The Ascent of Gravity

by Marcus Chown

  22 L. Chen et ah, ‘Correlations between solid tides and worldwide earthquakes MS a 7.0 since 1900’, Natural Hazards & Earth System Science, vol. 12, 2012, p. 587.

  23 Actually, because of a wobble caused in the motion of the Moon known as ‘libration’ and the fact we see the Moon from different directions depending where we are on the planet – an effect known as ‘parallax’ – we see about 59 per cent of the lunar surface.

  24 The tidal bulge makes an angle of 3 degrees with the Moon, so there is a 3/360 hours x 24 hours = 12 minutes difference between the time a high tide is expected to arrive and the time it actually arrives.

  25 Adam Hadhazy, ‘Fact or Fiction: The Days (and Nights) Are Getting Longer’, Scientific American, 14 June 2010.

  26 Marcus Chown, ‘In the shadow of the Moon’, New Scientist, 30 January 1999.

  27 The angular momentum of a point mass, m, is defined as its linear momentum, mv, multiplied by the distance, r, from the centre of rotation. Since the orbital velocity of a body at a distance, r, from the Earth is proportional to 1/r½, this means the angular momentum is proportional to r × 1/r½ – r½, So the angular momentum of the Moon does indeed go up as it recedes from the Earth.

  28 The Lunokhod 2 reflector works occasionally but the one on Lunokhod 1 was lost for almost forty years. But recently the Lunar Reconnaissance Observer probe imaged the landing site. The coordinates were passed to scientists in New Mexico. And, remarkably, they fired a pulse of laser light at the landing site and, on 22 April 2010, were stunned to receive a return burst of 2,000 particles of light, or ‘photons’. With four, and possibly five, corner-cubes now in action it will be possible to observe not only the recession of the Moon but changes in its shape as it is tidally stretched and squeezed by the Earth.

  29 J. O. Dickey et al., ‘Lunar Laser Ranging: A Continuing Legacy of the Apollo Program’, Science, vol. 265, 1994, p. 482.

  30 In a system of two large bodies bound together by gravity, the Lagrange points are locations at which the combined gravitational pull of the two bodies provides precisely the centripetal force (see Chapter 1) required to orbit with them. There are five such points, which are labeled L1 to L5.

  31 J. Green and Matthew Huber, ‘Tidal dissipation in the early Eocene and implications for ocean mixing’, Geophysical Research Letters, vol. 40, 2013.

  32 The Sun is actually using just about the most inefficient nuclear reaction imaginable. It is turning ‘nuclei’ of the lightest element, hydrogen, into nuclei of the next heaviest, helium. Hydrogen consists of 1 nuclear Lego brick and helium 4, so ‘hydrogen-burning’ is a multi-step process. The first step is the ‘fusion’ of two hydrogen nuclei, or protons. But, on average, it takes two protons in the Sun 10 billion years to meet each other and stick. This is the reason the Sun will take about 10 billion years to burn its hydrogen fuel – it is about half way through its life – and there has been sufficient time for the evolution of complex life like us. The Sun is so inefficient at generating heat that, if you were to take your stomach and a piece of the core of the Sun the same size and shape as your stomach, your stomach would generate more heat. You might then ask: how come the Sun is so hot? The answer is that the Sun does not simply contain one chunk of matter the size and shape of your stomach; it contains countless quadrillion chunks, all stacked together.

  Chapter 4

  1 Isaac Newton, The Principia, edited by Florian (1687).

  2 Despite research I have been unable to find the origin of this quote, which is widely attributed to Paul Dirac.

  3 A modern example of the scarcely believable, predictive power of science is the discovery of the ‘Higgs particle’ in July 2012. Hiking in the Cairngorm Mountains of Scotland in 1964, Peter Higgs realised that the fundamental building blocks of all matter must gain their mass by interacting with a kind of invisible treacle, now called the ‘Higgs field’, that fills all of space, and that, furthermore, a localised excitation of that field should manifest itself as a new subatomic particle. (To be fair, Higgs was one of five physicists to independently come up with the ‘Higgs mechanism’. But his is the name that has stuck.) Almost four decades later, at a cost of more than 10 billion euros, the biggest machine in the world – the Large Hadron Collider near Geneva – found the ‘Higgs particle’. It is just as profound a shock to physicists today, as it was to those in Le Verrier’s time, that nature dances to the tune of the arcane mathematical equations they scrawl across pieces of paper.

