Forces of Nature. Andrew Cohen

behave under the influence of gravity? We have two theoretical frameworks, both of which are still in use, depending on what we wish to calculate. Here we see an idea central to the success of science; there are no absolute truths! Usefulness is the figure of merit; if a theory can be used to make predictions that agree with experiment in certain circumstances, then as long as we understand the restrictions, we can continue to use the theory. The first theory of gravity was written down by Isaac Newton in 1687 in his Philosophiae Naturalis Principia Mathematica – the mathematical principles of natural philosophy, inspired at least in part by the work of our curious companion, Johannes Kepler.

      A more precise description of gravity was published in 1915 by Albert Einstein. Newton’s theory doesn’t have anything to say about the mechanism by which gravity acts between objects, but it does allow us to calculate the gravitational force between any objects, anywhere in the Universe. Einstein’s more accurate Theory of General Relativity provides an explanation for the force of gravity. Space and time are distorted by the presence of matter and energy, and objects travel in straight lines through this curved and distorted spacetime. Because of the distortion, it appears to us as if the objects are being acted upon by a force, which we call gravity. But in Einstein’s picture there isn’t a force; there is curved spacetime and the rule that everything travels in a straight line through it. We will encounter spacetime in much more detail in Chapter Two.

      To answer the question about spherical planets, we don’t need Einstein’s elegant but significantly more mathematically challenging Theory of General Relativity. It is a sledgehammer to crack a nut. We’ll therefore confine ourselves to Newton’s simpler theory; General Relativity would give the same answer. Here is Newton’s Law of Universal Gravitation:

F = G m M / r²

      In words, this equation says that there is a force between all objects, F, which is equal to the product of their masses, m and M, and inversely proportional to the square of their distance apart, r. If you double the distance between two objects, the gravitational force between them falls by a factor of 4. G is known as Newton’s Constant, and it tells us the strength of the gravitational force. If we measure mass in kilograms, distance in metres and wish to know the gravitational force in Newtons, then G = 6.6738 x 10^-11 m³ kg^-1s^-2.

      Newton’s Gravitational Constant is one of the fundamental physical constants. It describes a property of our Universe that can be measured, but not derived from some deeper principle, as far as we know. One of the great unsolved questions in physics is why Newton’s gravitational constant is so small, which is equivalent to asking why the gravitational force between objects is so weak. Comparing the strengths of forces is not entirely straightforward, because they change in strength depending on the energy scale at which you probe them; very close to the Big Bang, at what is known as the Planck temperature – 1.417 x 10³² degrees Celsius – we have good reason to think that all four forces had the same strength. To describe physics at such temperatures we require a quantum theory of gravity, which we don’t currently possess in detail. But at the energies we encounter in everyday life, gravity is around forty orders of magnitude weaker than the electromagnetic force; that’s 1 followed by 40 zeroes. This smallness seems absurd, and demands an explanation. Physicists speculate about extra spatial dimensions in the Universe and other exotic ideas, but as yet we have no experimental evidence to point the way. One possibility is that the constants of Nature were randomly selected at the Big Bang, in which case they are simply a set of incalculable fundamental numbers that define what sort of Universe we happen to live in. Or maybe we will one day possess a theory that is able to explain why the fundamental numbers take on the values they do.

      Newton discovered his law of gravity by looking for a simple equation that could describe the apparent complexity of the motions of the planets around the Sun. Kepler’s three empirical laws of planetary motion can be derived from Newton’s Law of Gravitation and his laws of motion. This is why we might describe Newton’s theory as elegant, in line with our discussion of quantum theory earlier in the chapter. Newton discovered a simple equation that is able to describe a wide range of phenomena: the flight of artillery shells on Earth, the orbits of planets around the Sun, the orbits of the moons of Jupiter and Saturn, the motion of stars within galaxies. His was the first truly universal law of Nature to be discovered.

      The answer to our question ‘why is the Earth spherical?’ must be contained within Newton’s equation, because the Earth formed by the action of gravity. The gravitational force is the sculptor of planets. Our Solar System formed from a cloud of gas and dust, collapsing due to the attractive force of gravity around 4.6 billion years ago. The Sun formed first, followed by the planets. Let’s fast-forward a few million years to a time when the infant Sun is shining in the centre of a planet-less Solar System. Circling the young Sun are the remains of the cloud of dust and gas out of which the Sun formed, containing all the ingredients to make a planet. This is known as a protoplanetary disc. The fine details of the formation of planets are still a matter of active research, and the mechanisms may be different for rocky planets such as the Earth and gas giants such as Jupiter. For Earth-like planets, random collisions between dust particles can result in the formation of objects of around 1 kilometre in diameter known as planetesimals. These grow larger as they attract smaller lumps of rock and dust by their gravitational pull, increasing their mass, which increases their gravitational pull, attracting more objects, and so on. This is known as runaway accretion, and computer simulations using Newton’s laws suggest that through a series of collisions between these ever-growing planetesimals, a small number of rocky planets emerge from the protoplanetary disc orbiting the young star.

      Models of planetary formation can be checked using the telescopic observation of young star systems. In 2014 the ALMA (Atacama Large Millimeter/submillimeter Array) observatory in Chile captured a beautiful image of a planetary system forming inside a protoplanetary disc around HL Tauri, a system less than 100,000 years old and only 450 light years from Earth. A series of bright concentric rings is clearly visible, separated by darker areas. It is thought that these dark gaps are being cleared by embryonic planets orbiting around the star and sweeping up material – they are the shadow of the planetary orbits. It is interesting to note that planetary formation appears to be well advanced in this very young system. This image is perhaps a glimpse of what our Solar System looked like 4.5 billion years ago.

      Rocky planets begin life as small, irregular planetesimals and evolve over time into spheres. To make progress in understanding why, we might make an observation; all objects in the Solar System are not spheres. The Martian moon Phobos has a radius of approximately 11 kilometres. It is a misshapen lump. Smaller still are the asteroids, comets and grains of dust that formed at the same time as the planets. The Comet 67P/Churyumov–Gerasimenko is less than 5 kilometres across and is an intriguing dumbbell shape. Analysis of data from the Rosetta spacecraft, in orbit around the comet at the time of writing, has shown that 67P was formed by a low-velocity collision of two larger objects. Perhaps this is a snapshot of the processes that previously resulted in the formation of much larger objects such as planets and moons. Smaller lumps of rock merge together under the influence of gravity, and if there is enough material in the vicinity, as there would have been early in the life of the Solar System, the objects will undergo many such collisions and grow. Why isn’t comet 67P spherical?

      ‘FORÇA, EQUILIBRI, VALOR I SENY’

      (STRENGTH, BALANCE, COURAGE AND COMMON SENSE)

      Let’s return to the human towers. What sets the maximum height of a tower? Consider an artificial situation in which the tower is a vertical stack of humans, one on top of the other. If there are only two people in the stack, then the force on the person at the base is the weight of the person above. Let’s understand that sentence. What is weight? Your weight at the Earth’s surface is given by Newton’s equation; it is defined to be the force exerted on you by the Earth. What numbers should we put into the equation to calculate it? Your mass: 75kg. The mass of the Earth: 5.972 x 10²⁴ kg. Newton’s gravitational constant, G: 6.6738 x 10^-11 m³ kg^-1s^-2. What should we use for r? This is the distance from the centre of the Earth to