Every Leap Second Was Already in the Spin

One

The day is not 86,400 seconds

Until 1967 the second was a piece of the day: one part in 86,400 of the mean solar day, and later a fraction of a particular year. Then the definition moved to a caesium atom, and the two came apart. The second stopped being something the Earth defines and became something the Earth is measured against.

What the Earth does, measured against it, is this. Every point below is one day of the IERS combined solution, from 1 January 1962 to the most recent day published: how much longer than 86,400 SI seconds that day ran. Scrub across it.

Two things are visible without any analysis. The day was running about three milliseconds long through the early 1970s, which is why leap seconds started arriving almost annually. And the trace has come down through the zero line: since 2020 the typical day has been shorter than 86,400 seconds.

Two

The clock, rebuilt from the planet

The rule that governs civil time is short. From ITU-R TF.460-6, the recommendation in force since 1972:

1.2 The departure of UTC from UT1 should not exceed ± 0.9 s.

2.1 A positive or negative leap-second should be the last second of a UTC month, but first preference should be given to the end of December and June, and second preference to the end of March and September.

Recommendation ITU-R TF.460-6, §1.2 and §2.1

Nothing in it mentions judgement. So take it literally. Start on 1 January 1972 with the published offset, add up the measured excess of each day, and step by a whole second at the end of June or December whenever the offset would otherwise leave the tolerance before the next such date. One free number: the tolerance. Everything else is the planet.

Set the tolerance to the 0.9 s the standard prints and the machine produces the right number of leap seconds, 27, but puts most of them six months late. Drag it down and watch the dates snap into place.

So the leap seconds really are in the spin. What is not in the spin is the number 0.9. The record's own tolerance is about two thirds of a second, and the reason is written into the standard itself: the IERS has to predict where the offset is going, six months at a time, and it keeps a margin. The same recommendation caps the broadcast approximation DUT1 at 0.8 s and calls the remaining tenth a safeguard for the IERS against unpredictable changes in the rate of rotation of the Earth. What the record shows is a bigger safeguard than that, taken in practice.

Three

The Moon is inside the day

The Sun and the Moon do not only raise the sea. They deform the whole planet, and the axially symmetric part of that deformation changes the Earth's moment of inertia. Angular momentum is conserved, so the spin rate answers. The effect is entirely predictable from the lunar and solar orbits, and the IERS Conventions publish it as 62 terms in the Delaunay arguments, which is what the curve below is: a prediction that has never seen an Earth-rotation measurement.

You do not have to take the overlay on trust. Take the amplitude of the best-fitting sinusoid at every period from 8 to 400 days, over the 26 years of GPS-quality data, and do it twice: once on the measurement, once on the measurement minus the prediction. The lunar lines should collapse. The solar ones should not, because the winds have an annual and a semiannual cycle of their own sitting at exactly those frequencies.

Four

Nine and a half years of silence

The last leap second was inserted at the end of 2016. Nothing has been inserted since, and that is now much the longest quiet stretch in the history of UTC. The reason is the thing you already saw in section one: the day stopped running long.

In 2024 Duncan Agnew put a date on it in Nature: removing the effect of polar ice melt from the observed angular velocity leaves the liquid core losing angular momentum at a steady rate, and extrapolating that, his paper concludes that UTC as now defined will require a negative discontinuity by 2029, three years later than it would have without the ice.

That is not a refutation of the mechanism. A steady core trend and a four-year pause are entirely compatible: the decadal variability visible everywhere in section one is exactly the size of the effect being argued about. It is a statement about what the predicted quantity has actually done since the prediction, which anyone can check against the same file, on any later day, and which will read differently then.

The question may be settled administratively first. In 2022 the 27th General Conference on Weights and Measures resolved that the maximum value for the difference (UT1-UTC) will be increased in, or before, 2035, and asked for a specific new value to be drafted for agreement at its 28th meeting. That meeting runs from 13 to 15 October 2026 at Versailles. If it passes, the tolerance you have been dragging around in section two stops being 0.9 s, and the leap second stops.

Five

What sixty-four years of the best data cannot tell you

Everyone knows the Moon is slowing the Earth down. The tide it raises leads the Earth-Moon line, torques the planet, and lengthens the day. Here is the world's most precise record of the length of the day, 23,560 consecutive daily values from the best instruments ever pointed at the problem. Fit a straight line to it and ask for the rate in milliseconds per century, the number the textbooks quote.

Over the whole record the answer is about , and it has the wrong sign. Slide the window and it swings between roughly without ever getting near the truth. The signal being asked for is a couple of milliseconds per century; the core-driven wobble sitting on top of it is a couple of milliseconds outright, and it turns over on a timescale longer than the record.

The number that survives comes from a much worse instrument used over a much longer baseline. Stephenson, Morrison and Hohenkerk assembled Babylonian, Chinese, Arab and European reports of eclipses back to 720 BC, with lunar occultations from 1600 onward, and got +1.78 ± 0.03 ms per century for the change in the length of the day, against the +2.3 ms per century that lunar tidal friction alone predicts. The gap is mostly the crust still rising from the last ice age, redistributing mass toward the poles and spinning the Earth up.

A clay tablet recording a total eclipse over Babylon, dated to within a day, constrains the Earth's rotation better than the entire satellite era. Not because it is precise, but because it is old. Twenty-seven centuries of lever arm beats sixty-four years of resolution, and no amount of better measurement in the present can substitute.