The Ascent of Gravity

by Marcus Chown

  Newton knew his heretical ‘Unitarian’ belief was enough to make him an outcast. In fact, there were laws in England which explicitly banned anyone with Newton’s belief from holding any office of importance and which could even have seen him imprisoned. Newton was a fellow of Trinity College, Cambridge, so no one – absolutely no one – was ever to suspect just how much he abhorred the founding principles of that institution. Newton may have learnt to live a secret life because, in a world where religious beliefs were rigidly and ruthlessly enforced, his life depended on it. And that secrecy, perhaps, had seeped into every crevice, every last cranny, of his life.

  So Newton, pacing the rutted lanes around Woolsthorpe, wandering the fields and paths, discovered remarkable things about the world but shared them with no one. He never punched the air and shouted ‘Eureka!’ but kept his discoveries to himself.

  Of course, it is possible to build speculation on speculation about why Newton chose not to share his discoveries in 1666. The fact remains that Newton did not publish his universal theory of gravity for twenty years. What changed everything was a visit to Cambridge by his friend Edmond Halley in August 1684 and a momentous question that Halley asked.

  Further reading

  Ackroyd, Peter, Newton, Vintage, London, 2007.

  Feynman, Richard, Leighton, Robert and Sands, Matthew, The Feynman Lectures in Physics, Volume I, Addison-Wesley, Boston, 1989.

  Gleick, James, Isaac Newton, HarperCollins, London, 2004.

  Goodstein, David and Goodstein, Judith, Feynman’s Lost Lecture: The Motion of the Planets around the Sun, Jonathan Cape, London, 1996.

  Gott, Richard and Vanderbei, Robert, Sizing up the Universe, National Geographic, Washington DC, 2010.

  Pask, Colin, Magnificent Principia, Prometheus Books, New York, 2013.

  Shu, Frank, The Physical Universe, University Science Books, Mill Valley, 1982.

  2

  The last of the magicians

  How Newton created a system of the world and found the key to understanding the Universe

  Newton was the greatest genius who ever lived and the most fortunate; for we cannot find more than once a system of the world to establish.

  Joseph Louis Lagrange1

  Newton was able to combine prodigious mental faculty with credulities and delusions that would disgrace a rabbit.

  George Bernard Shaw2

  Edmond Halley was a great fan of Newton’s. He might even be described as his friend – though, as far as personal relationships were concerned, Newton appeared almost autistic.3 His meeting with Newton had come about because of an argument he had got into in a London coffee house with two friends. One was Robert Hooke, the man who coined the term ‘cell’ for the tiny compartments he had observed stacked together in the tissue of plants. The other was Christopher Wren, the architect working on the construction of St Paul’s cathedral after the destruction of its medieval predecessor in the Great Fire of 1666.

  Halley had puzzled long and hard over Kepler’s third law and its peculiar diktat that the square of the time taken for a planet to orbit the Sun is related to the cube of its distance from the Sun. He had deduced, like Newton, that this could be true only if the planets are responding to an inverse-square law of force. Wren and Hooke, sipping their steaming black coffee and blowing wreaths of smoke from their clay pipes, claimed also to have guessed the inverse-square law. In fact, Wren even asserted that he had known of it many years before Hooke. Hooke, not to be outdone, boasted that, by using an inverse-square law of force, he could explain every last feature of planetary motion. But, when Halley and Wren challenged him to reveal the details, he maintained he was keeping them a secret. Only when more people had tried to do the same as him and failed would he reveal to the world his tour de force.

  Halley was convinced it was all bluster, a childish game of one-upmanship. As he got up to leave, his friends still arguing, he knew what he must do. Only one man was likely to settle the argument with Wren and Hooke. And that was why, in August 1684, he had taken a hot and uncomfortable coach ride from London to Cambridge.

