Precise Eclipse Track Calculations

Modern science and computers have allowed the calculation of precise times and paths for eclipses, and so we know exactly when and where one should travel to experience totality. We might take pause to consider just how accurately we need to know the eclipse time so as to be best positioned.

The Moon's shadow sweeps across the Earth at between one-third and one-half of a mile per second (1,200 to 1,800 mph). That's the speed along the ground track, typically 60 to 100 miles wide. Taking into account the track orientation, an error of a single second in reckoning the instant of the eclipse could shift it east-west by a quarter-mile, or one part in a few hundred of its width. That's a rough estimate, but it's in the correct ballpark.

Looking back at the timings of eclipses 70 or 80 years ago, pre-eclipse predictions were often found to be out by maybe a dozen seconds, translating into a few miles as the shift in the path of totality. Analyses of historical eclipses like that of 1715, and much earlier, have been possible only since we developed the capacity to compute them with a precision rather better than a mile. Recall that Edmond Halley's predictions for 1715 were out by just 3 miles for the northern edge, but by 20 miles for the southern. Another example is the 1878 eclipse in the western parts of North America. The astronomical almanacs prepared independently in those days by astronomers at the U.S. Naval Observatory in Washington, D.C., and the Royal Greenwich Observatory in London, had maps of the track that differed by 4 miles at its borders.

Because of this timing problem it was not at all certain where the edge of the eclipse track in January 1925 would pass. One way to improve knowledge of such things was by obtaining accurate measures of when totality reached different points along the path. To this end Bell Laboratories set up a telegraphic ring of stations within the track, recording signals from them on a common chart so as to ensure uniformity. That chart is shown in Figure 10-2.

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FIGURE 10-2. A chart of the time signals marking the beginning and end of totality as transmitted by telegraph, for Buffalo, Ithaca, and Poughkeepsie in New York and New Haven and East Hampton in Connecticut.

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FIGURE 10-2. A chart of the time signals marking the beginning and end of totality as transmitted by telegraph, for Buffalo, Ithaca, and Poughkeepsie in New York and New Haven and East Hampton in Connecticut.

The other way of determining the edge of the track is obvious: have people spread out across the possible limits as estimated beforehand, and this is something to which we will come shortly. For the present, though, let us stick with eclipse timings. One matter that springs to mind would be the effect of the introduction of leap seconds, the need for which we discussed in Chapter 6.

Consider, for example, the next eclipse to cross the continental United States in August 2017. The track of that eclipse has been calculated already, and it is shown in Figures 15-7 and 15-8. In the decade and a half between now and then it would be anticipated that about ten leap seconds might be inserted, shifting our clocks. But will they shift the eclipse path?

The answer, of course, is no. Leap seconds are inserted only for human convenience, and eclipse phenomena are computed using astronomers' dynamical or ephemeris time systems. The leap seconds alter the time at which the eclipse will occur as displayed on a clock, but not the absolute time or the path followed.

You may think, then, that my question was misleading, but there is an important point that follows from this thought process. Although leap seconds themselves do not affect eclipse tracks, the phenomenon that makes leap seconds necessary does cause shifts in such tracks. Think back to Figure 6-2: the slowing of our planet's rotation rate moves eclipse paths from those that would occur if the Earth spun at a constant rate. It doesn't, because tidal drag slows it down, and leap seconds represent our solution to the problem, given the desire to keep the second a constant interval of time for various technological reasons. However, it is not possible to know ahead of time precisely how much the Earth's spin will slow before 2017.

It follows that the prediction of eclipse paths cannot be an exact science. In writing computer programs to delineate the track for some eclipse, an assumption must be made that the terrestrial rotation rate will continue to behave as it has done in recent times (and it has not decelerated uniformly over the past several millennia: we know that from eclipse records). We can monitor the spin of the planet on a day-to-day basis, and know it to be erratic, but the deviations from the overall trend are not huge. The derived peripheries of the eclipse track predicted a year or so ahead of time will not be off by more than a handful of yards. In consequence the argument might be considered moot because most observers will anyway be aiming to position themselves as close as possible to the central line. Recall, though, what was written in Chapter 8 concerning the desirability of being located nearer its edge.

Over extended periods the errors in the predictions enlarge. Until the time gets close, we cannot know the spin phase of the Earth at any specified juncture in the future. One may compute eclipse tracks for a century hence, but these are predicated upon an assumption that the day will continue to lengthen at the present rate, and it is virtually certain that this will not be the case. The fact of the eclipse is known, because the relevant orbits are determined with the necessary precision, but precise tracks of totality cannot be stipulated more than a century or so into the future.

The situation is analogous to flying a paper airplane. Especially given some experience one can predict with some confidence the path it will take in the inch, the foot, and maybe even the yard after it departs your fingertips. After that, who knows? Similarly there is a limit to the forward planning of eclipses, but on the scale of a human lifetime they can be predicted well enough for you to know precisely where you should be to see totality in 2045, say.

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