The Equations of Life

by Charles S. Cockell

  Within these restricted boundaries, planets might certainly host more or less bounteous biospheres than Earth. Some features may make other Earth-like worlds more fecund for life. René Heller from McMaster University in Canada and John Armstrong from Weber State University in Utah speculated on what it would take to make a planet more habitable than Earth. They imagined many things that might make a “superhabitable” planet even better for life than our own verdant oasis. Planets slightly larger than Earth might accommodate more biomass or even more diversity. Ecologists know well that the more land or continental shelf there is, the more diversity of life you can fit in. Planets with more water bodies in the interior of continents and fewer arid areas might support greater biomass. Under the light of stars with lower levels of UV radiation, planets might be less hostile on their surfaces, where radiation damage is less of a concern for exposed life. We can imagine how differences in planetary size, the ratio of land to ocean, the surface temperature, or atmospheric composition would alter the conditions for life.

  However, even throughout the history of Earth, there have been large transitions that have influenced the diversity and biomass of the planet. Continents have shifted, the atmospheric composition has changed, and continents have become less or more arid. Astronomical events, such as asteroid and comet impacts, have periodically harassed our planet. Some of these events have been so profound that they have caused mass extinctions. Defined in terms of animal and plant biomass, Earth today is more habitable than it was five hundred million years ago. Yet none of these alterations to planetary conditions have changed the restrictive influence of physics on life.

  Am I saying that life on these exoplanets would be tediously like that on Earth? Not exactly. Even though the scope of the evolutionary experiment, restricted by physics, would obviate the wild forms of life that Wells imagined, there is still room for great variety to be produced on worlds where different physical conditions prevail.

  To explore how different physical conditions elsewhere might shape life, but nevertheless allow for fascinating diversity, it is enlightening, even entertaining, to speculate briefly on some possibilities. One physical factor exerts itself on life across the whole of Earth and would do so on any other planet in the universe. Even Darwin, in the final paragraph of his book, cared to mention this factor: gravity. On many rocky exoplanets, gravity would be different from this phenomenon on Earth. How would this single factor influence life? We can work out the surface gravitational acceleration (g) on any world using the simple relationship that the acceleration of gravity is proportional to the mass of a planet and inversely proportional to its radius squared, so

  g = GM/r2

  where G is the gravitational constant (6.67 × 10−11 m3kg−1s−2) and M is the mass of the planet.

  Consider an exoplanet ten times the diameter of Earth. The mass of the planet is related to its volume, given by (4/3)πr3. The mass therefore scales as the radius is cubed. To get the gravity, we divide the mass by r2, showing simply that the gravity scales as r3/r2 = r. Assuming for simplicity that the bulk density of the planet is much the same as it is for Earth, then on this planet with ten times the diameter of Earth, its gravity will be ten times greater.

  Let us consider a large cow-like creature wandering the fields of this distant planet. All other factors being equal, the weight (given by mg, the mass of the organism multiplied by the gravitational acceleration) will be ten times greater. The weight of the animal must be supported by the cross-section of the legs, and if the weight is increased by ten, then by increasing the diameter of the legs by 3.2 times, the cross-sectional area of the legs is increased by ten times. This increased diameter will produce the same downward force per cross-sectional area of a leg as on an Earth cow’s leg cross-section.

  The alien cow must have thicker legs than our familiar cows and maybe a smaller body to compensate. Although stronger bones or muscles, evolved under a higher gravity, might yield some organisms not much different from life on Earth, large life forms on this high-gravity planet would probably bear the anatomical imprint of this higher-gravity environment.

  And what about our alien fish? You will recall that the force acting in a fluid is given by mg—ρVg. The first term gives the weight of the animal. On our exoplanet with ten times the gravity, the weight of our fish is therefore ten times greater. However, because the weight of the water being displaced by the fish also scales with the gravity, the buoyancy term, ρVg, which contains g, is ten times greater on this new world. Increase the gravity by ten times, and there is no net effect on the fish. Fish and whales care little whether they are on Earth or a super-Earth.

  Diminutive creatures would be even less affected by the difference in gravity. At the scale of a ladybug, gravitational forces become almost irrelevant. As we learned, molecular forces are what dominate the ladybug’s world. Even the forces of attraction in a thin layer of water under its feet are sufficient to keep it attached to a vertical wall, competing against gravity that would otherwise yank the bug off. Ladybugs, however, are not immune to the force of gravity. When a ladybug closes its wing cases in mid-flight, it will fall to the ground as surely as will a person leaping off a wall, but the resistance from the atmosphere is more effective in limiting the speed of the descent of such a light-weighted creature.

  We might think about the effects of gravity on creatures jumping off alien cliffs or from the branches of tree-like plants. When an object falls, it reaches a terminal velocity, which is the fastest speed it will go. It is a trade-off between gravity pulling down and the drag of the air or fluid that prevents it going any faster. We can work out this maximum speed (Vt) using an equation:

  Vt = √(2mg/ρACd)

  where m is the mass of the object, g is the gravitational acceleration, ρ is the density of the air or fluid through which the object drops, A is the surface area of the object, and Cd is the drag coefficient of the object, which expresses the extent to which drag or resistance will slow it down.

