THE GROUND / STRATUM / VERIFICATION VENUE
The Sun is a bad timekeeper. Measured against the steady clock on your wall, it runs as much as 16 minutes fast and 14 minutes slow over a year — and if you photograph it at clock-noon every week, that error draws a slow figure-eight across the sky. Two numbers make the whole shape. One of them hides a surprise almost no one believes the first time.
I am a sundial, and I make a botch
Of what is done far better by a watch.— Hilaire Belloc, sundial epigram
Noon is supposed to be simple: the moment the Sun crosses due south, the highest point of its day. Set a sundial to it and you have the oldest clock there is. But carry a good mechanical clock alongside the sundial for a year and they will quarrel. Sometimes the Sun arrives at the meridian early; sometimes late; the gap swings between about +16 and −14 minutes and crosses zero only four times a year. That swinging gap has a name — the equation of time — and it is not a defect in either instrument. It is the shape of a planet's year, read off the sky.
"Clock time" is a deliberate fiction. We agreed to let an imaginary mean Sun march around the sky at a perfectly even pace, because the real Sun does not. The equation of time is exactly the difference: apparent solar time minus mean solar time, true noon minus clock noon. Remarkably, the entire curve falls out of just two facts about the Earth — and you can watch each one do its work below.
Mark the Sun's position at the same clock-time each week for a year — its height above the horizon, and how far it sits east or west of due south — and the marks do not pile up in one spot. They trace a long, lopsided figure-eight: the analemma. The up-and-down is the seasons (the Sun climbs in June, sinks in December). The side-to-side is the equation of time — the Sun running ahead of or behind the clock. Drag through the year and watch the single point walk the eight.
The eight is lopsided on purpose. Its big lower loop is winter, its small upper loop is summer — and the asymmetry between them is the whole story.
The equation of time is a sum of two independent effects, and the page splits them so you can switch each off:
The orbit (eccentricity). Earth's orbit is a slightly squashed circle, so by Kepler's law the Earth sweeps faster when it is nearest the Sun (early January) and slower when it is farthest (early July). The real Sun therefore drifts ahead of the steady mean Sun and back again — a smooth wave that rises and falls once a year (period: one year), about ±7.7 minutes.
The tilt (obliquity). Even in a perfectly circular orbit the Sun would still keep bad time, because it moves along the tilted ecliptic, not along the equator that our clocks are ruled by. Near the solstices that tilted motion is mostly "sideways" along the equator and the Sun races; near the equinoxes it climbs and the clock catches up. That gives a wave with two humps a year (period: half a year), about ±9.9 minutes.
Add them and you get the crooked curve. Toggle the causes below — kill the orbit and you get a pure annual wave; untilt the axis and you get a clean semiannual one; the truth is their sum.
Now the surprise. Everyone knows the shortest day of the year is the winter solstice, around December 21 — the day with the least sunlight. It is natural to assume that is also the day of the earliest sunset and the latest sunrise. It is not. At mid-northern latitudes the earliest sunset comes about two weeks before the solstice, and the latest sunrise about two weeks after it.
The reason is the crooked clock. Through December solar noon itself keeps sliding later by the clock (the equation of time is plunging). Right at the solstice the length of the day is barely changing — it is at its flat minimum — so that steady drift of noon wins: it drags sunset earlier well before the solstice, and holds sunrise later well after it. Pick a latitude and watch the three dates pull apart.
Slide toward the equator and the gap yawns open — at 20°N the earliest sunset beats the solstice by more than three weeks. Slide toward the pole and it narrows, because up there the day-length is changing so violently near the solstice that it overwhelms the clock's drift. The effect is real everywhere; only its size depends on where you stand.
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research/equation-of-time/verify.mjs). The four extrema and zero-crossings match the values the USNO, Meeus and the Astronomical Almanac publish; the apparent-position variant reproduces Meeus's own worked Example 28.b (1992 Oct 13 → +13m 42.7s) to a second. Declared free choices: a reference year of 2026 — the dates drift by ~1 day across the four-year leap cycle, and very slowly over centuries as the tilt and orbit change; the standard sunrise altitude −0.833° (refraction + the Sun's half-width); and the observer's longitude, which is irrelevant to the asymmetry because it shifts every sunrise and sunset by the same amount. The day-resolution dates above are good to about a day; that is the honest grain of this model, and it is far finer than the two-week effect it is measuring.
There is a small record-correction folded into all of this, and it is the venue's favourite kind: the thing "everyone knows" is half true. The shortest day really is the solstice — that part is exact. But the earliest sunset and the latest sunrise are not, and a calendar that quietly equates "least daylight" with "earliest dark" is averaging away a real, computable, two-week structure. The mean Sun was invented for convenience, and convenience always costs a little truth; the equation of time is the size of the bill, written in minutes.
It is the same lesson the rest of this venue keeps finding in other clothes. A summary — a mean, an average rate, a single steady clock — is a projection, and a projection throws shape away. Here the shape it throws away is a figure-eight, and you can stand outside on a clear December afternoon and watch the part of it that says: the dark is already coming earlier, and the solstice is still two weeks off.
Kindred ground — The Farthest Point (another fact about the Earth re-derived from its defining constants) · The Fixed Point (the venue's self-checking instrument) · Incommensurable (a calendar's debt to a number that won't divide).