by Marcus Chown
8 Richard Westfall, Never at Rest: A Biography of Isaac Newton, 1983, p. 53.
9 Defoe, Journal o f the Plague Year.
10 William Wordsworth, The Prelude, 1888.
11 The planets crawl across the night sky in a narrow band named the Zodiac along which there are twelve prominent groups of stars, or ‘constellations’, corresponding to the ‘twelve signs of the Zodiac’. The reason for this is that the orbits of the planets are confined more or less to a single plane, known as the ‘ecliptic’. And the reason for this is that the planets all formed from a flat disc of debris swirling around the newborn Sun.
12 The stars appear fixed relative to each other simply because of their immense distances from us. Travelling to even the nearest would be equivalent to flying a billion times around the Earth. But the stars are flying through space, and, over very long periods of, say, tens of thousands of years, they do move significantly enough to alter some of the constellations beyond recognition.
13 The Solar System is defined as the Sun plus its planets and moons plus the assorted debris – asteroids and comets — left over from its formation 4.55 billion years ago.
14 W. W. Rouse Ball, History of Mathematics, 1901.
15 This aspect of Newton’s character was noted by a twentieth-century biographer, John Maynard Keynes: ‘His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen it through.’ Keynes, ‘Newton, the Man’. In Essays in Biography, 1933.
16 The area of a small triangle swept out by a planet in a given time is ½vrt. The fact that ½vrt does not change is telling us that mvr, the planet’s ‘angular momentum’, does not change either. This can happen only if there is no turning force, or ‘torque’ — no force along the trajectory of the planet. In other words, the force must always be directed towards the Sun.
17 Even today it is a mystery why the Universe appears to be describable by mathematical formulae. The twentieth-century Austrian physicist Eugene Wigner remarked on ‘the unreasonable effectiveness of mathematics in the physical sciences’. Why is there a mathematical world which is a perfect analogue of the real world? No one knows.
18 Laws of Physics for Cats (http://www.funny2.com/catlaws.htm).
19 The planets are moving because they were set in motion around the Sun when the Solar System was born and, ever since, have just kept on going. In the modern picture the Sun and planets formed from an interstellar cloud of dust and gas, which began shrinking under its own gravity. The cloud would have been rotating a little because our Galaxy, the Milky Way, is rotating — once every 220 million years – and that rotation would have been amplified as the cloud shrank, just as a ballet dancer’s spin quickens as she pulls in her arms. Inevitably, the planets that formed within the cloud, from the accretion of debris, would have inherited the rotational motion, and thus been born moving around the new-born Sun.
20 Actually, a little bit of simple reasoning can yield the exact form of the centripetal force. If a body is moving slowly in a circle, it needs only a small velocity correction towards the centre to stop it flying off on a tangent; if it is moving fast, it requires a big velocity correction. So the velocity correction goes up with the body’s velocity (it is proportional to v). Now, the ‘acceleration’ of a body is how fast its velocity is changing, which is its velocity change in a given time. The time the body takes to cover a given distance is obviously shorter if the circle is small and longer if it is moving slowly (it is proportional to r/v). Consequently, the acceleration is proportional to v divided by r/v, which is v2/r. And the force, which is simply the mass times the acceleration, is mv2lr.
21 mv2/r = F(r). T2 ~ r3 =>v2 ~ Hr. And so F(r) ~ 1/r1. (Here m stands for the mass of a planet; v for its velocity, F the force of gravity exerted on it by the Sun, and r the distance of the planet from the Sun.)
22 In fact, there is one significant anomaly concerning the orbits of Jupiter’s moons. It was discovered by Ole Christensen Rømer in 1676. The Danish astronomer had spied the moons go around Jupiter many times and timed how long on average it takes each to make a complete orbit — since they periodically go behind Jupiter, the moment they re-emerge is a good moment to begin timing. Röemer was surprised to discover that the moons sometimes appear to be ahead of schedule and sometimes behind. They are ahead when Jupiter is at its closest to the Earth and behind when Jupiter is at its furthest away. What is going on? Rømer realised that it takes time for the light from Jupiter’s moons to cross the space from Jupiter to the Earth. And when Jupiter is at its furthest from us the light takes longer than when it is at its nearest. This is why the moons emerge from behind Jupiter early or late, depending on whether they are closer to or further from the Earth. The phenomenon shows that light does not travel instantaneously. Furthermore, by knowing the extra distance the light has to travel when Jupiter is far away – the diameter of the Earth’s orbit – and the time delay – 22 minutes, Rømer was able to make the first-ever estimate of the speed of light. He got 225, 000 kilometres per second. Not bad considering that the modern estimate is 299,792 kilometres a second. The reason for Rømer’s error was that his estimate of the size of the Earth’s orbit was wrong and the time delay is not 22 minutes but 16 minutes and 40 seconds.