  You will notice that the equation involves the mass of the creature, which is important, as the more massive you are, the higher the terminal velocity. For a human on Earth, the terminal velocity is around 195 kilometers per hour, and that is rather fast. You would reach that speed in about twelve seconds after falling about 450 meters. In general, hitting the ground at 195 kilometers per hour will kill you instantly, but you do not need to reach terminal velocity to do serious damage. Jumping from the top of a tree is bad enough.

  There have been some extraordinary stories of survival. Juliane Koepcke, a German-Peruvian biologist, survived a fall from about three kilometers after the plane she was in was struck by lightning and exploded over the Peruvian rain forest in December 1971 during a severe thunderstorm. She fell to the ground still strapped into her seat and merely suffered a gash to her right arm and a broken collarbone. Other anecdotes tell of World War II pilots surviving high falls from aircraft into snowfields. However, these are rare anomalies.

  Compare this challenge of surviving falls with that of an ant, whose mass gives it a terminal velocity of about six kilometers per hour, about thirty times less than for a human. Most ants can survive a fall at this speed with little damage.

  Now let us increase the gravity, another factor in this equation, on an exoplanet to ten times that of Earth. The terminal velocity correspondingly increases. For a large animal, this will merely add to its woes in jumping off obstacles or falling from flight, but for a small insect, the terminal velocity, although now higher, may still be sufficiently low to prevent a great deal of damage. An ant’s terminal velocity, assuming the same density of atmosphere, increases to about twenty kilometers per hour, still lower than that of a mouse on our world. These ants can reach terminal velocity, land, and walk off little the worse for their experience. In this return to the ants, we have an illustration of how gravity is a less significant force for small things. A distant super-Earth with a high gravity would have little influence on its smalles
t forms of life.

  In these examples, we see no compelling reasons to think that rerunning the tape of evolution on another planet would give rise to entirely new and unrecognizable forms of life. Instead, we would probably witness the immutable laws of physics merely shaping life in ways predictable in the context of the universal laws in which life operates. These laws would probably give rise to forms different in their minutia, but still narrowly channeled into a limited set of solutions, many of which would be familiar to us.

  But let’s have a little more fun. Sticking with gravity, we might consider for a moment how this factor would affect flying creatures, our alien starling and geese equivalents.

  Whether you are watching a plane taking off from Edinburgh Airport or the murmurations of starlings we have already met, these flying contraptions must maintain the lift to stay airborne. We can work out the force needed to stay aloft using the lift equation:

  L = (CLA ρv2)/2

  where the lift (L), which is the upward force that keeps the object in the sky, is the product of the surface area of the wing (A) and the density of the air (ρ) through which the object moves and the velocity (v) squared.

  You will also notice another strange term in the equation. CL is the lift coefficient. This sort of thing is sometimes politely called a fudge factor. It is not some sort of fundamental constant, but it mops up all the complexities this equation cannot quite deal with: the problem that lift is not merely related to the surface area of the wing, but also to the wingspan, how the air interacts with different materials the wing is made of, and the angle of the wing (the angle of attack). CL is something you must work out by doing experiments, and that is why aerodynamicists put model aircraft into wind tunnels—so they can determine what number they must use to get the right answer.

  The equation tells us some simple things. The thicker the atmosphere, generally the more massive the creatures you can get off the ground. The lower the gravity, the less the creature is yanked down, and so again, we can get more-massive animals airborne.

  There is no better place to illustrate the strange consequences of this simple physical principle than on Titan. This remarkable Saturnian moon is a mere 5,152 kilometers in diameter, 40 percent Earth’s diameter, giving it a gravitational acceleration of 1.34 meters per second per second, just 13.7 percent of Earth’s gravitational acceleration. Yet its thick atmosphere has a density of about 5.9 kilograms per cubic meter, compared with Earth’s more meager 1.2 kilograms per cubic meter.

  These numbers have not gone unnoticed to the imaginative. By reducing the weight of a person by over seven times but increasing the lift because of the higher density of the atmosphere, we suddenly arrive at the prospect of human flight.

  Consider a typical human, say, with a mass of 70 kilograms. The person’s weight on Titan is about 94 newtons. We must achieve this value or greater in lift if we are to fly. Using the lift equation, we might assume they are flying at a leisurely 5 meters per second (about 18 kilometers per hour). The lift coefficient we will take as 0.5 (a typical value). Using the density of Titan’s atmosphere, we arrive at a required surface area of the wing of 2.5 meters squared. A wing this size will easily fit onto a wearable suit. Humans could jump off a cliff on Titan (in a spacesuit, of course) and soar in its skies like birds in slow, dignified, and elegant swoops.

  Even on our own planet, with enough speed, people can fly using wing-suits. But on Titan, the lower gravity and thicker atmosphere mean you can glide slowly and gracefully without all that YouTube drama and death.

