Year
Non-SI astronomical unit · quantity: time
By 1582 the spring equinox had slipped from 21 March to the 11th. Easter was still being computed by a rule anchored to 21 March, and so it was slowly wandering into summer. Gregory XIII ordered ten days struck from October: the 4th was followed straight by the 15th. The reason was simple — the Julian year is 11 minutes longer than the real one, and over the 1257 years since Nicaea those minutes added up to almost ten days.
And it turns out the “real year” is not one thing either. The Earth comes back to the equinox in one span of time, to the same star in another, to perihelion in a third. The differences are minutes, but over centuries they become days — which is exactly what the calendar reformers kept running into.
01 · Definition
A year is the time of one orbit of the Earth around the Sun. The catch is where you start counting from. The tropical year runs from equinox to equinox and lasts 365.242190 days; the sidereal year returns to the same star and is longer; the Julian year is simply defined as 365.25 days exactly. Which of them you mean decides everything that follows.
The tropical year is 20 minutes 24 seconds shorter than the sidereal one. Precession is to blame: the Earth’s axis slowly sweeps a cone, and the equinox point creeps backwards along the orbit to meet the Earth early. Those twenty minutes a year are the whole of precession, divided out over a single orbit.
The anomalistic year is longer than the sidereal one: the orbit itself also turns, but forwards, so the Earth needs a little extra to reach perihelion again. Three different years, three different answers to the same question of when the Earth is “back”.
The calendar keeps to the tropical year: people care about seasons, not stars. There is no whole number of days in it, and that single fact is the source of every leap rule ever written. Whatever you do, the quarter-day has to go somewhere.
Set the leap rule — how many extra days to insert per 400 years — and watch where the equinox goes. The dashed line is the Egyptian year of 365 days with no leap days at all; the solid one is your rule. Anything above 97 runs the calendar fast, anything below runs it slow.
The dashed oval above is the path the Earth’s axis traces in 25 771 years. Because of it the equinox point slides backwards along the orbit, which is why the tropical year is shorter than the sidereal one. In about thirteen thousand years Vega will be the pole star.
02 · Conversion
Enter a value — the sheet will convert it
Prefixes on the year are allowed and geologists use them freely: ka for a thousand years, Ma for a million, Ga for a billion. The age of the Earth is written 4.54 Ga, and that is proper notation.
The third family in the table is the year in documents. There it is sometimes exactly 365 days and sometimes 360: the banking year of twelve equal months was invented so that interest would divide without remainder, and it has outlived the abacus by a wide margin.
The Julian year is the only one whose length is fixed exactly: 365.25 days, precisely 31 557 600 seconds. It matches nothing in nature — it was simply agreed on, because astronomy needs a year that does not drift. The light-year is defined through it.
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03 · Orders of magnitude
from a single orbit to the age of the universe04 · Measuring instruments
What catches the length of the year
A hole in a cathedral dome and a brass strip across the floor. Every noon the spot of sunlight falls on the strip, and its position tells the date. Such meridian lines were built into churches across Italy in the seventeenth century, and they measured the length of the year better than any instrument of their age.
The ring is set in the plane of the celestial equator. While the Sun is south of it the shadow falls inside; at the moment of the equinox the ring’s shadow lands exactly on the ring itself. Simple enough to build in bronze, and precise to within a few hours.
A tube fixed strictly in the plane of the meridian: it can only tilt up and down. The astronomer records the instant a star crosses the crosshair, and from a series of such crossings the length of the year is derived. This is how it was measured from the eighteenth century until well into the twentieth.
Today the year is not measured against the Sun. Antennas on different continents listen to the same quasar, and from the difference in arrival times the orientation of the Earth is recovered to fractions of a millisecond. The year comes out as a by-product of tracking the planet’s attitude in space.
05 · Writing rules
a, ka, Ma — and the everyday yr
The symbol for the year is the lowercase Latin a, from annus. SI prefixes on it are allowed: ka, Ma, Ga. A capital A would be the ampere, so the lowercase matters. In English yr is common in everyday writing, and in Russian the abbreviation is «г.» with a full stop.
A separate trap is which year is meant. In astronomy, and in the definition of the light-year, it is the Julian year of exactly 365.25 days. In the calendar it is the Gregorian mean of 365.2425. In nature it is the tropical year of 365.242190. Three numbers, one symbol, and no way to tell them apart from the symbol alone.
06 · Neighbouring units
The year sits between the day and the century, and both joints are uneven. The number of days in it is not whole, and the century is simply a round hundred with nothing astronomical behind it. The only exact relation the year has is with the Gregorian cycle: 400 years make 146 097 days.
1/365.2422 of a year
31 556 925 s
10 centuries
Gregory’s rule comes down to one fraction: 97 leap days per 400 years instead of a hundred. Hence 146 097 days in the cycle and a mean year of 365.2425 days — 26 seconds longer than the tropical one. A day of error accumulates in 3226 years; nobody was designing a calendar to last that long.
07 · Historical section
How the year was mended four times
The pontiffs inserted an extra month whenever they saw fit, and the calendar drifted three months away from the seasons. Caesar brought it back in one blow: the year 46 BC was given 445 days and is remembered as the year of confusion. From then on, one extra day every fourth year.
The Council tied the reckoning of Easter to the spring equinox, and the equinox to 21 March. From that moment the calendar’s error stopped being an astronomer’s concern and became a matter of church practice: the drift was moving the feast itself.
Gregory XIII’s bull removed the ten accumulated days and changed the rule: years divisible by 100 are not leap years unless they are also divisible by 400. Catholic countries adopted it at once; Britain held out until 1752 and by then had to strike eleven days, not ten. Russia came over only in 1918.
Milutin Milanković proposed making century years leap when the remainder of division by 900 is 200 or 600: 218 leap days per 900 years, a mean year of 365.242222 days. That is closer to the real one than the Gregorian rule, and the Orthodox conference of 1923 adopted it — though the two calendars will not part company until 2800.
A unit that will not hold still
The metre has a definition through the speed of light, the second through the caesium frequency. The year has none: it is not fixed by an experiment but read off a planet that keeps changing its own motion. There is nothing to anchor it to.
That is why the year is not part of the SI. For their computations astronomers took the Julian year and simply assigned it an exact length — 365.25 days, 31 557 600 seconds. Not because nature says so, but because a fixed number is needed, and this one is the roundest.
Catalogue · units of measurement
A passport for every quantity
Seven base SI units, twenty-two derived ones with their own names, and units outside the system without which neither engineering nor the calendar would work.