  By now, Newton had a formidable reputation. He had held a permanent chair at the University since 1669. He had been a fellow of the newly founded Royal Society of London since 1672. One year before that he had even delivered to the Fellows of the Society a revolutionary new ‘reflecting’ telescope. By focusing light with a concave mirror rather than lenses, it created images without the shimmering rainbow colours that plagued all ‘refracting’ telescopes.4

  Newton lodged on the first floor of Trinity College between the Great Gate and the Chapel. In his stuffy rooms with the latticed windows flung wide open, Halley looked down on Newton’s large and spacious garden. Hemmed in on all sides by high stone walls, it was accessible only via a staircase inside a wooden loggia projecting from Newton’s rooms. The grass in the garden was neatly trimmed. Newton, with his desire for order and perfection, could not bear the sight of a single weed. There was a mature apple tree, a water pump against a wall, and at one end a wooden shed, where Halley knew fires often burned night and day while Newton carried out his most secretive alchemical experiments.

  Halley turned to the peculiar, unfathomable man, sitting on the couch, waiting expectantly to hear why his visitor had journeyed all the way from London. He cleared his throat and asked his question: ‘Supposing the force of attraction towards the Sun to be reciprocal to the square of their distance from it, what would be the curve described by the planets?’5

  Newton, without hesitation, replied: ‘Why, an ellipse, of course.’

  Halley was stunned. He asked Newton how he knew.

  ‘I have calculated it,’ replied Newton.

  But, though Newton searched among his notebooks and teetering piles of papers, he failed to find any sign of the proof. He promised Halley to redo the calculation and send it to him in London.

  Newton was as good as his word. Several months later, Halley in London received a proof entitled ‘On the motion of bodies in orbit’. In nine short pages of definitions, equations and geometrical drawings, Newton demonstrated that the path of a body experiencing an inverse-square law is an ellipse, as stated by Kepler’s first law of planetary motion. In fact, he showed that an inverse-square law of gravity, together with some basic principles of motion, accounts not only for Kepler’s first law but for all of Kepler’s laws. Actually, Newton went even further than this. He showed that Kepler’s first law in fact describes only a special instance of a body moving under the influence of an inverse-square law of attraction. In general, the path is not an ellipse but a ‘conic section’.

  Picture a cone standing on its base and a sharp knife that can slice clean through the cone. If the knife simply slices through the cone from one side to the other, the cross-section exposed is elliptical. If the knife cuts down through one side of the cone and out through the base, parallel to the other side, the exposed cross-section is an open-ended ‘parabola’. And if the knife cuts down through one side of the cone and out through the base, vertically, the result is an open-ended ‘hyperbola’.

  The three types of path correspond to three different physical situations. If a body experiencing an inverse-square law force has insufficient speed – or energy – to escape the Sun, it will travel for ever in an ellipse around the Sun. If it has sufficient energy to escape, on the other hand, it will follow a hyperbola, flying off to the stars and never coming back. The parabola is the path of a body that sits on the knife-edge between being bound and unbound. It can escape the Sun’s gravitational tyranny only when it has put an infinite amount of distance between it and the Sun, which, in practice, would take an infinite amount of time.

  Newton’s achievement was monumental. He formulated three laws of motion of a radically differ kind to Kepler’s. Although Kepler’s are brilliant and precise, they are no more than mathematical descriptions of the manner in which the planets move about the Sun. They are not explanations of why the planets move in the way they do
. Newton’s laws, on the other hand, describe the motion of all masses, from cannonballs to carriages to planets. They are assumptions about the innermost nature of reality: the relations between matter, forces and motion. And with these three laws, supplemented by his law of gravity, Newton had explained Kepler’s second and third laws. He had also taken his laws of motion plus his inverse-square law of gravity and explained Kepler’s first law – that the planets travel in ellipses. And he had done it in the tedious toddler language of geometry, understandable by his contemporaries, rather than in the few lines of formulae necessary if he had used his mathematical invention of calculus.6

  ‘Newton’s demonstration of the law of ellipses is a watershed that separates the ancient world from the modern world,’ says physicist David Goodstein of the California Institute of Technology in Pasadena. ‘It is one of the crowning achievements of the human mind, comparable to Beethoven’s symphonies, or Shakespeare’s plays, or Michelangelo’s Sistine Chapel.’7

  The Principia – taming the Universe

  When Halley finished reading the nine-page treatise Newton had sent him, he was astounded. In his hands, he knew he held nothing less than the key to understanding the Universe.

