information:extraction
Rationale

Earth's rotational speed is very slowly decreasing because of tidal deceleration; this increases the length of the mean solar day. The length of the SI second was calibrated on the basis of the second of ephemeris time and can now be seen to have a relationship with the mean solar day observed between 1750 and 1892, analysed by Simon Newcomb. As a result, the SI second is close to 1 / 86400 of a mean solar day in the mid‑19th century. In earlier centuries, the mean solar day was shorter than 86,400 SI seconds, and in more recent centuries it is longer than 86,400 seconds. Near the end of the 20th century, the length of the mean solar day (also known simply as "length of day" or "LOD") was approximately 86,400.0013 s. For this reason, UT is now "slower" than TAI by the difference (or "excess" LOD) of 1.3 ms/day.

The excess of the LOD over the nominal 86,400 s accumulates over time, causing the UTC day, initially synchronised with the mean sun, to become desynchronised and run ahead of it. Near the end of the 20th century, with the LOD at 1.3 ms above the nominal value, UTC ran faster than UT by 1.3 ms per day, getting a second ahead roughly every 800 days. Thus, leap seconds were inserted at approximately this interval, retarding UTC to keep it synchronised in the long term. The actual rotational period varies on unpredictable factors such as tectonic motion and has to be observed, rather than computed.

Just as adding a leap day every four years does not mean the year is getting longer by one day every four years, the insertion of a leap second every 800 days does not indicate that the mean solar day is getting longer by a second every 800 days. It will take about 50,000 years for a mean solar day to lengthen by one second (at a rate of 2 ms per century). This rate fluctuates within the range of 1.7–2.3 ms/cy. While the rate due to tidal friction alone is about 2.3 ms/cy, the uplift of Canada and Scandinavia by several metres since the last ice age has temporarily reduced this to 1.7 ms/cy over the last 2,700 years. The correct reason for leap seconds, then, is not the current difference between actual and nominal LOD, but rather the accumulation of this difference over a period of time: Near the end of the 20th century, this difference was about 1 / 800 of a second per day; therefore, after about 800 days, it accumulated to 1 second (and a leap second was then added).

In the graph of DUT1 above, the excess of LOD above the nominal 86,400 s corresponds to the downward slope of the graph between vertical segments. (The slope became shallower in the 1980s, 2000s and late 2010s to 2020s because of slight accelerations of Earth's rotation temporarily shortening the day.) Vertical position on the graph corresponds to the accumulation of this difference over time, and the vertical segments correspond to leap seconds introduced to match this accumulated difference. Leap seconds are timed to keep DUT1 within the vertical range depicted by the adjacent graph. The frequency of leap seconds therefore corresponds to the slope of the diagonal graph segments, and thus to the excess LOD. Time periods when the slope reverses direction (slopes upwards, not the vertical segments) are times when the excess LOD is negative, that is, when the LOD is below 86,400 s.