Size up the sky

When you look up at the night sky, you have the benefit of centuries of astronomical knowledge telling you that the stars you see are hundreds or thousands of light-years away – some might even be quasars in the heart of galaxies millions of light-years away.

You can look at the Moon, see the inner planets hugging the horizon at twilight, or look out to see the red-tinged Mars along with Jupiter and Saturn and know how far all these celestial bodies are from where you're standing.

This wasn't always the case, however. Ancient Greek astronomers were the first to record their attempts to measure up the size of our stellar neighborhood, and they managed to succeed in some important ways.

In the 2nd century BCE, the astronomer Hipparchus utilized the phenomenon of parallax (where two objects — one behind the other — are measured from two different locations or angles to determine the distance of the nearer of the two objects from the observer) to calculate the distance to the Moon with a remarkable degree of accuracy.

Anyone who has stared out the passenger window of a car or train knows this phenomenon very well: the bushes, trees, or fence posts zip by in a flash, but a farmhouse in the middle of a field, far back from the road, appears to slowly drift by.

You can even use your two index fingers in a line, one hand near to your face and the other outstretched as far as it goes, and close one eye, then the other. Your nearer finger will probably bounce from the left side of the farther finger to the right side of it and back again. This is parallax, and it was one of early astronomy's most powerful tools.

Hipparchus observed the Moon during a total solar eclipse from one location and used the observations in another city where the sun was only partially eclipsed to determine the lunar parallax.

Since the distance between the two cities was known to him, it was just a matter of geometry to determine the distance to the moon, and he was remarkably close, calculating to within seven percent of the moon's actual average distance from the Earth.

Another Greek astronomer, Aristarchus, made a valiant attempt at calculating the distance to the Sun, now that the distance to the Moon was known by Greek astronomers.

Correctly understanding that a half-Moon means the Earth and the Moon are forming a right angle, Aristarchus used geometry again to try to compute the angle between the Sun and the Moon relative to Earth (with the Moon in the first quarter phase), computing an angle of 87 degrees. This was close — it's actually 89.83 degrees — but it was off by enough that when combined with Hipparchus's seven percent error and other smaller discrepancies, came up with a distance that was off by more than a factor of 1,000.

Later astronomers would come after and refine this number down, but they were still badly off the mark. In the end, the only thing that would give the true distance to the Sun would be finding its parallax, and that was a problem that centuries of astronomers failed to solve.

Even the most ancient astronomers knew an awful lot about the observable solar system. The inner planets, Mercury and Venus, along with Mars, Jupiter, and Saturn were known and observed by Chinese, Babylonian, and ancient Greek astronomers for nearly as long as records have been kept.

When Johannes Kepler discovered his third law of planetary motion, he unlocked the relative distances of all the observable bodies in our solar system, since the ratio of the cube of an object's mean distance to the sun and the square of its orbital period is the same for all planets.

So, we knew that Mars orbited a known percentage of the distance between Earth and Jupiter. Likewise, that Venus and Mercury were some known percentages of the distance between the Earth and the Sun, but this didn't actually tell us how far away anything actually was from the Sun.

It also couldn't tell us anything about the size of anything in the solar system. The Sun's disk is near-perfectly covered by the Moon during a solar eclipse, but what can that tell us about the size of the Sun?

If the Sun were nearer to us but smaller, and if it were even further away than it is but many times its actual size, we wouldn't be able to tell the difference since they would appear the same apparent size.

Without a single absolute figure to work with, the true scale of the solar system, the size of the Sun and the planets, and their distances from each other was frustratingly out of reach.

In 1629, Kepler predicted that two transits (when one of the inner planets passed directly between the Earth and the Sun and thus appears in silhouette against the solar disk) would occur in 1631 – the Transit of Mercury in November and the Transit of Venus in December.

Kepler died in 1630, so he didn't get to see his predictions validated, but his contemporaries were very interested in predicting subsequent transits. However, it wasn't until Scottish mathematician James Gregory in 1663 that anyone appears to have made the connection between using planetary transits to find the solar parallax and calculate the absolute distance between the Earth and the Sun.

In 1677, Edmond Halley was at an observatory on St Helena, in the southern Atlantic, compiling a star chart of the southern skies. He was able to observe the Transit of Mercury and realized that it could be used to calculate the solar parallax.