  Immediately, he wrote back to Newton, urging to him to allow Halley to arrange the publication of his treatise. But Newton, the perfectionist, said no. He was not satisfied with his work. He was sure he could improve on it, extend it. He had lots more to say about his laws of motion and his law of gravity and, most importantly, their consequences in the world.

  But the dam had finally burst. Halley had created the breach. Newton, for so long the jealous guardian of his discoveries, was now willing to pour them forth. He embarked on a frenetic eighteenth-month period in which he honed his ideas and presented them in a form so convincing and so inevitable that no one would for a moment doubt them. The result was the Philosophies Naturalis Principia Mathematica – ‘The Mathematical Principles of Natural Philosophy’. Published on 5 July 1687, the three volumes and 550 pages of the Principia not only made Newton’s name but they presented an all-encompassing, Universe-explaining ‘system of the world’.

  Newton’s achievement in distilling from the bewildering complexity of the world simple fundamental laws cannot be overestimated. Today, we think in terms of ‘force’ and ‘mass’ and ‘velocity’. But someone had to create that vocabulary, invent that framework of thought. And that person was Newton.

  He struggled with the chaos of contemporary language, zeroing in on fundamental concepts, giving them knife-sharp definitions above and beyond the slippery vagueness of their everyday usage: ‘Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external.’8 It was a titanic struggle, like wrestling a bank of fog to the ground. He was taming the Universe.

  According to Pakistani-born Nobel prizewinner Abdus Salam:

  Three centuries ago, around the year 1660, two of the greatest monuments of modern history were erected, one in the West and one in the East: St Paul’s Cathedral in London and the Taj Mahal in Agra. Between them, the two symbolise, perhaps better than words can describe, the comparative level of architectural technology, the comparative level of craftsmanship and the comparative level of affluence and sophistication the two cultures had attained at that epoch of history. But about the same time there was also created – and this time only in the West – a third monument, a monument still greater in its eventual import for humanity. This was Newton’s Principia.9

  Halley himself used the ideas in Newton’s Principia to show that comets sighted in 1456, 1531, 1607 and 1682 were one and the same body. Travelling in a highly elongated elliptical orbit that takes it far from the Sun, it returns to the inner Solar System and the vicinity of the Earth once every seventy-six years. Halley predicted, correctly, that the comet would return to Earth’s skies in 1758. Although he was not alive to see his triumph – not to mention the triumph of Newtonian science — the comet was henceforth known as Halley’s Comet.

  What is so remarkable about the Principia is that here is a man of the seventeenth century discovering deep truth after deep truth about the world with unerring accuracy. ‘Nature to him was an open book, whose letters he could read without effort,’ said Einstein. Or as Alexander Pope put it: ‘Nature and Nature’s laws lay hid in night: God said: “Let Newton be!” and all was light.’ Newton himself was more modest about his achievements: ‘I do not know what I may appear to the world but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.’10

  Despite Newton’s humility, the Principia is an extraordinary achievement. Three compact volumes that have enabled humans to cross space and set foot on another world, to send space probes sailing out towards the stars, and to understand the motion of distant galaxies turning ponderously in the night.

  The last of the magicians

  The Principia marks Newton out as the pre-eminent thinker of the Age of Enlightenment. This is an extraordinary thing, given his life, because it turns out that science was but one of his interests. In the box Newton left on his death – the one which contained his heretical writings on the Trinity – are other documents. They contained hundreds of thousands of words on his experiments and his thoughts on alchemy, and on his Biblical studies – calculations of the dimensions of the Temple of Solomon, and so on.

