Forces of Nature. Andrew Cohen

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СКАЧАТЬ Why is the Earth a sphere?

      There is a photograph of our planet known as the Blue Marble. It was taken on 7 December 1972 by the crew of Apollo 17 during their journey to the Moon. Close to the winter solstice, Antarctica is a continent of permanent light, and Madagascar, the island of lemurs, takes centre stage. Ochre deserts set against blue oceans, green hues hinting at life.

      On 5 December 2012, NASA released the Black Marble, an image of the Americas at night. Now we see a civilisation on the planet; the lights herald the dawn of the Anthropocene – the age of human dominance. What do we see in these images? What is the most basic property of Earth? Alexei Leonov, on completing the first human spacewalk on 18 March 1965, had an answer.

       ‘I never knew what the word round meant until I saw Earth from space.’

      Alexei Leonov, Voskhod 2, Soyuz 19/ASTP

      Seen from space, the Earth is a near-perfect sphere. All the planets in the Solar System, all the large moons and the Sun itself share this property, as does every star in the Universe. Why? If lots of different objects share a common feature, there must be an explanation. To make progress, let’s think about what could affect the shape of a planet, moon or star. It can’t be much to do with their composition because planets are made of different stuff to stars. The Earth is made up of heavy chemical elements such as iron, oxygen, silicon and carbon. The Sun, on the other hand, is primarily hydrogen and helium; it’s a giant ball of plasma with no solid surface. Giant planets such as Jupiter have more in common with stars than with Earth, at least in terms of their composition. They too are primarily composed of hydrogen and helium. Stars and planets are united, however, by the force that formed them and holds them together – gravity. So to understand why they are all spherical, we should explore the nature of the gravitational force further.

      Defying gravity

      For most of the time Tarragona is a quiet Mediterranean port on the northeastern coast of Spain, but each September it explodes into vivid, violent colour as teams compete against gravity in the Tarragona Castells competition. Castells are human towers, reaching ten people high and involving an intricate mix of strength, balance, strategy and teamwork to be built up to the top. Each team begins by forming the foundations of the tower, with up to two hundred people creating the pinya. Once the foundation is in place, a variety of human geometries are used to build as high as possible, with each level taking shape before the next is added. The most successful team is the Castellers de Vilafranca, having won the Tarragona competition eight times since 1972. A mass of green shirts acting in unison flows from one level to the next, with higher levels consisting of fewer people, until two children form a final stable platform for the enxaneta – the casteller who ascends daringly to the summit; since low mass, agility – and perhaps a lack of fear – are called for, the enxaneta will be as young as 6 or 7 years old. This is what the crowds have come to see. Towers give way, human buildings come tumbling down, falls softened by the elbows, knees, heads and shoulders, colliding and crashing, usually delivering only bruises, bumps and the occasional lost tooth. Serious injuries are very rare.

      It is obvious why people fall to the ground if they lose their balance: gravity. But how precisely do objects 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. СКАЧАТЬ