  In these simple considerations, we have an example of how although the laws of physics are unyielding, small changes in the characteristics of distant worlds may open up evolutionary possibilities. Sometimes, large planets with thin atmospheres may preclude atmospheric flight altogether, yielding biospheres where flight is limited to short bursts into the sky, like flying fish or flying squirrels on Earth. On other worlds, thick atmospheres on small planets could lead to skies filled with flying creatures of immense size and variety.

  Could these differences cause something drastic to happen, something in evolution we were not expecting? Imagine that on a distant exoplanet, smaller than Earth but with a thick atmosphere, life had evolved. On that planet, large organisms, about the size of humans, had come into existence, and not only that, they had acquired intelligence. But there is something different about these creatures: they are of a birdlike lineage. They have wings.

  The airborne capacities of these sentient fliers have had profound consequences for their history. From the beginning of their recorded time, they have been able to circumnavigate their planet and travel immense distances. They do not commute to work on long roads, but rather they fly. And so, the invention of automobiles was never developed with any enthusiasm. Like all sentient beings, they have some aggressive tendencies, but their ability to fly, to see other people and conurbations from far up in the sky, gave them a perspective on other life and dulled their tendency for destruction. This view of entire landmasses spurred an ecological and environmental awareness in their most primitive ages. The effect was that an effort started from the nascent days of discovery of the scientific method to map their entire planet and its environmental systems. This effort created a planetary-scale sense of camaraderie in their species.

  Their ability to fly meant that they quickly grasped the concepts of artificial flight. Merely by observing their own wings during boring classroom lessons, early teenage geniuses figured out how the airfoil worked, leading to artificial flight. As flying hundreds of beings across their planet for tourist or business purposes still had a use alongside their natural capacities, they developed aircraft early.

  Now, they generally led a peaceful existence because of their early environmental awareness. However, when war occurred, and sporadically it did, it was highly destructive. The beings’ ability to drop objects from high above onto an enemy brought aerial warfare to their world when their society was young.

  An important impetus brought on by their wings was spaceflight. With their natural tendency to see the world in three dimensions, their supernal view of society meant they quickly dreamed of flying beyond the atmosphere. As soon as they gathered the skills to mold metals and manipulate basic chemistry, they were already experimenting with rockets. A spacefaring capability rapidly followed their construction of aircraft.

  I have taken you on this slightly bizarre excursion merely to illustrate that the claim that physics greatly constrains the forms of life does not mean we cannot generate an extraordinary variety of possible outcomes. I use the rather speculative example of intelligence to show that even though physical principles are the same everywhere, a small change in the physical conditions on a planet, in this case, a thick atmosphere, might well lead to biological outcomes and trajectories that have all sorts of indirect effects down the line, none more tangible to you and me than cultural implications. I have used the example of gravity to show that physical principles, given expression in equations, can be used, albeit rather simply in the examples I have chosen, to explore the potential effects on a hypothetical biota.

  The discovery of exoplanets has shown us that the universe is full of a vast assortment of planetary possibilities. None may be exactly like Earth. Subtle differences in gravity, atmospheric density, landscapes, land-to-ocean ratios, and other factors will all influence the scope and content of any evolutionary experiments, if they exist. None would generate an exact replica of Earth’s biosphere. The infinite diversity of small modifications in color and shapes will produce a fantastic and bewildering diversity of creatures. However, throughout these biospheres will run—at the small scale—the same architecture, the same construction from complex carbon molecules, the same repeating motifs in their major molecules, and the same compartmentalization. And at the large scale, they will run the same solutions to cope with gravity, to take to the air, or to swim in the sea. The equations of life permit variety and contingency within the underlying
tapestry of striking conformity on Earth, and if life exists elsewhere, there as well.

  For now, there is no immediate prospect of studying life forms in distant exoplanet biospheres directly, expanding the sample size of evolutionary experiments we can analyze beyond one. Only life in our own Solar System can provide us with that prospect in the near term. Regardless of the extent of our success or lack of it in finding an independent evolutionary experiment to explore, the discovery of exoplanets and the characterization of the environments they host will increasingly provide us with empirical knowledge of the diversity of physical conditions on rocky worlds. This new panorama will enrich and fuel our thoughts about how the characteristics of our own evolutionary experiment might have been different if it had been run on these distant worlds. From this vantage point, we may better understand how the physical conditions of Earth have fashioned the forms of life that have evolved here. With this new vista, we can deepen our insights of what might be universal about life.

  CHAPTER 12

  THE LAWS OF LIFE: EVOLUTION AND PHYSICS UNIFIED

  THAT THE LAWS OF physics and life are the same should surprise no one. The dissipation of energy into equilibrium in the universe is an inexorable process that allows for local complexity, of which life is a part. However, ultimately even the material within these oases of molecular diversity and the planet on which they reside must themselves disperse into the cold abyss. At the grandest scale, life is a flicker of light, eventually to be extinguished by one of the universe’s most insistent physical laws, the second law of thermodynamics.