How far from the Earth to the Sun – the Astronomical Unit

Next year is the 250th anniversary of James Cook's voyage to the Pacific Ocean. One the things he did was contribute to a more accurate calculation of the distance between the Earth and the Sun by observing the transit of Venus.

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Measuring the distance between two things is pretty simple if you have a tape measure and the objects aren’t very far apart. Though, it’s not the preferred method for measuring the distance between planets or stars. To do this you have to use trigonometry and for things more than a couple of hundred light years away you’ll need a lot more than basic maths. Understanding the distance between celestial objects was not an easy journey and it’s something we’re still figuring out. Fortunately we have a very good understanding of the distances within the Solar System thanks to the laws Johannes Kepler devised and a bunch of other famous scientists since Kepler’s time who have successfully measured and calculated distances.

The key bit of information that eluded astronomers for most of history was an accurate measurement of the distance between the Earth and Sun. This was almost like the last piece in the puzzle that enabled scientists to piece together how most of the close celestial objects fitted together. This distance is called the astronomical unit and it is defined exactly as 149,597,870,700 metres (from the centre of the Sun to the centre of Earth). The challenge to figure this out led to one of the first international science collaborations and it spanned the globe and the complex international relations of the late 1700s. The key astronomical event at the centre of understanding the astronomical unit was the transit of Venus.

Time for a little bit of trigonometry: the key to finding the distance between the Sun and the Earth is measuring the angle the radius of the Earth subtends at the Sun.

What does this mean? If you were standing on the Sun’s surface and could measure the angular difference between the Earth’s centre and its edge you’d get a very small angular measurement (and very severe radiation burns!), that angle is called the Solar Parallax. But because you already know the radius of the Earth then the angle you just measured would help you figure out the distance between the Earth and the Sun by using some simple maths. Measuring that angle is a lot more tricky if you’re not standing on the Sun but on the Earth’s surface, like all of us and all of the humans before us (except those of our species that stood on the Moon).

The 1600s was when early astronomers started to figure out, with improving accuracy, the distance between the Earth and the Sun. Up until then the Ptolemaic view of the world had been used which was based on a solar parallax of 2′ 50″ which gave an estimated distance of the Sun to Earth of about 1210 Earth radii (the actual figure is 23,455 Earth radii and an angle of 8.794143″), so rather a long way off. The discovery of Kepler’s laws of planetary motion enabled astronomers to understand the relative relationship between the celestial bodies though had not uncovered the real distances between them, but his work sparked a renewed interest in trying to measure this critical distance. The solar parallax angle can’t be measured directly and it had been figured out that the best way to measure it was to take multiple measurements of a transit of Venus from different spots around the globe and work out the angle based on Venus, basically figuring out the distance to Venus then using Kepler’s laws to work out the distance to the Sun. The famous astronomer Edmund Halley in 1677 outlined how the transit could be used to get an accurate estimation of the distance to the Sun, unfortunately he died in 1742 so was unable to witness the results of the two Venus transits in 1761 and 1769 that were, in part, inspired by his work.

What ensued was a series of amazing and dangerous voyages for many astronomers as the great powers of Europe sought to be the first to calculate the distance between Sun and Earth. For Britain, the Royal Society commissioned a number of voyages and one was given to James Cook and Charles Green. Green was a prominent astronomer and had worked for the Royal Astronomer for a number of years and Cook was Royal Navy officer given his first command for the voyage. They headed off to Tahiti to conduct their observations of the transit in 1769. The Royal Society also organised another four voyages to different parts of the world, with one of them being William Wales and Joseph Dymond’s trip to Hudson Bay in Canada. In 1771 The French astronomer, Jérôme Lalande, compiled many of the observations from both transits and was able to calculate a value of 24,000 Earth radii (or 153 million kilometres, only just under 3.5 million off the figure we know today). Then in 1772 Maximilian Hell calculated a more accurate result from his own expedition combined with data from James Cook’s and William Wales’ voyages. This result pushed the distance to 151.7 million kilometres. With this astronomers knew, to ever increasing accuracy, the dimensions of the Solar System.

The next advancement happened towards the end of the 1800s when the American astronomer Simon Newcomb combined data from four transits (including the two in 1874 and 1882) and got the distance down to 149.59 +/-0.31 million kilometres. Improvements continued throughout the 20th century until the distance was agreed as a standard in 2012. That distance was based on a theoretical circular orbit and as so much is known about the dimensions of the Solar System and beyond the value of the AU has diminished somewhat.

Understanding the distance from the Sun to the Earth also helped astronomers figure out the distance to some of the closest stars by using stellar parallax. This is where a star is observed and measured and then six months later is also measured and the differences are used to calculate the angle between the viewing positions and then the distance can be found. Now that the distance from the sun to the Earth was known, the distances to some of the nearest stars could be found. This required very careful measurement and was not the easiest thing to do with the equipment available in the 1800s. That all changed when photography was combined with astronomy so more detailed measurements could be made and higher accuracies obtained.

Next year is the 250th anniversary of James Cook’s voyage to the Pacific and following his observation of the transit of Venus, that contributed to the more accurate calculation of the AU, he continued on his voyage and became the first European to land in New Zealand where he went on to observe the transit of Mercury and extensively map the coastline of the country.