Our Place in Space

Most of us have heard of black holes and supernovas, galaxies and the Big Bang. But few of us understand more than the bare facts about the universe we call home. What is really out there? How did it all begin? Where are we going? In Our Universe: An Astronomer’s Guide, Jo Dunkley traces the evolution of the universe from the Big Bang fourteen billion years ago, past the birth of the Sun and our planets, to today and beyond. She explains cutting-edge debates about such perplexing phenomena as the accelerating expansion of the universe and the possibility that our universe is only one of many. Our Universe conveys with authority and grace the thrill of scientific discovery and a contagious enthusiasm for the endless wonders of space-time. Here is a brief excerpt looking at Edmund Halley’s efforts to find out the size of the Solar System and the first example of the global astronomy community in action.

In 1677 Edmund Halley travelled to the island of St Helena in the Atlantic to map the stars that were only visible from the southern hemisphere, and while there watched the transit of Mercury across the Sun. Inspired, he realized that a transit of Venus provided the key to finding out the size of the Solar System. His method uses parallax, which is an easy concept to understand as you can also use it to measure the length of your arm. You can do it by holding out your index finger at arm’s length, closing one eye and noting where on the opposite wall or backdrop your finger appears to be. Then switch eyes, closing the other one instead. Your finger appears to move sideways. This movement is called parallax, and you can use it to work out how far your finger is from your eye, without actually measuring the length of your arm.

You should notice that if you hold your finger much closer to your eye, as if you have a shorter arm, your finger appears to move sideways a greater amount. The pattern is that the shorter your arm, the more your finger moves sideways. It is convenient to measure the amount of sideways motion as an angle that your finger has moved through. If you were to spin all the way around once, your finger would sweep through an angle of 360 degrees. You should find that your finger appears to move sideways by a few finger-widths when you switch eyes. For reference, a single finger or thumb held at arm’s length takes up an angle of about 2 degrees from side to side. If you know the distance between your two eyes, which might be a few centimetres, you can figure out the exact length of your arm. Here you are using triangle trigonometry. If you know the length of one side of a right-angled triangle, and the size of one angle, you can find out how long the other sides are. Here you have two right-angled triangles, back to back. They are each perhaps 4 centimetres long on their short sides (that is, between each eye and the bridge of your nose). If you measure the angle that your finger moves between closing one eye and the next, that is the same as twice the angle at the far tip of each right-angled triangle. So, if your finger moves 8 degrees, for example, you can work out that the length of your arm is almost 60 centimetres.

This has little practical use, of course, as there are easier ways to measure the length of your arm. But this same method can let us find the distance from Earth to Venus, and there it is invaluable. To use parallax to do this, your two eyes become two positions in the northern and southern hemispheres on the Earth, spread as widely apart as possible. Your finger becomes the planet Venus, which you are trying to find out the distance to. And the backdrop to your finger becomes the Sun. As with many other measurements in space, the triangles here are vast, their short sides being half the distance between the viewing positions on Earth.

You do the equivalent of closing one eye by looking at Venus from the northern hemisphere location as it transits the Sun and noting its position. Then you close the other eye by looking at Venus now from the southern hemisphere and once again seeing where it appears against the background of the Sun. Just like your arm, the more Venus moves against the backdrop of the Sun, the nearer it is to Earth. To work out the distance to Venus, you then just need to know the distance between your two observers on Earth.

There is a complication with this plan. The surface of the Sun is rather featureless, so back in the eighteenth century it would have been too difficult to accurately judge the precise position of Venus seen from different locations on Earth. Halley had an elegant solution, realizing that not only would Venus’ position change depending on the viewing position, but also its transit time across the Sun. The two paths across the circular disc of the Sun would be different in length. The larger the difference in length, or the longer the difference in transit time, the larger the movement of the position of Venus would be against the Sun’s backdrop, and the closer Venus would be to Earth.

This measurement would tell us the distance to Venus, and from there it would be a simple leap to get the distance to the Sun and to the other planets. Johannes Kepler had worked out the pattern that relates the orbit time of a planet with its distance from the Sun, with more distant planets taking longer to orbit. Astronomers had long known the length of a year on Venus by observing its changing position in the night sky. Knowing the length of a year both on Venus and on Earth, and the distance from Earth to Venus, was enough to set the scale of the whole Solar System.

Halley had worked out how to do it, but he knew that he would not live until 1761 to see the next transit of Venus himself. Undaunted, he left inspirational instructions to the next generation of astronomers, exhorting them to go and measure the transits:

I recommend it therefore, again and again, to those curious astronomers who (when I am dead) will have an opportunity of observing these things, that they would remember this my admonition, and diligently apply themselves with all their might to the making this observation; and I earnestly wish them all imaginable success. (Edmund Halley, 1716)

Halley’s message worked. Almost twenty years after his death, astronomers from around the world came together to measure the transits. They were brought together by the French astronomer Joseph-Nicolas Delisle, who strongly encouraged the international scientific community to coordinate observations. Venus takes several hours to cross the Sun, and the difference in this transit time seen from widely spaced locations would be several minutes. To be able to make this measurement accurately, astronomers would not only need to visit far-flung locations in the two hemispheres of the Earth, but would also need to be able to accurately time the duration of the transit, measure their longitude and latitude accurately and have good enough weather to see it. This was not a project for a lone astronomer. Delisle managed to inspire hundreds of astronomers from the United Kingdom, France, Sweden, Germany, Russia and America to take part in this extraordinary coordinated endeavour, in what would be the first example of the global astronomy community in action.