  4 In physics, the only system that is ‘exactly soluble’ – that is, whose evolution can be deduced for all time – is the two-body system. This includes the Earth and Moon moving under the influence of their mutual gravitational force and the proton and an electron of a hydrogen atom moving under the influence of their mutual electric force. Once a third body is introduced, things become so horrendously complicated that approximation is the best mathematicians can do. (To calculate the trajectory of an interplanetary space probe, for instance, mission planners have to resort to a ‘brute force’ method. At each location, they have to sum up the forces on the space probe from all the planets, determine how it moves in response to that sum over the next minute; then repeat the whole process at the new location where the forces from all the planets will be slightly different; and so on.) In fact, the long-term evolution of a system of three or more masses under the influence of their mutual gravity, though predictable in theory, is unpredictable in practice. Because of this phenomenon, known as ‘deterministic chaos’, even a tiny difference in the starting locations of planets will, after a while, result in wildly differing behaviour in the distant future. Even worse, the Solar System is unstable in the long term. Like a clock mechanism that unpredictably goes wild, its cogs and wheels flying off in all directions, the Solar System could one day eject Mercury or Mars or any other body. In fact, in the distant past, it may have flung a planet or two into the frigid darkness of interstellar space.

  5 Caroline Herschel has the distinction of discovering more comets than any other woman apart from another Caroline, Caroline Shoemaker, in the late twentieth and early twenty-first centuries.

  6 William Sheehan and Steven Thurber, ‘John Couch Adams’s Asperger syndrome and the British non-discovery of Neptune’, Notes and Records of the Royal Society Journal of the History of Science, vol. 61, issue 3, 22 September 2007 (http://rsnr.royalsocietypublishing.org/ content/61/3/285).

  7 The planets all orbit in the same plane as if they are confined to a giant transparent dinner plate centred on the Sun. This is because of the way in which the Solar System formed 4.55 billion years ago. A spherical cloud of gas and dust shrank under its own self-gravity. Because it was spinning – our Milky Way is a spinning whirlpool of stars, so it is plausible that it was – the cloud shrank faster between its poles than it did around its waist, where gravity was counteracted by a tendency of the cloud material to be flung outwards. As a result, the spherical cloud collapsed to form a thin disc of gas and dust swirling around the newborn Sun. It is because the planets were built up from rubble that collided and stuck together within this disc that they orbit in roughly the same plane and also go around the Sun in the same direction.

  8 See Chapter 3.

  9 See Chapter 3.

  10 Konstantin Batygin and Mike Brown, ‘Evidence for a distant giant planet in the Solar System’, Astronomical Journal, vol. 151, 20 January 2016, p. 22.

  11 A planet shines principally by reflected light from its star, whereas a star generates its own light via nuclear reactions in its core. Such nuclear reactions require a temperature of millions of degrees to ignite, which in turn requires a lot of mass to be bearing down on the star’s core – when things are squeezed they get hot, as anyone who has squeezed the air in a bicycle pump knows. The threshold that divides planets from stars is about 0.08 times the mass of the Sun, or about 80 times the mass of Jupiter. Bodies less massive than this are planets, objects more massive are stars.

  12 A spectrograph uses a ‘diffraction gr
ating’ to fan starlight out into its constituent rainbow colours. A grating often consists of many parallel scratches on the surface of a flat piece of transparent material, and is superior to a glass ‘prism’. Atoms of a particular element in the outer atmospheres of stars create dark bands at characteristic frequencies. Measuring the Doppler shift simply involves seeing how far such bands are shifted in frequency from similar bands created by their earthbound cousins.

  13 Exoplanets are not only found by observing a ‘wobble’ in their parent star. If a planet orbits a star in such a way that it passes periodically across the face of the star as seen from the Earth, then it can dim the light of the star, by about 1 per cent for a Jupiter-mass planet and 0.01 per cent for an Earth-mass planet. The Kepler space observatory, launched into Earth orbit in 2009, has monitored the light of more than 100,000 stars, and found more than 1,000 exoplanets this way.

