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Earth's Day Lengthens By Two Milliseconds a Century, Astronomers Find (theguardian.com)
Researchers at Durham University and the UK's Nautical Almanac Office compiled nearly 3,000 years of celestial records and found that with every passing century, the day on Earth lengthens by two milliseconds as the planet's rotation gradually winds down. The Guardian reports: The split second gained since the first world war may not seem much, but the time it takes for a sunbeam to travel 600km towards Earth can cost an Olympic gold medal, as the American Tim McKee found out when he lost to Sweden's Gunnar Larsson in 1972. For those holding out for a whole extra hour a day, be prepared for a long wait. Barring any change in the rate of slowing down, an Earth day will not last 25 hours for about two million centuries more. Researchers at Durham University and the UK's Nautical Almanac Office gathered historical accounts of eclipses and other celestial events from 720BC to 2015. The oldest records came from Babylonian clay tablets written in cuneiform, with more added from ancient Greek texts, such as Ptolemy's 2nd century Almagest, and scripts from China, medieval Europe and the Arab dominions. The ancient records captured the times and places that people witnessed various stages of solar and lunar eclipses, while documents from 1600AD onwards described lunar occultations, when the moon passed in front of particular stars and blocked them from view. To find out how the Earth's rotation has varied over the 2,735-year-long period, the researchers compared the historical records with a computer model that calculated where and when people would have seen past events if Earth's spin had remained constant. The astronomers found that Earth's spin would have slowed down even more had it not been for a counteracting process. Since the end of the most recent ice age, land masses that were once buried under slabs of frozen water have been unloaded and sprung back into place. The shift caused the Earth to be less oblate -- or squished -- on its axis. And just as a spinning ice skater speeds up when she pulls in her arms, so the Earth spins faster when its poles are less compressed. Changes in the world's sea levels and electromagnetic forces between Earth's core and its rocky mantle had effects on Earth's spin too, according to the scientists' report in Proceedings of the Royal Society.
Interestingly, this also has an effect on the moon. The reason why the earth's rotation is slowing are the tidal forces. Part of the energy lost from the Earth's momentum goes into the Moon's own orbit. As a result, the moon is actually getting further and further away from us, at a rate of 38 mm (1.5 in) per year. Somewhat counter-intuitively, the Moon actually gets slower that way, despite the energy put in is in the prograde direction, i.e. increases its velocity. The reason is the higher orbit. Sources:
Tidal effects on the Moon
Earth's rotation
Using computer modelling I suspect the location of the shadow of the eclipse is dependent on the spin rate of the Earth. Therefore, by knowing where people saw the eclipse and how much of the sun could be seen will be sufficient to calculate the rotational position of the Earth at the time of the eclipse. Then compare that position with the computer model. So knowing the exact time of the observations of the eclipse to the order of milliseconds is unnecessary.
Erm... A century contains 36500 days... not 365. That's a year. And every 4th year has 366 days.
So that's 25*366 +75*365 = 36575 days in a century.
You may want to correct the rest of your maths to account for there being more than 100 times more days in that period than you counted.
Unicode killed the ASCII-art *
The article says 2 milliseconds per century, but we've already added 27 leap seconds since 1972 ..
So, what am I missing..?
Leap seconds (and leap years) are due to the number of rotations of the earth in a year not being exactly 365. If you think about it, why would they be. There is no reason the earth should rotate exactly 365 time in one trip around the sun. So, to keep December from gradually creeping into the summer, we have to fiddle a bit with the calendar.
In this case, we are just talking about the rotation speed of the earth. In a closed system, the rotation speed can be changed by moving the mass around the Earth, such as from the equator to the poles or from the the earth surface to under the surface. Changing the shape of the Earth is essentially the same as moving the mass around so would also affect speed (going from sphere to pair shape to ellipsoid).
Since we don't live in a closed system (e.g. the moon is out there), one can also change the earths rotation speed by adding (or in our case with the moon) taking away momentum. So this also affects the rotation speed.