@Frog:
"Let me clarify. This is also assuming that the Earth continues on its current rate of rotational deccelaration, and assuming that inmpacts by other large bodies of mass, and distribution of mass on the planet's surface changing have no hypothetical effect on the speed of rotation."
This assumption is wrong. By far the largest influence on our rotation is tidal friction caused by the Moon. This causes the speed of the Moon's rotation about the Earth to increase (and hence the Moon is receding from us), and the Earth's speed of rotation to decrease.
Eventually the Moon and Earth will become tidally locked. At this time the Moon will not appear to rise or set, there will be no more tides, and Earth's days and nights will each average half a lunar month (which will be longer than today's lunar month).
As long as with have a moon, we can never become tidally locked to the Sun.
@ArmandT:
"Every year is longer than the previous year by about 1.6 seconds. There used to be 420 days in the year 500 million years ago. For that reason, scientists add a 'leap second' every now and then to compensate for that discrepancy."
No, years are (as near as dammit) the same length now as always, since to have a longer year the Earth would need to move further from the Sun, which there is no evidence it is doing. What has changed is the length of a solar day (elapsed time between successive noons).
And the figure is not 1.6 seconds/year but 1.6 milliseconds per century (on average, it is not a constant rate year-on-year). This is the amount each solar day gets longer by, and when enough of these little differences have accumulated, the Atomic clocks are resynchronised to the solar noon via a leap second.
http://curious.astro.cornell.edu/question.php?number=124
http://hpiers.obspm.fr/
http://www.cl.cam.ac.uk/~mgk25/time/metrologia-leapsecond.pdf
