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Your claim that "starting the beginning of the 20th century the Earth is systematically slowing its rotation" is false. The Earth has always been slowing down. Don't be fooled by that diagram which shows aU-shaped curve coming down to the zero line and starting up again at the beginning of the 20th century. That curve does not show acceleration, it shows the accumulated difference between ET and UT. In 700 BC the difference was about 5.5 hours, the day was about 40 milliseconds shorter than today, and on average the length of the day has since been increasing by 1.7 milliseconds per century. Nothing to worry about either. During the last decades each day was on average about two milliseconds longer than 86400s. In 1.5 years this sums up to 1.5 * 365 * 0.002s = 1 second. This is why a leap second had to be inserted on average every 1.5 years. On the other hand, it is clearly seen that during the last five years the LOD has become shorter and is now around the nominal 86400s. This is why currently no leap seconds are needed. The last leap second was introduced at the end of 1998, and it has been announced that no leap second will be introduced at the end of 2001. In other words, the Earth has been noticeably speeding up during the last 5 years and is currently back to nominal.
Thomas Schmidt

I absolutely agree with you that Earth did not start slowing beginning the 20th century. It is correct to say that the known data show the Earth is slowing for more the twenty centuries. However it is hard to believe that we have enough data to say "always been slowing down" nor "nothing to worry about". I just want to say that when I look on the data showing long-term changes in the rotation of the Earth they do not make me confident about our past and future.The length of day (LOD) for the period 700 B.C. to A.D. 1980 taking from the classical paper "Long-term changes in the rotation of the Earth:700 B.C. to A.D. 1980 by F.R. Stephenson and L.V. Morrison in Phil. Trans. R. Soc. Lond. A 313, 47-70, 1984. It seems that the slowing of the Earth was not always the same. According to the authors, the long-term changes before and after A.D. 950 were very different. From 700 B.C. to A. D. 950 the change in l.o.d. was +2.4 ms/century, and the slope was expected on the basis of tidal friction model. But after A.D 950 it is 1.4 ms/century and it indicates the non-tidal changes.

Authors do not suggest a sudden change at this epoch, but the contribution of non-tidal component is very significant. I know that by saying what I am about to say I call for troubles but I will say it any way. I speculate that those non-tidal effects at the epoch after A.D. 950 produced by approaching Planet X. If we believe that Planet X was close to the Earth at about 1600 B.C. then in 900 years, at 700 B.C., when all known to people astronomical observation began, the Planet X was about half way to another star. It was very far to influence the Earth rotation. At about A.D 200 the Planet X returns to the vicinity of this other star and starts its journey to our Sun again. At epoch after A.D. 950, and after A.D.1100, when the Planet X is in middle way to Earth, the effects of the planet may be appreciated and can reach maximum at 2003.

Astronomical data shown in the Stephenson and Morrison figure are not going very far in the past to show the LOD. changes at around 1600 B.C. when we would of expect large changes due to approaching Planet X. Only historical records about the complete stop of the Earth rotation happened at about this time were discussed by Zecharia Sitchin in his book The Lost Realm, Bear & Co, Santa Fe, NM, 1990, p. 154. A strong scientific evidence for a strong global environmental disruption in 1628 B.C. is given in paper of H. Grudd, K.R. Briffa, B.E. Gunnarson, and H.W. Linderholm " Swedish tree rings provide new evidence in support of a major, widespread evironmental disruption in 1628 BC", Geophysical Research Letters, 27 (18), 2957-2960, 2000.

Offered by Jacob.