Human Universe. Andrew Cohen

without interest, being a binary star system of two orange K-type dwarf stars, slightly smaller and cooler than the Sun, orbiting each other at the lethargic rate of around 700 years. Despite the pair’s relative visual anonymity, however, 61 Cygni has great historical significance. The reason for this quiet fame is that this faint star system was the first to have its distance from Earth measured by parallax.

      Friedrich Bessel is best known to a physicist or mathematician for his work on the mathematical functions that bear his name. Pretty much any engineering or physical problem that involves a cylindrical or spherical geometry ends up with the use of Bessel functions, and, in blissful ignorance, you will probably encounter some piece of technology that has relied on them in the design process at some point today. But Bessel was first and foremost an astronomer, being appointed director of the Königsberg Observatory at the age of only 25. In 1838, Bessel observed that 61 Cygni shifted its position in the sky by approximately two-thirds of an arcsecond over a period of a year as viewed from Earth. That’s not very much – an arcsecond is one 3600th of a degree. It is enough, however, to do a bit of trigonometry and calculate that 61 Cygni is 10.3 light years away from our solar system. This compares very favourably with the modern measurement of the distance, 11.41 ± 0.02 light years. Parallax is so important in astronomy that there is a measurement system completely based on it, which allows you to do these sums in your head. Astronomers use a distance measurement known as a parsec – which stands for ‘per arcsecond’. This is the distance of a star from the Sun that has a parallax of 1 arcsecond. One parsec is 3.26 light years. Bessel’s measurement of the parallax of 61 Cygni was 0.314 arcseconds, and this immediately implies that it’s around 10 light years away.

      Even today, stellar parallax remains the most accurate way of determining the distance to nearby stars, because it is a direct measurement which uses only trigonometry and requires no assumptions or physical models. On 19 December 2013 the Gaia space telescope was launched on a Soyuz rocket from French Guiana. The mission will measure, by parallax, the positions and motions of a billion stars in our galaxy over five years. This data will provide an accurate and dynamic 3D map of the galaxy, which in turn will allow for an exploration of the history of the Milky Way, because Newton’s laws, which govern the motions of all these stars under the gravitational pull of each other, can be run backwards as well as forwards in time. Given precise measurements of the positions and velocities of 1 per cent of the stars in the Milky Way, it is possible to ask what the configuration of the stars looked like millions or even billions of years ago. This enables astronomers to build simulations of the evolution of our galaxy, revealing its history of collisions and mergers with other galaxies over 13 billion years, stretching back to the beginning of the universe. Newton and Bessel would have loved it.

      Stellar parallax, when deployed using a twenty-first-century orbiting observatory, is a powerful technique for mapping our galaxy out to distances of many thousands of light years. Beyond our galaxy, however, the distances are far too great to employ this direct method of distance measurement. In the mid-nineteenth century, this might have appeared an insurmountable problem, but science doesn’t proceed by measurement alone. As Newton so powerfully demonstrated, scientific progress often proceeds through the interaction between theory and observation. Newton’s Law of Gravitation is a theory; in physics this usually means a mathematical model that can be applied to explain or predict the behaviour of some part of the natural world. How might we measure the mass of a planet? We can’t ‘weigh’ it directly, but given Newton’s laws we can determine the planet’s mass very accurately if it has a moon. The logic is quite simple – the moon’s orbit clearly has something to do with the planet’s gravity, which in turn has something to do with its mass. These relationships are encoded in Newton’s law, and careful observation of the moon’s orbit around the planet therefore allows for the planet’s mass to be determined. For the more mathematical reader, the equation is:

      where a is the (time-averaged) distance between the planet and the moon, G is Newton’s gravitational constant and P is the period of the orbit. (This equation is in fact Kepler’s third law, discovered empirically by Kepler in 1619. Kepler’s laws can be derived from Newton’s law of gravitation.) Under the assumption that the mass of the planet is far larger than the mass of the Moon, this equation allows for the mass of the planet to be measured. This is how theoretical physics can be used to extract measurements from observation, given a mathematical model of the system. To measure the distance to objects that are too far away to use parallax, therefore, we need to find a theory or mathematical relationship that allows for a measurement of something – anything – to be related to distance. The first relationship of this type, which opened the door to all other methods of distance measurement out to the edge of the observable universe, was discovered at the end of the nineteenth century by an American astronomer named Henrietta Leavitt.

       SEARCHING FOR PATTERNS IN STARLIGHT

      The Earth is replete with features named after rogues, because history is the province of the rich and powerful and the deserving rarely become either. To find more worthy geographical nomenclature it is necessary to look further afield, to a place that escaped the attention of the vain. The dark side of the Moon is such a place, because nobody had seen it until the Soviet spacecraft Luna 3 photographed it in 1959. It isn’t dark, by the way; it permanently faces away from Earth due to an effect called tidal locking, and receives the same amount of sunlight as the familiar Earth-facing side. The first humans to see it were the crew of Apollo 8, when Bill Anders memorably described it as looking like ‘a sand pile my kids have played in for some time. It’s all beat up, no definition, just a lot of bumps and holes.’ Lacking the smooth lunar maria, the dark side is an expanse of craters, and many of these have been named entirely appropriately after deserving scientists. Giordano Bruno is there, of course, alongside Pasteur, Hertz, Millikan, D’Alembert, Planck, Pauli, Van der Waals, Poincaré, Leibnitz, Van der Graaf and Landau. Arthur Schuster, the father of the physics department at the University of Manchester, is honoured. And tucked away in the southern hemisphere, next to a plain named Apollo, is a 65-kilometre-wide partly eroded crater called Leavitt.

      Henrietta Swan Leavitt was one of the ‘Harvard Computers’, a group of women employed to work at the Harvard College Observatory by Professor Edward Charles Pickering. By the late nineteenth century Harvard had collected a large amount of data in the form of photographic plates, but the professional astronomers had neither the time nor resources to process the reams of material. Pickering’s answer was to hire women as skilled, and cheap, analysts. Scottish astronomer Williamina Fleming was his first recruit, whom he employed after proclaiming that ‘even his maid’ could do a better job than the overworked males at the observatory. Fleming became a respected astronomer; she was made an honorary member of the Royal Astronomical Society in London and, amongst many important published works, discovered the Horsehead Nebula in Orion. Buoyed by this successful policy, Pickering continued to expand his ‘computers’ throughout the later years of the nineteenth century, bringing Henrietta Leavitt into the team in 1893. Pickering assigned her to the study of stars known as variables, whose brightness changes over a period of days, weeks or months. In 1908, Leavitt published a paper based on a series of observations of variable stars in the Small Magellanic Cloud, which we now know to be a satellite galaxy of the Milky Way. It consists of a detailed list of the positions and periods of 1777 variable stars, and towards the end, a brief but extremely important observation: ‘It is worthy of note that in Table VI the brighter variables have the longer periods. It is also noticeable that those having the longest periods appear to be as regular in their variations as those which pass through their changes in a day or two.’

       The history of astronomy is a history of receding horizons.

       Edwin Hubble

      This discovery immediately caught the interest of Pickering, and for good reason. If a star’s intrinsic brightness is known, then