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Recently read that Earth is rotating faster than earlier1. However so far it is understood that earth's rotation is slowing down and to conserve the angular momentum Moon is going away from the Earth. What is true?
1for example see answers and comments at What effect does climate change have on the Earth's rotation? in Earth Science SE, and the 2015 Smithsonian article Is Global Warming Changing How Fast the Earth Spins?
Earth's rotation is slowing down, but it's a little bit irregular, which is why leap seconds can't be predicted in advance. There's provision for negative leap seconds, but they've never been used.
You can get the current list of leap seconds, maintained by The Internet Engineering Task Force (IETF), at https://www.ietf.org/timezones/data/leap-seconds.list
The decision to insert a leap second is made by the International Earth Rotation and Reference Systems Service (IERS), who coordinate the operations that gather the actual Earth rotation data. There is a wealth of information on their very extensive website.
Measuring the irregularities of the Earth's rotation
The variability of the earth-rotation vector relative to the body of the planet or in inertial space is caused by the gravitational torque exerted by the Moon, Sun and planets, displacements of matter in different parts of the planet and other excitation mechanisms. The observed oscillations can be interpreted in terms of mantle elasticity, earth flattening, structure and properties of the core-mantle boundary, rheology of the core, underground water, oceanic variability, and atmospheric variability on time scales of weather or climate. The understanding of the coupling between the various layers of our planet is also a key aspect of this research.
Several space geodesy techniques contribute to the permanent monitoring of the earth's rotation by IERS. For all these techniques, the IERS applications are only one part of their contribution to the study of planet earth and of the rest of the universe.
The measurements of the earth's rotation are under the form of time series of the so-called Earth Orientation Parameters (EOP). Universal time (UT1), polar motion and the celestial motion of the pole (precession/nutation) are determined by VLBI. The satellite-geodesy techniques, GPS, SLR and DORIS, determine polar motion and the rapid variations of universal time.
The satellite-geodesy programs used in the IERS give access to the time variations of the earth's gravity field, reflecting the evolution of the earth's shape, as well as the redistribution of masses in the planet. They have also detected changes in the location of the centre of mass of the earth relative to the crust. This makes it possible to investigate global phenomena such as mass redistributions in the atmosphere, oceans and solid earth.
Universal time and polar motion are available daily with an accuracy of 0.5 mas [milliarcseconds] and celestial pole motion are available every five to seven days at the same level of accuracy - this estimation of accuracy includes both short term and long term noise. Sub-daily variations in Universal time and polar motion are also measured on a campaign basis. Past data, going back to the 17th century in some cases, are also available.
EOP series are provided by the IERS in bulletins and as permanently updated series (long term earth orientation data).
Also, from the Wikipedia article on DUT1:
the SI second (as now used for UTC) was already, when adopted, a little shorter than the current value of the second of mean solar time [a].
So even if the Earth's rotation speed were perfectly constant, we'd still need leap seconds to keep UTC in synch with mean solar time because of the size of the SI second.
Astronomer Steve Allen maintains an extensive website on leap seconds and related matters, eg the history of time scales.