By recording the time at specific events — the moment when a planet's silhouette first touches the solar disk, the moment a planet's silhouette fully enters the solar disk, the moment the planet's silhouette touches the edge of the solar disk on its opposite edge and the moment that the planet's silhouette last touches the solar disk at the end of the transit — the difference in the recorded times of each of the four events at different locations could be used to finally solve this astronomical mystery.

Considering the difficulty in seeing Mercury's ingress and egress from the solar disk, Halley determined that the Transit of Venus offered the best chance to record enough accurate data to make the calculations. Unfortunately for Halley, the next Transit of Venus was predicted for 1761, more than 80 years away. Halley was a young man at the time, but not so young that he had any real hope of making any observations himself.

Instead, he made several public pleas for international scientific cooperation to observe the next transit, as well as the one shortly after in 1769, to finally determine the solar parallax. If they didn't do it by 1769, scientists wouldn't get another chance until 1874, almost two centuries in the future.

Halley died in 1742, but scientists the world over would soon step up and take over where he left off.

There was a lot going on in the 1760s in Europe. England and France were busy fighting the Seven Year's War, the first truly global war in human history, so the prospects for international scientific cooperation should have been considered slim at best.

Fortunately, this turned out not to be the case, and scientists the world over, regardless of nationality, took it upon themselves to answer Halley's call.

"Unfortunately," writes Donald Teets in a 2003 article in Mathematics Magazine [PDF] about the 1761 transit,

"it is impossible to describe in this short article all the adventures of those who set out to observe the 1761 transit: of Charles Mason and Jeremiah Dixon who set out for the East Indies, but hadn't so much as left the English channel when their ship was attacked by a French warship, leaving 11 dead and 37 wounded; of the Frenchman Chappe who traveled 1500 miles across Russia to Tobolsk by horse-drawn sleigh, once having to round up his deserting guides at gunpoint; of the Frenchman Le Gentil who was prevented by the war from reaching his destination in India, and so was forced to observe the transit from the rolling deck of a ship in the Indian Ocean."

When the 1761 Transit of Venus took place, at least 122 scientists and observers in 62 different locations around the globe recorded the times of Venus's ingress and egress, the single largest international scientific collaboration ever attempted at the time.

Unfortunately for all involved, not all of the data was sufficient and it gave wildly different results when the calculation was attempted. Far from being dissuaded, the international scientific community put even more of an effort into accurately recording the 1769 Transit of Venus than was attempted in 1761, knowing that this would be their last chance for more than 100 years.

The second attempt, and its many expeditions — including the famous voyage of Captain James Cook to the South Pacific island of Tahiti to observe the transit, before going on to claim Australia for the British Empire and dying while attempting to do the same with Hawaii — turned out to be far more successful.

"Although England was third in the number of observations of the earlier transit," the European Southern Observatory's history of the 1769 Transit reads, "it came first with 69 distinct observations at the 1769 transit. France followed with only 34 observations, which marked a decline of the scientific dominance of France in Europe. In total, the 1769 transit involved 151 professional observing teams distributed over 77 sites."

Thomas Hornsby, a British astronomer, and mathematician at Oxford arrived at the most precise of the calculations to come out of the 1769 Transit of Venus.

"The parallax on the 3d of June being 8.65", the mean parallax will be found to be = 8.78";" Hornsby wrote in 1771, "and if the semidiameter of the Earth be supposed = 3985 English miles, the mean distance of the Earth from the Sun will be 93,726,900 English miles."

Our most accurate measurement of the astronomical unit (AU), the mean distance between the Earth and the Sun, is 92,955,000; Teets notes with admiration that Hornsby's figure was an overcalculation of just 0.8%.

Since every other known distance in the solar system was known in relative terms, once the AU was finally defined, every other measurement in the solar system could be quickly calculated, as could the true size of the Sun, using its angular diameter and the new AU.

There would be more to discover in our solar system, including new planets, but the model of our solar system, first begun by astronomers in antiquity, largely fell into place after 1769.

The parallax method that proved so essential to determining the AU would also become an essential tool for probing the distances of the stars in the sky, identifying the distances to stars like Alpha Centauri and Sirius, as well as distant galaxies and other celestial objects in the night sky.

All told, the effort to observe and record the Transits of Venus in 1761 and 1769 is an incredible feat of human cooperation that shows just how much you can do with a little math when we all come together for a common purpose.