Astronomy & Celestial Mechanics
the sky, computed
Concept

Leap second — where it appears

A second inserted into Coordinated Universal Time to keep it within 0.9 seconds of the Earth's irregular rotation. Twenty-seven were added between 1972 and 2016, and the practice is to end by 2035.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as tidal friction, δt — the same set of essays touches all of them, so they are one junction rather than several.

A clock that has lost 5.7 hours in 2720 years. ΔT = TT − UT1, the accumulated difference between a uniform time scale and the Earth's own rotation, from 700 BC to 2020, on a logarithmic scale. The points are the published record; the smooth curve is the parabola 31.94·u² fitted to the entries at or before 1000, with u in centuries from 1820. It is a parabola and not a line because the Earth is not merely slow, it is slowing: a day lengthening at a constant rate makes a clock fall behind by the integral of the lag. That coefficient is a length-of-day rate and nothing else — 31.94 = ½ × r × 36525 days per century gives r = 1.75 ms per century, against the 1.78 ms computed from tidal angular momentum with no eclipse anywhere in the derivation. At 700 BC the offset is 5.7 hours, which is 85° of the Earth's rotation, and that is why the ancient measurements are records of the place a total eclipse was seen from rather than of the hour: the hour was never written down accurately enough to matter, and the shadow's track on the ground was.

Six kinds of second

The Earth is a clock that loses, and it has lost five and a half hours since 700 BC. That number was measured from the places ancient eclipses were seen from, not the times they were seen at — because the record carries a longitude and no clock.

sky · Timescales How far the clock drifts from the Sun once leap seconds stop. The accumulated difference between the Earth's rotation and atomic clock time, in seconds, that builds up after leap seconds are abandoned, against years since then, for a day that now exceeds 86,400 SI seconds by −0.3 ms, 0.5 ms, 1.5 ms, each lengthening by 1.7 milliseconds a century as the tides brake the Earth. The drift is the integral of the excess: 20 s after 100 years, a minute after 158 for −0.3 ms; 49 s after 100 years, a minute after 113 for 0.5 ms; 86 s after 100 years, a minute after 76 for 1.5 ms. The present excess is close to zero — the day has recently been slightly shorter than 86,400 seconds — so the drift starts slowly or even backwards, and the tidal term then takes over and bends every curve upward. The time for the difference to reach a minute is set far more by the next century's core-driven fluctuations, which have swung the excess by two or three milliseconds within a few decades before, than by anything that can be predicted.

A clock allowed to leave the Sun

Twenty-seven leap seconds have kept civil time within a second of the Earth's rotation since 1972. By 2035 they will stop, and the clock will be allowed to drift from the Sun. How far it drifts, and how soon a minute accumulates, depends on a length of day that no one can forecast.

sky · Timescales

Named alongside it

The objects these essays reach for when they reach for this one.

ΔTLength of dayTidal frictionAtomic clockCoordinated Universal TimeCore–mantle couplingEclipseEphemeris timeEquation of timeInternational Atomic TimeSidereal timeTimescales

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