  14 Not everyone has an unshakeable faith in Newton’s law of gravity. A sizeable minority of astronomers, led by Mordehai Milgrom of the Weizmann Institute in Rehovot, Israel, believe that, below an acceleration of about one-billionth of a g, gravity changes to a stronger form that does not weaken as quickly with distance as an inverse-square-law force. This Modified Newtonian Dynamics, or MOND, can describe the motions of stars orbiting in all spiral galaxies with a single formula. By comparison, a different amount of dark matter with a different distribution is required to explain the motion of stars in each spiral galaxy. A form of MOND which is compatible with Einstein’s theory of relativity was found by Jacob Bekenstein of the Hebrew University of Jerusalem in 2000. See Jacob Bekenstein, 'Relativistic gravitation theory for the MOND paradigm’ (http://arxiv.org/pdf/ astro-ph/0403694v6.pdf).

  15 Vera Rubin, N. Thonnard and Kent Ford, ‘Rotational Properties of 21 Sc Galaxies with a Large Range of Luminosities and Radii from NGC 4605 (R=4kpc) to UGC 2885 (R=122kpc)’, Astrophysical Journal, vol. 238, 1980, p. 471 (http://adsabs.harvard.edu/abs/1980ApJ. . .238..47111).

  16 For more about the Large Synoptic Survey Telecope, see http://www. lsst.org/

  17 See Marcus Chown, Afterglow of Creation, Faber & Faber, London, 2010.

  18 Ibid.

  19 A black hole is a region of space where gravity is so strong that nothing can escape, not even light, hence its blackness. We have discovered two types. There are stellar-mass black holes, formed when gravity crushes a massive star out of existence at the end of its life. And there are ‘supermassive’ black holes, up to 50 billion times as massive as the Sun, of unknown origin, which lurk in the heart of every galaxy, including our own. But some physicists suggest that there could be a third type of black hole: miniature versions created in the first split-second of the big bang and which have survived until the present day.

  20 Table 2 here shows the perihelion precession rates of the eight planets of the Solar System (http://farside.ph.utexas.edu/teaching/336k/ Newtonhtml/nodell5.html).

  21 Ceres, the largest asteroid, visited by NASA’s ‘Dawn’ spacecraft in 2015, was discovered on the first day of the nineteenth century. It was followed in 1807 by Vesta, and then a host of others. Initially, Ceres was thought to be a new planet. But the combined mass of all the hundreds of thousands of asteroids is barely 1 per cent of the mass of the Earth. The asteroids are believed to be builder’s rubble left over from the birth of the Solar System. They were unable to aggregate together to form a planet because of the disruptive gravitational effect of nearby Jupiter. Ceres is now classified as one of the Solar System’s five ‘dwarf planets’.

  22 Sunspots are regions of the Sun where intense loops of magnetic field burst through the ‘surface’, or photosphere. The outward pressure of hot gas within a sunspot need not be as great as elsewhere since it is supplemented by the outward pressure of the magnetic field. Consequently, the gas is a couple of thousand degrees cooler than the 5,800 degrees Celsius temperature of its surroundings. It is because sunspots are cooler than average that they appear black. See Lucie Green, 15 Million Degrees, Viking Penguin, London, 2016.

  Chapter 5

  1 Roberto Trotta, The Edge of the Sky, Basic Books, New York, 2014.

  2 Albert Einstein, ‘On the electrodynamics of moving bodies’, Annalen der Physik, vol. 17, 1905, pp. 891-921. Completed June 1905, received 30 June 1905.

  3 ‘During this year in Aarau, the following question occurred to me: If one pursues a beam of light with the velocity c (velocity of light in a vacuum) one should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. Unfortunately, there seems to be no such thing! This was the first childlike thought experiment that was concerned with the special theory of relativity . . .’ Albert Einstein, Autobiographische Skizze. In Carl Seelig (ed.), Bright Times – Dark Times, Europa Verlag, Zurich, 1956, p. 146.

  4 Thomas Young, who lived in London, may have noticed raindrops falling on a puddle and the way in which concentric ripples spread out from the impact sites and overlap, reinforcing wherever two crests coincide and cancelling out wherever a crest and a trough coincide. If a vertical barrier were placed across the puddle, locations on the barrier hit by strong ripples would alternate with places where the water is calm. Young reasoned that, if he could demonstrate a similar ‘interference’ effect with light, he would prove that it is a wave. He shone a light on a screen with two vertical slits. On the far side, there emerged concentric ripples of light. In the region where they overlapped, he placed a vertical white barrier. Instantly, he saw a pattern of illuminated and dark bands, reminiscent of a supermarket barcode. He had proved light was a wave. Not only that but the spacing of the bands enabled him to deduce that its ‘wavelength’ – the distance over which it makes a complete up-and-down oscillation — is less than a thousandth of a millimetre.

