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Astronomy · the equation of time, day by day

Sixteen minutes

The sun doesn't keep your clock's time. The gap shifts every day of the year, and four times it drops, for a moment, to zero.

For centuries, sundials were the only public instrument for measuring time: a shadow sliding across an engraved plate, assumed to move in step with the sun. But the sun itself doesn't keep uniform time. Earth's orbit is slightly elliptical, and its axis is tilted against the plane of that orbit, so the true solar day — the time between two consecutive passes of the sun through its highest point in the sky — stretches and shrinks through the year. A mechanical clock ticks the same way every day of its life; the sun doesn't.

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The equation of time

The gap between the two clocks has a name centuries old: the equation of time. In late October, the sun reaches its true noon — its highest point in the sky — sixteen minutes ahead of your clock, around 11:44, not 12:00. By mid-February, it runs late: solar noon falls closer to 12:15. Over a full year, the clock in the sky drifts back and forth against the clock on the wall across a range of just over thirty minutes, and the motion isn't linear — it speeds up, stalls, then reverses, twice.

Sixteen minutes sounds small. On an ordinary clock face, where the minute hand covers six degrees per minute, it's still more than a quarter turn — drawn to scale, the sun's hand would swing almost to three o'clock or to nine.

Drag the slider across the year and watch the two hands: one keeps your time, the other keeps the sun's.

12 3 6 9

October 31

Your clock: 12:00

The sun: 11:44

The sun reaches its noon 16 minutes ahead of your clock.

JanFebMarAprMayJunJulAugSepOctNovDec

Only 4 days a year do the two clocks agree exactly: April 16, June 14, August 31, and December 24.

+16 min · October 31the sun's earliest noon
−15 min · February 13the sun's latest noon
31 minthe full swing, end to end

The cause has two overlapping components. The first comes from the shape of the orbit: Earth moves faster in January, when it's closest to the sun, and slower in July, when it's farthest — Kepler's second law, the same one that keeps planets pinned to physics textbooks, translating here directly into minutes gained or lost. The second comes from the tilt of the axis: the sun doesn't move along the celestial equator but along the ecliptic, tilted 23.4° against it, and the projection of its motion onto the equator — the one that matters for civil time — compresses and stretches four times a year, around the equinoxes and solstices. The two effects run on different periods, adding to and canceling each other in turn.

The result is the figure-eight the sun traces if photographed at the same clock time, every day, for a full year — the analemma, the thin silhouette sometimes drawn on globes, out over the Pacific, with no explanation attached.

Each point is one day of the year: horizontally, how early or late the sun reaches its noon; vertically, how high it climbs that day.

The clocks on our wrists haven't followed the real sun in a long time. From the 19th century on, railways and the telegraph needed a single hour, the same at every station down the line, whatever the sun's height above it — and so mean time was born, then time zones, then today's coordinated universal time. The sun stayed exactly as irregular as ever; we simply stopped listening to it.

The gap is computed from Earth's actual position in orbit, using a standard solar-astronomy formula (the equation of time, plus solar declination), accurate to about a minute. Times shown are local mean solar time, without time-zone or daylight-saving correction, which is added separately, as a fixed constant for each place on Earth.