Bewilderbeast Droppings

Venus silhouetted against the Sun, seen from our dear planet Earth from different viewpoints in 2012.

Three times exposures on the right, showing the path of Venus tracking across the face of our Sun.
A transit of Venus is one of the rarest and most historically significant planetary alignments. Since the invention of the telescope in 1608, there have been only seven. It did not occur at all during the twentieth century, and when it occurred in 2004 and 2012, not one soul was living who observed the last one in 1882.

It was by studying the 1769 transit that atronomers calculated the distance from Earth to the Sun. For this event, Captain Cook famously sailed the Endeavour to uncharted Tahiti. Mission: Observe the transit.

Anyone interested in the ceaseless, wondrous movements of the planets in our solar system needs to read about Venus crossing the face of the sun, as observed from Earth (excerpts from books by Nick Lomb & David Sellers).
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In the 18th century, scientists realised that by timing the event from different locations, the transits of 1761 and 1769 could be triangulated and give the distance between Earth and the Sun – “the noblest problem in astronomy,” for it would at last place mankind in the cosmos.
Britain and France, the two superpowers at the time, jockeyed for the glory, dispatching missions to far-flung places.
Among them were British surveyors Charles Mason and Jeremiah Dixon, who were attacked by French warships in 1761 just after they left Plymouth and headed back to port. Discouraged, they wanted to cancel the trip. After receiving a now-legendary letter from the Royal Society, the British scientific academy which was sponsoring them, they ventured straight back out to sea, suitably chastened. To give up would “bring an indelible Scandal upon their Character, and probably end in their Utter Ruin,” the letter said stonily. Or, Get your asses the hell out there, girlfriends, in 21st century jargon.

Drama was also in store for the 1769 transit, when Britain sent James Cook to Tahiti to view the event from there.
After his mission, Cook opened the instructions for the secret – and most important – part of his expedition: to search for and map for the Crown a mysterious “southern continent,” which turned out to be New Zealand and eastern Australia.
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Hundreds of scientists set sail to locations throughout the world, hoping to catch a glimpse of the transit and be the first to bask in the glory of priority. Most of the expeditions would end in failure. Some were of such comically devastating proportions they sound like something dreamed up in an ancient Greek tragedy. Bill Bryson recounts one such misfortune in A Short History of Nearly Everything:
Le Gentil set off from France in 1760, a year ahead of time, to observe the transit from India, but various setbacks left him still at sea on the day of the transit―just about the worst place to be, since steady measurements were impossible on a pitching ship.
Undaunted, Le Gentil continued on to India to await the next transit in 1769. With eight years to prepare, he erected a first-rate viewing station, tested and retested his instruments and had everything in a state of perfect readiness. On the morning of the second transit, 4 June 1769, he awoke to a fine day; but, just as Venus began its pass, a cloud slid in front of the Sun and remained there for almost exactly the duration of the transit of three hours, fourteen minutes and seven seconds.
Stoically, Le Gentil packed up his instruments and set off for the nearest port, but en route he contracted dysentery and was laid up for nearly a year. Still weakened, he finally made it onto a ship. It was nearly wrecked in a hurricane off the African coast. When at last he reached home, eleven and a half years after setting off, and having achieved nothing, he discovered that his relatives had had him declared dead in his absence and had enthusiastically plundered his estate. (Thanks, Nick Risinger’s blog)
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How did they do it?
The mathematician James Gregory recognised that the distance from Earth to the sun could be calculated by observing a transit of Venus from two points on Earth that are far away from one another. Edmond Halley and Joseph-Nicolas Delisle came up with different ways of doing this. In 1761 and 1769 (Venus transits come in pairs around 8 years apart with a gap of around 105 years between pairs), scientists made epic journeys to take part in this measurement.
Here’s an outline of how Delisle’s method worked. Two people with accurately synched time pieces (another challenge in the 18th and 19th century) would observe the exact time that the transit began from two places on Earth. They would not see the transit start at the same time because of a phenomenon called parallax.
At some point, the red observer will see the Venus transit begin and will mark the time.

At a later point (because the Earth is spinning, and Earth and Venus are orbiting around the sun), the blue observer will see the transit begin.

Using Kepler’s Third Law and some high school geometry, you can determine the distance Venus has orbited in this short amount of time, and then the absolute distance from Venus to the sun (Thanks Avery Pickford’s blog).

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PS: Do find and read Bill Bryson’s entertaining account of the transit of Venus!