elliptical orbit of the Earth to hula-hoop around the sun), countless other calenders, alternate proposals that were discarded in favor of the Gregorian calendar, different types of months, different definitions of a day, relativistic effects on time measurement, and the day/month/year relationships of other planets. But no. This post is long enough already, and there’s no way I could ever put down everything that is worth knowing. I’d be writing eternally; there is always more to learn.
Does your child’s homework look different lately?
This may as well be titled “how to subtract in your head.” It’s not a bad or wrong way to do it, it’s just abstract rather than visual.