How fast is the rotation of the Earth slowing down ?
The period of rotation increases by 2 milliseconds per century.
Due to tidal resistance right ?
What about the Suns rotation, do we know anything about that period too is increasing?
it is due to a transfer of Earth's rotational momentum to the Moon's orbital momentum as tidal friction slows the Earth's rotation. for the sun, I believe it is the same.
Perhaps a bit misleading. For example, the length of a day decreased by 3.35 milliseconds over the last century. The excess length of day was 0.36 milliseconds for 2009, 3.71 milliseconds for 1909. Before you accuse you of cherry-picking: Guilty as charged. Excess length of day peaked in 1910.
The Earth's rotation rate also varies because of internal changes in the Earth. Over the short term (short here meaning hundreds or even thousands of years), these internal changes swamp the small but steady change due to transfer of angular momentum to the Moon's orbit. These internal changes arise from changes in the Earth's inertia tensor. They do not change the Earth's angular momentum. Over the long haul these internal changes average out to a null effect. The change in the Earth's rotation due to transfer of angular momentum to the Moon's orbit is a secular effect. Over millions of years or longer this is the only effect that stands out.
As far as the Sun goes, that effect is negligible. While tidal forces are inversely proportional to the cube of distance, the change in rotation rate due to tidal interactions is inversely proportional to distance6.
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