  5 Charles Darwin, On the Origin of Species, 1859.

  6 Actually, a connection between electricity and magnetism and light had been suspected earlier by Michael Faraday. In a letter dated 13 November 1845, he wrote: ‘I happen to have discovered a direct relation between magnetism and light, also electricity and light, and the field it opens is so large and I think rich’ (The Letters of Faraday and Schoenbein, 1836—1862, 1899, p. 148). Among other things, Faraday had found that a magnetic field could change the vibration plane, or ‘polarisation’, of a light wave, a phenomenon now known as ‘Faraday rotation’.

  7 Maxwell’s equations predict the existence of a whole ‘spectrum’ of invisible-to-the-naked-eye electromagnetic waves, of which the waves of visible light are but a tiny portion. ‘Radio waves’ have a wavelength more than 1,000 times longer than visible light.

  8 Richard Feynman, Robert Leighton and Matthew Sands, The Feynman Lectures on Physics, Volume 11, Addison-Wesley, Boston, 1989, pp. 1-11.

  9 The aether had to be stiff enough to ripple at the enormous frequency of a light wave yet insubstantial enough not to noticeably impede the orbit of planets around the Sun. This meant it had to be much stiffer than steel yet much thinner than air. No wonder physicists were in trouble trying to imagine it!

  10 It was Einstein’s friend, Marcel Grossman, a mathematics student he had met when a student in Zurich, who was instrumental in Einstein getting his job at the Patent Office. Grossman had spoken to his father, who had recommended Einstein to Friedrich Haller, the director of the Bern Patent Office. Even at the end of his life, Einstein wrote of his gratitude for what Grossman had done for him.

  11 Abraham Pais, Subtle is the Lord, Oxford University Press, Oxford, 1982.

  12 Albert Einstein, ‘On a heuristic viewpoint concerning the generation and transformation of light’, Annalen der Physik, vol. 17, 1905, pp. 132-84. Completed 17 March 1905, received 18 March 1905.

  13 Albert Einstein, ‘On a new determination of molecular dimensions’. Doctoral thesis. Completed 30 April 1905.

  14 Albert Einstein, ‘On the movement of particles suspended in fluids at rest, as postulated by the molecular theory of heat’, Annalen der Physik, vol. 17, 1905, pp. 549-60. Complete
d May 1905, received 11 May 1905.

  15 Albert Einstein, ‘On the electrodynamics of moving bodies’, Annalen der Physik, vol. 17, 1905, pp. 891-921. Completed June 1905, received 30 June 1905.

  16 Albrecht Fölsing, Albert Einstein, Penguin Books, London, 1997, p. 53.

  17 Kyoto lecture, 14 December 1922. See Physics Today, August 1982, p. 46.

  18 Ibid.

  19 Douglas Adams, Mostly Harmless, Pan, London, 2009.

  20 Although relativity predicts that someone moving relative to you should appear to shrink in the direction of their motion, this is not what you would see because another effect is at play. Light from more distant parts of the person takes longer to reach you than from closer parts. This causes them to appear to rotate. So, if their face is pointing towards you, you will see some of the back of their head. This peculiar effect is known as ‘relativistic aberration’, or ‘relativistic beaming’.

  21 Igor Novikov, The River of Time, Canto, Cambridge, 2001.

  22 The Dutch physicist Hendrik Lorentz and the Irish physicist George FitzGerald had realised that bodies must appear to shrink in their direction of motion – an effect now known as ‘Lorentz-FitzGerald contraction’. But, unlike Einstein, they had not seen it as an inevitable consequence of the principle of relativity and the principle of the constancy of the speed of light.

  23 Although Einstein’s theory was initially known as the ‘theory of relativity’, once he generalised and extended the theory in 1915, it became known as the ‘special theory of relativity’ to distinguish it from the ‘general theory of relativity’.

  24 The fact there is no aether was revealed observationally by the American physicists Albert Michelson and Edward Morley. In 1888, they measured the speed of light when the Earth, in its orbit around the Sun, was flying in the same direction as their light beam; and, six months later, when the Earth was moving in the opposite direction. Just as a boat sailing into a wind has a different speed to one with the wind at its back, they expected the speed of their light to depend on how it met the aether wind. To their utter amazement, they measured the same speed of their light in both cases. The speed of light was constant. For his work, Michelson won the 1907 Nobel Prize for Physics.