23 Douglas Adams, Life, the Universe and Everything, Picador, London, 2002.
24 The first person to determine accurately both the size and distance of the Moon was the Greek astronomer, geographer, and mathematician Hipparchus, who lived between 190 and 120 BC. During a lunar eclipse he estimated the size of the Earth’s shadow on the Moon, and found it to be 2.5 times the diameter of the Moon. He realised, correctly, that, because the shadow is cast on the curved surface of the Moon, it was shrunk – by 1 Moon diameter – so the Earth is actually 3.5 times the diameter of the Moon. So, if the Earth were viewed from the same distance as the Moon it would appear 3.5 times bigger – that is, instead of appearing only about 0.5 degrees across, as the Moon does, it would appear 1.75 degrees across. (Your thumb held at arm’s length will just cover the Moon — that is, it ‘subtends’ about 0.5 degrees.) The only way something that is the diameter of the Earth can appear 1.75 degrees across in the sky is if it is about 30 Earth diameters away. So the distance between the Earth and Moon is 384,400 kilometres. Obviously, Hipparchus did not get precisely this figure. But he was close.
25 The diameter of the Earth was first estimated by Eratosthenes, chief librarian of the Museum at Alexandria, in 240 BC. Actually, apart from wrinkles like mountains, the Earth seems flat. But, as Eratosthenes realised, this is because the Earth is big and its curvature imperceptible. Evidence that the Earth is round comes from ships at sea, which disappear over the horizon while still sizeable whereas they should dwindle to dots first if the Earth were flat. Also, during a lunar eclipse, when the Earth passes between the Sun and Moon, the Earth’s shadow on the Moon is curved, and the only body that produces a curved shadow from every direction is a sphere. The cleverness of Eratosthenes was to notice that, at the summer solstice when the Sun reached its highest point in the sky, a vertical pillar at Syene (modern-day Aswan) had no shadow – the Sun was directly overhead. On the same day, a pillar at Alexandria had a short shadow, revealing that the Sun was 7 degrees from the vertical. Knowing the separation of Syene and Alexandria, and that 7 degrees is about 1/50th of a full circle, Eratosthenes calculated the Earth’s circumference. From this he obtained a diameter of 7,800 miles, which, incredibly, was only 100 miles out!
26 It’s Only A Theory, BBC4, 2009.
27 A. C. Grayling, The Good Book, Bloomsbury, London, 2013.
28 New York Post, 24 June 1965.
29 ‘Fragments from a Treatise on Revelation’. In Frank E. Manuel, The Religion of Isaac Newton, Oxford University Press, Oxford, 1974.
30 I speculate on why the Universe is simple in Chapter 6 of my book The Never-Ending Days of Being Dead, Faber & Faber, 2007. In Chapter 2 of the same book, I speculate on why the simplicity may be an illusion, caused by ph
ysicists focusing only on the simple bits of the Universe! And in Chapter 8 of my book The Universe Next Door, Headline, 2002,1 speculate on why the Universe is mathematical.
31 Isaac Newton, Query 31, Opticks, 1730.
32 ‘The Potentialities and Limitations of Computers’, lectures by Richard Feynman and Gerry Sussman attended by the author, California Institute of Technology, Pasadena, 1984.
33 Actually, in Germany, the mathematician Gottfried Leibniz had independently invented calculus. In fact, he had invented it before Newton published anything about it, though Newton claimed he knew it even earlier, in 1666, and had described it to Leibniz in correspondence. In his later incarnation as President of the Royal Society, Newton did everything in his power to crush his rival and take sole credit for the invention of calculus.
34 Peter Ackroyd, Newton, Vintage, London, 2007, p. 10.
35 George Gamow, The Great Physicists from Galileo to Einstein, Dover, New York, 1988.
36 Eyesight deteriorates with age for a variety of reasons and it is very likely that Newton’s did too. Often, the deterioration takes the form of a cataract – a clouding of the eye’s natural lens, which lies behind the iris and the pupil. One type, known as a nuclear cataract, forms deep in the central zone, or nucleus, of the lens. When a nuclear cataract first develops, it can bring about a temporary improvement in near vision, dubbed ‘second sight’. Such improved vision is short-lived and will disappear as the cataract worsens. So is the explanation of Newton’s exceptional eyesight at eighty-four that he was benefiting from the temporary improvement of a nuclear cataract and fortunately died before the improvement disappeared?
