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Transits, Travels and Tribulations, V

J. Donald Fernie

The Black Drop

Three problems permeated the analysis: first, the curious and unexpected phenomenon called "the black drop"; second, uncertainties in the distances between observers; and third, the problem of how to combine redundant observations.

Figure 2. Black-drop phenomenonClick to Enlarge Image

The black-drop problem surprised observers. They were trying to determine the exact moment when the edge of Venus's disk was just tangent to the edge of the sun's disk as Venus began or ended its transit, but what they saw was an elongated black ligament joining the two edges and persisting even when Venus's disk was clearly within that of the sun. This so surprised and unsettled the observers that even when two of them were standing alongside each other their reported times could be half-a-minute apart, when they were expecting agreement to within a few seconds. As Cook himself reported,

This day prov'd as favourable to our purpose as we could wish, not a Clowd was to be seen the whole day and the Air was perfectly clear . . . [yet] we very distinctly saw a . . . dusky shade round the body of the Planet which very much disturbed the times of the Contacts . . . . We differ'd from one another in observeing the times of the contacts much more than could be expected.

Today we understand this as being the result of sunlight refracting through the very dense atmosphere of Venus, but it certainly degraded the timing of the transits.

The accuracy of the final results also depended directly on knowing the length of the baseline between observers—in effect knowing accurately the latitude and longitude of each observer. But since methods for determining longitude in the 1760s were inadequate, to say the least, these baselines were not well determined, and the accuracy of the final results was correspondingly diminished.

The third problem reminds us that although this series of articles has described those few expeditions that went to remote parts of the earth to observe the transits in 1761 and 1769 (and their observations carried the most weight), there were additionally many other observers who saw the transits from home, if home happened to be in the right hemisphere at the right time. The initial analysts of the data faced the problem of getting the best single answer from multiple locations and observations, when in principle only two observations were needed. Methods for combining redundant observations were only in their infancy and would not come to fruition until the work of Legendre, Gauss and Laplace in the early 19th century led to the method of least-squares.

Thus contemporary analyses of the 1760s data yielded a variety of answers. Typical was the analysis of Lalande in 1771, who found values of the earth's mean distance from the sun (the astronomical unit) in the range of 152 to 154 million kilometers (Mkm). But more than a century later in 1891, when locations had been much better determined and mathematical methods improved, Simon Newcomb, dean of late-19th-century American astronomy, from the same data determined a value of 149.7 ± 0.9 Mkm, and when he combined the 1761 and 1769 transits with those of 1874 and 1882, he found an overall transit value of 149.59 ± 0.31 Mkm.

Before we compare this to the latest determination, let it be said we now know that of the methods developed after the last transit of Venus up to the mid-20th century (which included trigonometric parallaxes of asteroids, gravitational perturbations by the sun and improvements in the constant of stellar aberration), none would surpass in accuracy (although often in claimed precision) the results of the transits of Venus.

Modern astronomy has turned back to Venus to calibrate the astronomical unit, but now in quite a different way. Today giant radiotelescopes are used as radar guns, pumping out a tremendously powerful radio signal directed at Venus, and minutes later, switched to receiver mode, detecting the faint echo returning from the planet, the round-trip time being measured by atomic clocks. This interval, together with the speed of electromagnetic waves, yields the distance of Venus at that moment—and thus, through Kepler's third law (see Part I of this series), the value of the astronomical unit. The current value stands at 149,597,870.691 ± 0.030 kilometers. This astonishing result, if taken at its claimed precision, almost defies comprehension. It is the equivalent of measuring the distance between a point in Los Angeles and one in New York with an uncertainty of only 0.7 millimeter!

So when the next transit of Venus finally comes along in about five years (June 8, 2004), we are not likely to expect new exactitude in determining the astronomical unit, but we might give thought to the words of William Harkness, a key American figure in the 19th-century transits, writing just after those transits:

There will be no other [transit of Venus] till the twenty-first century of our era has dawned upon the earth, and the June flowers are blooming in 2004. When the last [18th century] transit occurred the intellectual world was awakening from the slumber of ages, and that wondrous scientific activity which has led to our present advanced knowledge was just beginning. What will be the state of science when the next transit season arrives God only knows.

© J. Donald Fernie

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