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In reply to the discussion: Earth's spin is slowing at a rate of 1.8 milliseconds per century [View all]muriel_volestrangler
(101,308 posts)(mainly eclipses) and then fit a parabolic curve to that (and then look at deviations from that). See figure 9, and their equation 4.1. (They've already said, in section 1(b), that theory gives a constant rate of change in day length, so that the accumulated delta T should be parabolic). Then, in section 5.1, they differentiate that to get the long term figure of 1.78 milliseconds per century.
In fact, the 7 hours is the figure for the currently calculated 2.3 ms per century - calculated from satellite measurements of earth-moon tidal friction. Their analysis of the eclipse etc. records gives delta T of about 22000 seconds (figure 9), which is more like 6 hours. So the 'news' from this paper, which is in the abstract, is " the change in the length of the mean solar day (lod) increases at an average rate of +1.8?ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3?ms per century."