Century
Non-SI unit for counting time · quantity: time
In 1859 Urbain Le Verrier finished his calculation of Mercury’s motion and found a discrepancy. The perihelion was advancing faster than the pull of the known planets allowed — by about 38 arcseconds per century by his reckoning. The figure was small, but the calculation was solid, and the gap would not close.
Le Verrier decided a planet was hiding between the Sun and Mercury and named it Vulcan. It was searched for during eclipses, it was “seen” by amateurs, its orbit was computed. Vulcan does not exist. The problem was not a missing planet but the equations themselves.
01 · Definition
A century is a hundred years. That is the whole definition: there is no motion of a planet in it, no oscillation of an atom, no standard of any kind. It is a counting unit — ten times ten, and nothing more.
For astronomers, though, the century is a working unit with an exact length. The Julian century is 36 525 days, which is a hundred Julian years of 365.25 days each, or 3 155 760 000 seconds. Nothing is measured here: the number was assigned, and that is precisely what makes it useful.
This is no accident of convenience. Slow effects in mechanics are called exactly that — secular. Precession, the drift of a perihelion, the braking of the Earth’s spin: all of them are quoted per century, because over a year they are too small to see and over a millennium the formula stops being linear.
The panel on the right works out four such drifts. The slider sets how many centuries have passed and shows when the accumulated amount becomes visible.
Four slow drifts. The blue curve is how much piles up over the chosen number of centuries; the red line is the threshold at which the effect becomes visible in observations. Some cross it in a single century, others need twenty.
Mercury does not return to the same point: the ellipse slowly rotates about the Sun, and the perihelion creeps forward. Most of that comes from the pull of the other planets. What is left over after they are all accounted for is 43 arcseconds per century — and for half a century nobody could explain it.
02 · Conversion
Enter a value — the sheet will convert it
The base is the Julian century: exactly 36 525 days. It is the only length of a century with no uncertainty, because it was assigned rather than measured.
The third family in the table is secular rates. Enter a number of centuries and the table shows how much each slow process piles up in that time.
The twentieth century means the years 1901–2000, not 1900–1999. The count of years began at one; there was no year zero, so the first century ran from 1 to 100, and every century since ends on a round number rather than starting with one.
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03 · Orders of magnitude
from a single century to the age of the universe04 · Measuring instruments
No instrument — an archive instead
Babylonian scribes wrote down eclipses with the date and the time. We know how far the Earth has fallen behind uniform time precisely because those records exist: an eclipse computed for a uniformly spinning Earth lands in the wrong place, and the shift gives ΔT.
An observatory measures star positions for decades and prints a catalogue. A century later the positions are compared with a new one, and from the difference come proper motions and precession. No single observer sees the whole measurement through.
A laser pulse goes to the corner reflectors left on the Moon and comes back a couple of seconds later. Since 1969 this has told us that the Moon is receding by 3.8 centimetres a year — 3.80 metres per century — and that the Earth’s spin is slowing to match.
Four hundred clocks in different countries are combined into a single scale, TAI. It runs evenly, while the Earth does not: the difference between them accumulates, and it is from this that we know the day is lengthening by about 1.8 milliseconds per century.
05 · Writing rules
In Roman numerals, and with no year zero
The century has no official symbol: it is not in the SI at all, and astronomers write cy or century, sometimes just c. That last one clashes with c for the speed of light, so in formulas the full word is preferred. SI prefixes go on the year — ka, Ma, Ga — never on the century.
A trap of its own is the years before our era. Historians have no year zero: 1 BC is followed directly by AD 1. Astronomers do have one — for them year 0 is 1 BC, and 2 BC is −1 — otherwise the arithmetic of intervals breaks down. The same date can therefore be written two ways, and they differ by one.
06 · Neighbouring units
Everything around the century rests on ten: the year, the century, the millennium. None of these boundaries corresponds to anything in nature. The one uneven join is with the week: 36 525 does not divide by seven, so the days of the week shift across centuries and never come back to the same place.
1/100 of a century
36 525 d
10 centuries
This is why the century is convenient. The day lengthens slowly, but the drift of clocks against the Earth’s rotation grows as the square of time, and over a hundred years it is already tens of seconds. A year is too short to see it in; a millennium is too long for the formula to stay simple.
07 · Historical section
First a lifetime, then a hundred years
Among the Etruscans a saeculum ended when the last person born at its beginning died. The length was therefore not fixed — a hundred years, a hundred and ten — and priests announced the end of one saeculum and the start of the next. The unit was measured against a human life, not against a number.
Dionysius Exiguus proposed counting years from the Nativity and began with the first: zero had no place in his reckoning, because Roman numerals had no zero at all. The convention has stood for fifteen hundred years, and every argument about when a century begins comes out of it.
Le Verrier had already found Neptune on paper, and he tried the same trick again: if Mercury is moving wrongly, something unseen must be pulling it. The reasoning had worked once, and there was every reason to expect it to work twice.
Einstein worked out Mercury’s motion with the new equations and got an extra advance of 43 arcseconds per century — the very number that had been left over. Nothing was fitted: the value fell out of the theory on its own. That is the moment general relativity stopped being an idea and became physics.
A unit longer than a person
A century cannot be measured with a single instrument. Any clock will either stop within a hundred years or be rebuilt, recalibrated and moved. What survives instead is the record: a tablet, a catalogue, a series of observations. The measurement outlives every device that took part in it.
Hence the odd property of the century. It has no standard, yet it has an exact length: 36 525 days, to the second. Every other unit is the other way round — a standard first, and the number after. Here the number came first, and no standard was ever needed.
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