Earths Rotation Period Variation Calculator

Length of day, or LOD, is the duration of one mean solar rotation measured against atomic time, and it is not constant. The dominant long-term term is lunar tidal friction: the tidal bulge raised in the oceans and solid Earth is dragged ahead of the Earth-Moon line by rotation, and the resulting gravitational torque brakes the planet while transferring angular momentum to the lunar orbit, which is why lunar laser ranging shows the Moon receding at about 3.8 cm per year. Astronomical and geological evidence puts the tidal contribution near 2.3 milliseconds per century. Opposing it is glacial isostatic adjustment: mantle material still flowing back beneath Fennoscandia and Hudson Bay since the last deglaciation reduces Earth oblateness, decreases the moment of inertia and speeds rotation by roughly 0.5 ms per century. Because these effects partly cancel, the net observed rate over the past few millennia is closer to 1.7 to 1.8 ms per century than to the tidal value alone. Superimposed are much faster fluctuations: a seasonal cycle of about 1 ms driven by atmospheric angular momentum exchange with the zonal winds, decadal wobbles of several milliseconds attributed to core-mantle coupling, and minute steps from great earthquakes, with the 2004 Sumatra event estimated to have shortened the day by a few microseconds. Clock error accumulates as the integral of the LOD excess, so the cumulative shift grows with the square of elapsed time. Extrapolating a fixed linear rate over a million years is illustrative only, since ocean tidal dissipation changes as continents move.

Edmond Halley inferred in 1695, from comparing ancient and contemporary eclipse records, that the Moon appeared to be accelerating in its orbit, an anomaly that puzzled astronomers for over two centuries. Immanuel Kant proposed in 1754 that tidal friction must be slowing Earth rotation, which supplies the other half of the explanation: part of the apparent lunar acceleration is really the lengthening of the timekeeping unit. Harold Spencer Jones showed in the 1930s that residuals in the motions of the Moon, Sun and planets were correlated, implying a variable Earth rather than variable orbits. The fix was to redefine time. Ephemeris time, tied to the orbital motion of the Earth, was adopted by the International Astronomical Union in the 1950s, then superseded once Louis Essen and Jack Parry built the first practical caesium atomic clock at the National Physical Laboratory in 1955; the SI second was redefined on caesium in 1967. Coordinated Universal Time has since been kept within a fraction of a second of Earth rotation by inserting leap seconds, a practice begun in 1972 and voted for discontinuation by around 2035. Monitoring passed to the International Earth Rotation and Reference Systems Service in 1988, which combines Very Long Baseline Interferometry on quasars with satellite laser ranging, while Richard Stephenson and Leslie Morrison used millennia of eclipse records to constrain the long-term rate.