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In reply to my earlier posting-

>"I know that delta-T has fluctuated significantly in the past, but this time
>there seems to have been a rather sudden increase in spin speed, by quite a
>large amount. What could be the cause of this rather dramatic change? "

Frank Reed responded-

>The recent changes in delta-t are not that dramatic. Here's some code I use
>for delta-t for the period 1750 to 2050 (gives a value for each decade year so
>for example DTtable(2) is 15 seconds for the year 1770):
>DTtable(0) = 12    '1750
>DTtable(1) = 14
>DTtable(2) = 15
>DTtable(3) = 16
>DTtable(4) = 16
>DTtable(5) = 13.1  '1800
>DTtable(6) = 12
>DTtable(7) = 11.6
>DTtable(8) = 7.1
>DTtable(9) = 5.4
>DTtable(10) = 6.8  '1850
>DTtable(11) = 7.7
>DTtable(12) = 1.4
>DTtable(13) = -5.5
>DTtable(14) = -6
>DTtable(15) = -2.8 '1900
>DTtable(16) = 10.4
>DTtable(17) = 21.1
>DTtable(18) = 24.0
>DTtable(19) = 24.3
>DTtable(20) = 29.1 '1950
>DTtable(21) = 33.1
>DTtable(22) = 40.2
>DTtable(23) = 50.5
>DTtable(24) = 56.9
>DTtable(25) = 63.1 '2000
>DTtable(26) = 69
>DTtable(27) = 76
>DTtable(28) = 83
>DTtable(29) = 90
>DTtable(30) = 97   '2050
>DTtable(31) = 104
>
>Except for the speculative extrapolation for future t, this table is taken
>from Meeus' "Astronomical Algorithms". Note that there are changes in the 19th
>century that are quite large and that they are both positive and negative.

================

Reply from George:

We shouldn't take seriously those entries in Frank's table after 1980,
which is the period we are considering when discussing recent sudden
changes in the Earth's spin rate.

In my 1998 edition of astronomical Algorithms, Meeus states that for the
years earlier than 1988, the values of delta-T were taken from the
Astronomical Almanac for 1988. Presumably, then, lacking more recent
observations, Meeus' later values, given for 1988 to 1998, were themselves
extrapolations based on certain assumptions of continuity.  Frank's table
(above) appears to have made further extrapolations, to take the
predictions as far as 2060. Frank, reasonably, describes those
extrapolations as speculative. With hindsight, we now know, with no
leap-seconds over a period of six years, that they have been contradicted
by more recent events. The previous steady increase in delta-T seems to
have, rather suddenly, ended (or nearly so). What the future will bring is
impossible to predict; so it might be an interesting matter for gamblers to
bet on.

Frank's table, then, gives us no hint of that sudden increase that occurred
in the Earth's spin-rate in the late 1990s. Also, because it's a series of
snapshot views taken at 10-year intervals, it's rather hard to pick out the
moments of sudden change in spin-rate, and just how rapidly the Earth's
spin is changing at those times. It's easier to extract that information
directly from the Meeus data (table 10A), which is given at 2-year
intervals rather than 10.  Such changes are shown well, graphically, in
Seidelmann, Explanatory Supplement to the Astronomical Almanac, 1992, fig.
4.51.1, in which the difference between the actual length of day and 86400
seconds is plotted year by year, (but only up to 1988).

The graph in Seidelmann shows deviations from the nominal day-length over a
range from about -3 milliseconds to +4 milliseconds. However, what I am
commenting on is not the AMOUNT of change in the day-length in recent
years, but the suddenness of that change. This corresponds to a measure of
the acceleration that has taken place, and therefore a measure of the
forces that have been acting on the Earth. Over past centuries,
Seidelmann's graph has shown jumps in spin rate that confirm what Frank has
said, that such a sharp change in spin rate as we have recently observed is
by no means unprecedented, even if such events are indeed rather rare.

George.

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