37 Keynes, ‘Newton, the Man’.
Chapter 2
1 Quoted in Forest Ray Moulton, Introduction to Astronomy, Macmillan, New York, 1906, p. 199.
2 In 1930, in an after-dinner toast to Albert Einstein, who was present. Quoted in Blanche Patch, Thirty Years with G.B.S., Gollancz, London, 1951.
3 Hazel Muir, ‘Einstein and Newton showed signs of autism’, New Scientist, 30 April 2003 (https://www.newscientist.com/article/ dn3676-einstein-and-newton-showed-signs-of-autism/).
4 Even Newton’s ‘reflecting telescope’ was a spin-off of his monumental work on light and optics, which was also secret and was to be dragged out of him – pretty much everything had to be dragged out of him -and published as Opticks as late as 1710.
5 Abraham DeMoivre, quoted in Richard Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge University Press, Cambridge, 1983.
6 More than three centuries later, another genius, the American physicist Richard Feynman, so wanted to get into the mind of Newton that he re-invented a geometrical proof that bodies under an inverse-square law force travel in ellipses. After Feynman’s death in 1988, his friends David and Judith Goodstein published it in Feynman’s Lost Lecture: The Motion of the Planets Around the Sun, Jonathan Cape, London, 1996.
7 Ibid.
8 Isaac Newton, Philosophic Naturalis Principia Mathematica (1687), ‘General Scholium’.
9 Abdus Salam, C. H. Lai and Azim Kidwai, Ideals and Realities: Selected Essays of Abdus Salam, World Scientific, Singapore, 1987.
10 Sir David Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton, 1855.
11 Peter Ackroyd, Newton, Vintage, London, 2007, p. 29.
12 James Gleick, Isaac Newton, HarperCollins, London, 2004, p. 8.
Chapter 3
1 William Shakespeare, Julius Caesar, Act IV, Scene 3.
2 Although this saying is often attributed to Geoffrey Chaucer, its first apppearance in this form dates from the eighteenth century. It is listed as an existing proverb by Nathan Bailey in his Dictionarium Britannicum: Or, A More Compleat Universal Etymological English Dictionary Than any Extant (Second edition, 1736).
3 The word bore derives from the Old Norse word bâra, meaning ‘wave’ or ‘swell’.
4 The bore can be as much as 7.5 metres high and reach a speed of 27 kilometres an hour.
5 Kieran Westley and Justin Dix, ‘Coastal environments and their role in prehistoric migrations’, Journal of Marine Archaeology, vol. 1,1 July 2006, p. 9 (http://www.science.ulster.ac.uk/cma/slan/westley_dix_2006. pdf).
6 Julius Caesar, ‘Caesar in Britain. Heavy Damage to the Fleet’, History of the Gallic Wars.
7 Martin Ekman, ‘A concise history of the theories of tides, precession-nutation and polar motion (from antiquity to 1950)’, 1993 (http:// www.afhalifax.ca/magazine/wp-content/sciences/vignettes/supernova/ nature/marees/histoiremarees.pdf).
8 The tidal force on the ocean furthest from the Moon is slightly smaller than on the ocean nearest the Moon by a factor of about (60/62)2 = 0.94 because the ocean there, rather than being 60 Earth radii from the Moon is 62 Earth radii from the Moon. Consequently, the tidal bulge is slightly smaller.
9 From the observation that the tides pulled by the Moon are about twice as big as those pulled by the Sun, Newton was able to deduce that the average density of the Moon is about twice that of the Sun. His logic is as follows: the tidal force exerted by a body depends on its mass. Tidal forces are also due to differences in gravity so they weaken not according to an inverse-square law but an inverse-cube law. The tidal force exerted by a mass m at a distance r is, therefore, ~m/r3. But m∼pd3, where p is its average density and d is its diameter, d is just rθ, where θ is the angle subtended by the body in the sky. Putting all this together implies that the tidal force ∼pθ3. But the angular size of the Moon and Sun, by a cosmic coincidence, are almost the same — it is why the Moon can exactly blot out the Sun during a total eclipse. Consequently, the Moon and Sun exert a tidal effect in proportion to their densities - a surprising result. Since the Moon pulls tides twice as big as the Sun, it follows that it must have twice the average density of the Sun.
10 The plane of the Moon’s orbit is inclined to the Earth’s equator, varying between 18.28 and 28.58 degrees of the equatorial plane.
