Forces of Nature. Andrew Cohen

with a mean radius of just over 11 kilometres and a mass of only 10¹⁶ kilograms, the gravitational force at its surface is far too weak to overcome the rigidity of rock and act to flatten the surface and sculpt Phobos into a sphere. At around 550 kilometres across, the asteroid Pallas is the largest known non-spherical object. Saturn’s moon, Mimas, with a radius of just under 200 kilometres, is the smallest known body in the Solar System that is spherical. It is made mostly of ice, which is much easier to deform than rock – this is why it is so small and still round. Our estimate is certainly in the right ballpark.

      As an important aside, ‘back-of-the-envelope’ estimates such as these are very important in physics; they tell us that we are on the right track, without overcomplicating things unnecessarily. We could have refined our calculation by taking into account the different compositions of different objects, and by computing the gravitational pull at different depths more carefully. We could even have tried to use General Relativity instead of Newton’s laws, but we wouldn’t have learnt a lot by doing so. Learning what to ignore and what to include is part and parcel of becoming a professional scientist – one might call it physical intuition. There is no precise size above which a body will be spherical; the limit depends on the object’s composition; a mixture of rock and ice is easier to deform than solid rock. As a general rule, any icy moon over 400 kilometres in diameter will be a sphere. Objects made of rock need to be larger, because the gravitational force needed to deform rock is greater. If a rocky moon has an internal heat source, perhaps as a result of the presence of large amounts of radioactive material in its core or tidal heating, the body is easier to deform and may be spherical at a smaller size than would be expected for a less active object. The Solar System is full of examples of this interplay of rigidity and gravity in action, but, very roughly, we have deduced that anything with a radius in excess of a few hundred kilometres must be spherical because the gravitational forces will overcome the strength of the rock.

      When gravity wins, the shape of the objects it creates reflects the underlying symmetry of the physical law, and this is why large single objects such as planets and stars are always spherical.

      At larger scales, however, things change. Our nearest galactic neighbour, Andromeda, contains around 400 billion stars, formed and bound together by gravity. It is disc-shaped, not spherical. The Solar System itself is also a disc and not a sphere. Why?

      Why are there discs as well as spheres in the Universe?

      We argued above that planets and large moons are spheres because, if the gravitational forces are large enough to overcome the electromagnetic forces that keep matter rigid, the underlying symmetry of the gravitational force is made manifest in the objects it creates. Because there is no special direction in Newton’s Law of Gravitation, there will be no special direction in the objects that it creates. This is not entirely true, however, even for planets, because they spin.

      Our planet turns on its axis once every 24 hours. The spin axis marks out a special direction, which means that all points on the Earth are not the same. Someone standing on Earth’s Equator is rotating at a speed of 1670 km/hour, whilst someone in Minnesota is rotating at a speed of 1180 km/hour. The spherical symmetry is broken – the two points are different. As we’ll see in Chapter Two, this difference leads to observable effects such as the rotation of storm systems and the deflection of artillery shells in flight. It also leads to a very slight flattening of the Earth – the equatorial circumference is 40,075 kilometres and the polar circumference is 40,008 kilometres. The Earth is not spherical, but an oblate spheroid, because of its spin. If it were spinning faster, the Earth would be more oblate. When our Solar System formed, the spin – or more correctly angular momentum – was ‘exported’ outwards from the newly forming Sun, primarily through collisions and magnetic interactions in the protoplanetary disc, resulting in the system becoming flattened into a disc.

      The transfer of spin outwards from the centre also results in the flattening of some galaxies; for example, Andromeda. Globular star clusters, such as the spectacular Messier 80, remained spherical because they were too diffuse for angular momentum to be transferred outwards. The shapes of objects that are bound together by gravity are therefore dependent on the amount and location of the ‘spin’. For the experts, the ratio of angular momentum L to gravitational potential energy E is the figure of merit. Large L/E = disc. Small L/E = spherical.

      Some of the many properties that have resulted in partial loss of the symmetry in the Solar System disc.

      There is a very important idea hiding here. We used the term ‘symmetry breaking’ to describe how the presence of a spin axis marks out a particular direction, resulting in an object deviating from the ‘perfect’ spherical shape that reflects the symmetry of the underlying law of Nature – in this case gravity. The disc of our Solar System is less symmetric than a sphere because it only remains the same when rotated about a particular axis in space – the spin axis. The symmetry has been partially lost. We might say that the symmetry of the law of gravity that created our Solar System has been hidden by the presence of a special direction in space – the spin axis. The spin itself came from the precise details of the collapse of the initial dust cloud almost 5 billion years ago, and the distribution of the spin between the Sun and planets depended on the precise speed of collapse, the density of the protoplanetary disc and myriad other subtle details over the history of the Solar System’s formation. This highlights one of the central challenges in modern science: which properties of the structures we see in Nature are reflections of the underlying laws of Nature, and which properties are determined by the history of formation or other influences? This is particularly difficult to answer when the physical systems in question are complicated. The shapes of planets, solar systems and galaxies, whilst astronomical in size, are easier to explain than the shapes of more mundane objects that we encounter every day. Let’s jump from simple planets to the most complex of all physical structures – living things. By exploring the symmetries and structures of living organisms, we can further explore the idea that the shape and form of physical objects are the result of a complex interplay between deep physical principles and the history of their formation.

Why does life come in so many shapes and sizes?

      The competition between the force of gravity and the electromagnetic force is responsible for smoothing the surface of planets and moons into spheres and limiting the maximum size of mountains on their surfaces. One of the central ideas in this book, which we will expand on in Chapter Three, is that there is no fundamental difference between inanimate things, such as planets, and living things, such as bacteria or human beings; all objects in the Universe are made of the same ingredients and are shaped by the same forces of Nature. We should therefore expect to see limits on the form and function of living things imposed by the laws of Nature. Basic physics is not the only driver of the structure of organisms, of course; there is also the undirected hand of evolution by natural selection, which moulds living things over time in response to their changing environment, their interaction with other living things, and the myriad available environmental niches. This creative interplay between the relentless determinism of physical laws and the seething, infinitely intertwined, ever-shifting genetic database of life on Earth is beautifully captured in Darwin’s closing lines of On the Origin of Species;

      ‘There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.’

      Another of our recurring themes is a celebration of the energetic curiosity of the early scientists. There is a breathless lyricism in their descriptions of ideas that remains relevant and essential; yet their presentation seems somehow unencumbered by the more serious and confining demands of modern professional science. There are great writers from the modern era who capture the logic, clarity and wonder of science – Richard Feynman, Richard Dawkins and Carl Sagan