Human Universe. Andrew Cohen
the Earth and not the planets themselves. Copernicus always intended Commentariolus to be the introduction to a much larger work, and included little if any detail about how he had come upon such a radical departure from classical ideas. The full justification for and description of his new cosmology took him a further 20 years, but by 1539 he had finished most of his six-volume De revolutionibus, although the completed books were not published until 1543. They contained the mathematical elaborations of his heliocentric model, an analysis of the precession of the equinoxes, the orbit of the Moon, and a catalogue of the stars, and are rightly regarded as foundational works in the development of modern science. They were widely read in universities across Europe and admired for the accuracy of the astronomical predictions contained within. It is interesting to note, however, that the intellectual turmoil caused by our relegation from the centre of all things still coloured the view of many of the great scientific names of the age. Tycho Brahe, the greatest astronomical observer before the invention of the telescope, referred to Copernicus as a second Ptolemy (which was meant as a compliment), but didn’t accept the Sun-centred solar system model in its entirety, partly because he perceived it to be in contradiction with the Bible, but partly because it does seem obvious that the Earth is at rest. This is not a trivial objection to a Copernican solar system, and a truly modern understanding of precisely what ‘at rest’ and ‘moving’ mean requires Einstein’s theories of relativity – which we will get to later! Even Copernicus himself was clear that the Sun still rested at the centre of the universe. But as the seventeenth century wore on, precision observations greatly improved due to the invention of the telescope and an increasingly mature application of mathematics to describe the data, and led a host of astronomers and mathematicians – including Johannes Kepler, Galileo and ultimately Isaac Newton – towards an understanding of the workings of the solar system. This theory is good enough even today to send space probes to the outer planets with absolute precision.
At first sight it is difficult to understand why Ptolemy’s contrived mess lasted so long, but there is a modern bias to this statement that is revealing. Today, a scientifically literate person assumes that there is a real, predictable universe beyond Earth that operates according to laws of nature – the same laws that objects obey here on Earth. This idea, which is correct, only emerged fully formed with the work of Isaac Newton in the 1680s, over a century after Copernicus. Ancient astronomers were interested primarily in predictions, and although the nature of physical reality was debated, the central scientific idea of universal laws of physics had simply not been discovered. Ptolemy created a model that makes predictions that agree with observation to a reasonable level of accuracy, and that was good enough for most people. There had been notable dissenting voices, of course – the history of ideas is never linear. Epicurus, writing around 300 BCE, proposed an eternal cosmos populated by an infinity of worlds, and around the same time Aristarchus proposed a Sun-centred universe about which the Earth and planets orbit. There was also a strong tradition of classic orthodoxy in the Islamic world in the tenth and eleventh centuries. The astronomer and mathematician Ibn al-Haytham pointed out that, whilst Ptolemy’s model had predictive power, the motions of the planets as shown in the figure here represent ‘an arrangement that is impossible to exist’.
The end of the revolution started by Copernicus around 1510, and the beginning of modern mathematical physics, can be dated to 5 July 1687, when Isaac Newton published the Principia. He demonstrated that the Earth-centred Ptolemaic jumble can be replaced by a Sun-centred solar system and a law of universal gravitation, which applies to all objects in the universe and can be expressed in a single mathematical equation:
The equation says that the gravitational force between two objects – a planet and a star, say – of masses m1 and m2 can be calculated by multiplying the masses together, dividing by the square of the distance r between them, and multiplying by G, which encodes the strength of the gravitational force itself. G, which is known as Newton’s Constant, is, as far as we know, a fundamental property of our universe – it is a single number which is the same everywhere and has remained so for all time. Henry Cavendish first measured G in a famous experiment in 1798, in which he managed (indirectly) to measure the gravitational force between lead balls of known mass using a torsion balance. This is yet another example of the central idea of modern physics – lead balls obey the same laws of nature as stars and planets. For the record, the current best measurement of G = 6.67 × 10-11 N m2/kg2, which tells you that the gravitational force between two balls of mass 1kg each, 1 metre apart, is just less than ten thousand millionths of a Newton. Gravity is a very weak force indeed, and this is why its strength was not measured until 71 years after Newton’s death.
NEWTON’S LAW OF GRAVITY
F
Force between the masses
G
Gravitational constant
m1
First mass
m2
Second mass
r
Distance between the centres of the masses
This is a quite brilliant simplification, and perhaps more importantly, the pivotal discovery of the deep relationship between mathematics and nature which underpins the success of science, described so eloquently by the philosopher and mathematician Bertrand Russell: ‘Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.’
Nowhere is this sentiment made more clearly manifest than in Newton’s Law of Gravitation. Given the position and velocity of the planets at a single moment, the geometry of the solar system at any time millions of years into the future can be calculated. Compare that economy – you could write all the necessary information on the back of an envelope – with Ptolemy’s whirling offset epicycles. Physicists greatly prize such economy; if a large array of complex phenomena can be described by a simple law or equation, this usually implies that we are on the right track.
The quest for elegance and economy in the description of nature guides theoretical physicists to this day, and will form a central part of our story as we trace the development of modern cosmology. Seen in this light, Copernicus assumes even greater historical importance. Not only did he catalyse the destruction of the Earth-centred cosmos, but he inspired Brahe, Kepler, Galileo, Newton and many others towards the development of modern mathematical physics – which is not only remarkably successful in its description of the universe, but was also necessary for the emergence of our modern technological civilisation. Take note, politicians, economists and science policy advisors of the twenty-first century: a prerequisite for the creation of the intellectual edifice upon which your spreadsheets, air-conditioned offices and mobile phones rest was the curiosity-driven quest to understand the motions of the planets and the Earth’s place amongst the stars.
AT THE CENTRE OF THE SOLAR SYSTEM
Matching the observations of the wandering stars – the planets – of the night sky with the idea that the Earth was at the centre of the solar system required extremely complex models. In the case of Venus, combining the Earth at the centre with the observations meant that Venus had a circular orbit around a point midway between the Earth and the Sun, so-called epicycles, with all the other planets having similar complicated orbits around various points scattered around the