11 To be precise, maximum bores occur one to three days after new and full moons.
12 Chaim Leib Pekeris, ‘Note on Tides in Wells’, Travaux de l’Association Internationale de Géodésie, Paris, vol. 16, 1940.
13 In 1905, Albert Einstein discovered that mass is simply a supercompact form of energy (his formula E = mc2 describes the exact connection, with c representing the speed of light). According to the law of conservation of energy, energy cannot be created or destroyed, only converted from one form to another. This means that the energy of motion (kinetic energy) of colliding subatomic particles can be converted into the mass-energy of new particles. This, in a nutshell, is how particle colliders such as the one at CERN work.
14 Technically, the protons have an energy of 7 teraelectronvolts (TeV), giving a total collision energy of 14 TeV At 99.9999991 per cent of the speed of light, they travel around the CERN ring 11,000 times a second. Their ‘Lorentz factor’, γ, is about 7,500, which means they are 7,500 times more massive than protons at rest. This is an effect of Einstein’s special theory of relativity, which ensures massive bodies become ever more massive and ever harder to push as they approach the speed of light, so that the speed of light is forever unreachable (see Chapter 5). Although the LHC protons travel within a mere 3 metres per second of the speed of light – about the speed of a jogger - boosting their velocity by that amount would require an infinite amount of energy.
15 Every subatomic particle has an antimatter twin with opposite properties such as electric charge and quantum ‘spin’. The antiparticle of the negatively charged electron is the positively charged positron.
16 L. Arnaudon et al., ‘Effects of terrestrial tides on the LEP beam energy’, CERN SL/94-07 (BI), 1995 (https://jwenning.web.cern.ch/jwenning/documents/EnergyCal/tide_slrep.pdf).
17 To keep a body of mass, m, moving in a circle of radius, r, at a velocity, V, requires a centrally directed ‘centripetal force’, F – mv2/r (see Chapter 1). If the radius of the ring gets bigger, the force, F, exerted by
the LEP magnets, which is constant, is too big to keep the particles travelling around the larger circle, unless v2, which is related to the energy of the particles, goes up in the same proportion. On the other hand, if the radius of the ring gets smaller, the force, F, exerted by the magnets is too small to keep the particles travelling around the smaller circle, unless the energy of the particles goes down in the same proportion.
18 The tidal effect on CERN’s accelerator ring is not the only effect that has been observed by the laboratory’s physicists. Every day, at very particular times, the energy of the beams has to be corrected. It took the physicists many months to discover why. Bizarrely, it was the fast TGV train linking Geneva and Paris. As it passed close to the LEP ring, it released a lot of electrical energy into the ground which perturbed the particle beams.
19 The same logic predicted that the tidal forces on the Mediterranean are less than half those on the Atlantic because the Mediterranean’s depth is on average less than half that of the Atlantic.
20 Arlin Crotts, ‘Transient Lunar Phenomena: Regularity and Reality’, 2007 (http://xxx.lanl.gov/PS_cache/arxiv/pdf/0706/0706.3947vl.pdf). Arlin Crotts, ‘Lunar Outgassing, Transient Phenomena and the Return to the Moon, I: Existing Data’, 2007 (http://xxx.lanl.gov/PS_cache/ arxiv/pdf/0706/0706.3949vl.pdf). Arlin Crotts and Cameron Hummels, ‘Lunar Outgassing, Transient Phenomena and the Return to the Moon, II: Predictions of Interaction between Outgassing and Regolith’, 2007 (http://xxx.lanl.gov/PS_cache/ arxiv/pdf/0706/0706.3952vl .pdf). Arlin Crotts,‘Lunar Outgassing, Transient Phenomena and the Return to the Moon, III: Observational and Experimental Techniques’, 2007 (http://xxx.lanl.gov/PS_cache/arxiv/pdf/0706/0706.3954vl.pdf). Marcus Chown, ‘Does the Moon have a volcanic surprise in store?’ New Scientist, 26 March 2008.
21 The creation of the Mare basins is associated with the Late Heavy Bombardment. This is believed to have happened when Jupiter and Saturn, in moving to their present locations, briefly entered a 2:1 resonance in which for every two orbits Jupiter made around the Sun, Saturn circled just once. This periodically brought the two planets close together, boosting their gravitational effect on other bodies. Like a child periodically pushed on a swing that gets ever higher, small bodies such as the rocky asteroids were pushed ever more from their orbits, and plunged into the inner Solar System, where they bombarded the inner planets such as the Earth and Moon.