Day
Non-SI unit accepted for use · quantity: time
The Sun does not come back to the same point in the sky after twenty-four hours. At the end of December the day runs half a minute longer than that, in mid-September some twenty seconds shorter, and over a year the difference draws a figure eight on the sky.
01 · Definition
A day is 86 400 seconds exactly, that is twenty-four hours. This is a definition through the SI second and not through the turning of the Earth: the planet is no longer tied to it and on average falls behind by roughly a millisecond a day.
There are in fact several sorts of day. The sidereal is the time of one turn of the Earth with respect to the distant stars, twenty-three hours fifty-six minutes. The solar is the time between two noons, and it is longer: while the Earth turns it also covers almost a degree along its orbit, and to bring the Sun back to the south it must turn those four minutes further. Over a year the extra turns add up to exactly one more sidereal day: there are 366 of them in a year against 365 solar ones.
But the solar day is not constant either. The orbit is elliptical, and in winter the Earth moves faster — so more turning is needed. The axis is tilted, and the projection of the motion onto the celestial equator changes with the season. The two effects add up, giving a spread of about a minute between the longest and the shortest apparent day. The mean solar day is a fiction, introduced by astronomers precisely because clocks cannot run unevenly.
The accumulated difference between apparent and mean time is called the equation of time. Because of it a sundial now runs ahead, now behind, and the Sun photographed at the same hour through the year traces a figure eight on the sky — the analemma. It is the only figure drawn not by an instrument but by the disagreement of two definitions of the same day.
On the left is the analemma: the position of the Sun at the same clock hour through the year. Horizontally the equation of time, vertically the declination. On the right is the length of the apparent solar day for that date against a flat twenty-four hours. The second slider moves your place within the time zone and shows when noon falls by the clock on the wall.
In a day the Earth covers about a degree along its orbit. The turn with respect to the stars is already complete, but the Sun has shifted, and the planet has to turn a little further — those extra four minutes.
02 · Conversion
Enter a value — the sheet will convert it
The day is accepted for use alongside the minute and the hour, but prefixes are not applied to it: there is no “kiloday” in the standard. For longer stretches one goes to the year, for shorter to the hour.
The Julian day in astronomy is exactly 86 400 SI seconds and nothing more: a continuous count from noon on 1 January 4713 BC, with no months, no leap years and no calendar reforms. It is what lets one compare an eclipse recorded by Babylonian scribes with a measurement made yesterday.
The Martian day is thirty-nine minutes longer than ours. Rover operators had to live by it for the first months of a mission, shifting their working day forty minutes later each time — the schedule drifted round the clock in about five weeks.
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03 · Orders of magnitude
days of other worlds04 · Measuring instruments
What catches the planet’s turn
A telescope fixed strictly in the plane of the meridian: it can only rise and fall. The astronomer notes the instant a star crosses the thread, and from a series of such crossings the length of the sidereal day follows. For two centuries this was the most accurate clock there was — accurate because the sky itself served as the pendulum.
A free pendulum in a vacuum vessel, with a slave twin outside. In the 1930s such clocks became more accurate than the rotation of the Earth, and it was they that first showed the planet does not keep to a schedule.
Since 1967 the second has been defined through a transition in the caesium atom, and the day became exactly 86 400 such seconds. The connection to the planet was broken: the Earth may now run fast or slow, and the day will not change by a hair.
Two antennas on different continents listen to the same quasar, and from the difference in arrival time the orientation of the Earth is worked out to fractions of a millisecond. This is how the length of the day is measured today — the planet is checked against the sky, not the other way round.
05 · Writing rules
d in lower case, no prefixes exist
The international symbol is a lower-case d with no full stop; there is no Russian-style abbreviation in English. A capital D is taken by the dioptre, so the case matters. In compound units the day goes with a middle dot or a slash: mg/(kg·d), mm/d.
The last line is not a quibble but the source of real failures. A day with a leap second holds 86 401 of them, and code that assumes exactly 86 400 breaks on that day — this happened in 2012 and again in 2015.
06 · Neighbouring units
The day stands between the hour and the year, and both links are awkward in their own way: there are exactly twenty-four hours in a day, but 365.2422 days in a year, and no rounding removes that fraction — it only moves the problem into the calendar.
1/24 of a day
86 400 s
365.25 d
In the first relation the sign flips for Venus: it turns the other way, and its solar day is shorter than its sidereal one. JD is the Julian date, a continuous count of days for astronomy.
07 · Historical section
How the day was cut loose from the Earth
The second is defined as 1/86 400 of a mean solar day. The definition held for nearly a century and a half and looked unshakeable: the Earth was the most reliable clock available.
Quartz and pendulum clocks show it: the length of the day wanders by milliseconds through the year. To blame are the seasonal redistribution of air masses and the tides — the planet is not a rigid body and does not keep to a schedule.
A compromise: the clocks run on the atom, but every few years an extra second is inserted into the scale so that noon does not drift away from the Sun. Twenty-seven insertions in half a century, all of them for the sake of a difference no one notices without instruments.
The General Conference decides to stop inserting seconds: digital systems break on them more often than the drift from the Sun troubles anyone. By 2035 the scale will finally part company with the planet.
A unit that stopped coinciding with the thing it names
Tidal friction brakes the Earth: the Moon pulls at the ocean, the bulge lags behind the rotation and drags the planet back. The day grows longer by about 1.8 milliseconds a century — in the Devonian it was under twenty-two hours, and coral growth bands confirm it: about 400 bands to a year.
So the modern day is a unit honestly cut loose from the phenomenon it is named after. 86 400 seconds is a number, and the turning of the planet is a process that no longer fits it — the difference is made up by leap seconds, and from 2035 it will simply be allowed to accumulate.
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.