  Newton was an alchemist, using skills first learnt from the apothecary he boarded with in Grantham to try and transmute lead into gold by recreating the experiments of old. He was also a Biblical scholar, trying to rediscover the wisdom of the ancients. He believed that the Creator had left clues everywhere for him to read. And those clues were not merely scientific ones.

  Newton was on a personal quest to understand the world – yet another reason why he felt no urge to share his discoveries with others and why they had to be dragged out of him by a man like Halley. ‘To know something that no one else in the world knew or understood — that was a most exhilarating experience of power,’ says novelist and historian Peter Ackroyd. ‘Perhaps he wished to prolong it for as long as possible.’11

  Science, alchemy, the Bible, all these things were to Newton equally legitimate ways to understand the Creator’s creation, equivalent avenues to God. In fact, Newton spent more time working on alchemy and decoding the Bible than he ever did on science – he even predicted that the world would end in 2060. And this is not to mention the twenty-eight years he spent standardising England’s coinage and pursuing counterfeiters as head of the Royal Mint in London.

  But if Newton was a man of contradictions it was probably because of his location in history, as author James Gleick points out:

  He was born into a world of darkness, obscurity and magic. His name betokens a system of the world. But for Newton himself there was no completeness, only a questing – dynamic, protean, unfinished. He never fully detached matter and space from God. He never purged occult, hidden, mystical qualities from his vision of nature. He sought order and believed in order but never averted his eyes from the chaos. He of all people was no Newtonian.12

  The twentieth-century economist John Maynard Keynes said something similar. On the 200th anniversary of Newton’s birth, he wrote: ‘He was the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago. He was not the first of the age of reason. He was the last of the magicians.’

  Further reading

  Ackroyd, Peter, Newton, Vintage, London, 2007.

  Gleick, James, Isaac Newton, HarperCollins, London, 2004.

  Pask, Colin, Magnificent Principia, Prometheus Books, New York, 2013.

  3

  Bewar
e the tides of March

  How Newton’s theory of gravity is rich in consequences and can explain not only the motion of the planets but also the tides in the oceans

  There is a tide in the affairs of men, which taken at the flood, leads on to fortune. Omitted, all the voyage of their life is bound in shallows and in miseries.

  William Shakespeare, Julius Caesar1

  Time and tide wait for no man.

  Proverb2

  It is a bright and frosty morning in mid-March and a washed-out Moon, close to full, is hanging in the blue sky. We are waiting, expectantly, on the river bank, hundreds of us. There is even a TV crew with a young woman in a red puffa jacket and Burberry scarf talking to camera. Now and then people glance down at their watches, then back downstream. But there is nothing to see except a wide river rolling languorously down to the ocean and a pair of comedy swans, repeatedly upending their white bottoms by the opposite bank.

  The scene is so tranquil here on the River Severn at Minster-worth in Gloucestershire that it is impossible to believe that anything out of the ordinary is going to happen. Could it be that we have driven to this location in the West of England and parked in this field for absolutely nothing? Could it be that we are all deluded, gullible victims of some ridiculous hoax?

  But then we hear it – a faint rumble like distant thunder. The swans, startled, right themselves and look all about. The TV reporter in the red puffa jacket breaks off in mid-sentence and swivels to look downstream. And there, suddenly, we see it, preceded by spray, spurting high into the air at a sharp bend in the river bank: a boiling, churning wall of froth and chocolate-brown water spanning the entire 90-metre width of the river and carrying with it kayakers and wet-suited surfers who have been riding the wave all the way from the Severn estuary (the world record, by the way, held by a surfer called Steve Ling, is 14.9 kilometres). Behold the Severn Bore, an angry, stirred-up metre-high hummock of water, racing at up to 21 kilometres an hour the wrong way up the River Severn.