The Effect Upon Eclipse Times

As it moves further away from us, the Moon takes longer to complete an orbit. Looking backwards in time, perhaps to 500 B.C., it was closer to us and so its orbital period was less. If the recession rate given above, an inch and a half per year, has continued throughout the intervening 2,500 years, this would imply that back then the Moon was about one-sixth of a mile closer, and the synodic month lasted for almost two seconds less than it does now.

Without accurate clocks in ancient times, how could we check the correctness of these calculations, which are based upon backward extrapolations of modern ultra precise measurements? The answer comes from eclipses. The milliseconds-per-day slowing of the terrestrial rate of rotation and the seconds-per-month discrepancies produced by the receding Moon, add together and result in severe displacements of the ground tracks of solar eclipse totality.

All those seconds accumulate to produce an eclipse time four hours earlier in 500 B.C., as foreshadowed above. This displaces the track of totality about 60 degrees east in longitude. For example, an eclipse that would otherwise have been expected to have had a track crossing the Italian peninsula 2,500 years ago might actually have been seen in Pakistan and western India, making a search through Roman republican accounts from that era futile. The problem can be attacked in the opposite way, however. With some ancient record of an observed total eclipse, knowing where it was observed, and approximately when, it is possible to back compute the circumstances of all feasible eclipses and identify the one responsible. Because the tracks of totality are so narrow, knowing a blacked out Sun was observed in Athens, Babylon, or Beijing on a certain date enables us to determine the spin phase of the Earth in that epoch.

There is a problem, though. If the rate of deceleration of the Earth's rotation were uniform, then the corrections needed would be straightforward. But this is not the case. Since the last Ice Age terminated about 10,000 years ago many continental regions (such as the northern parts of Europe, Asia, and North America), which were overlain for eons by thick ice layers, have been rebounding gradually. That is, their ice burden compressed them, but now they are expanding again. Like the skater raising her arms, this causes the spin rate to fall. One does not expect the deceleration in the Earth's rotation rate to be constant over millennial time scales, then. The eclipse records found on Babylonian clay tablets and in medieval chronicles are allowing investigators to track these changes in our planet's dynamical behavior rather precisely.

Having mentioned Beijing (formerly Peking) above, let us look at a specific record from ancient China. A couple of millennia back the imperial capital was Chang'an (known as Xi'an or Sian nowadays). A chronicle for 181 B.C. records that a total solar eclipse was witnessed there, and we can identify its circumstances through back-computations of the relevant orbits in all respects except one: the spin phase of the Earth. If one assumes that the planet rotated at its present rate throughout the years since 181 B.C. then the ground track of the eclipse would have missed Chang'an by about 50 degrees of longitude (equivalent to 3 hours and 20 minutes of spin), as shown in Figure 6-2. But the eclipse track did intersect Chang'an, indicating how much the Earth's rotation has slowed over all those centuries.

Many of the Babylonian clay tablets containing records of ancient eclipses are now archived at the British Museum, in London. It is not a coincidence that much of the leading work on ancient eclipse interpretation has been by British astronomers. In particular Richard Stephenson of the University of Durham, aided by Leslie Morrison of the Royal Greenwich Observatory and others, has found vital evidence for how the Earth's spin rate has varied since about 700 B.C. Mesopotamian tablets and Chinese records, plus various Arab chronicles and European annals, have all

FIGURE 6-2. A total solar eclipse was observed from the ancient Chinese capital of Chang'an in 181 B.C. The eclipse ground track can be computed and plotted onto the globe such that it passes through Chang'an, as on the left, indicating the spin phase of the Earth in that era. If our planet had continued to rotate at the same rate as at present over all the intervening years, then the track would have missed Chang'an by 50 degrees of longitude (equivalent to 3 hours and 20 minutes of time), as on the right. Such eclipse records allow us to understand how the Earth's spin rate has slowed under tidal friction in recent millennia.

FIGURE 6-2. A total solar eclipse was observed from the ancient Chinese capital of Chang'an in 181 B.C. The eclipse ground track can be computed and plotted onto the globe such that it passes through Chang'an, as on the left, indicating the spin phase of the Earth in that era. If our planet had continued to rotate at the same rate as at present over all the intervening years, then the track would have missed Chang'an by 50 degrees of longitude (equivalent to 3 hours and 20 minutes of time), as on the right. Such eclipse records allow us to understand how the Earth's spin rate has slowed under tidal friction in recent millennia.

been trawled for their useful eclipse data. The results have applications in a number of areas of science other than just astronomy, for instance in developing our understanding of the long-term climatic vagaries of the Earth.

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