CHAPTER FOURTEEN

DESIGNING A HABITABLE PLANET

Far too many stories merely give us a planet exactly like Earth except for having neither geography nor history.… The process of designing a world serves up innumerable story points.

—POUL ANDERSON, “HOW TO BUILD A PLANET”

A large number of science fiction stories take place on alien worlds, and the process of designing an alien world with alien life on it is perhaps as old as science fiction itself. Hard science fiction writers tend to pay attention to astrophysics and planetary science to make their worlds both realistic and exotic, a very difficult combination to achieve. Several examples of successful designs spring to mind, including Hal Clement’s Mesklin in the novel Mission of Gravity, a large planet whose rapid rotation spun it into an ellipsoid, with a surface gravity three times that of Earth at its poles but several hundred times Earth’s at its equators. There is also Plateau in Larry Niven’s A Gift from Earth, a Venus-like planet with one inhabitable point on it, Mt. Lookitthat, a tall mountain sticking out of most of the atmosphere [59, 175]. The balancing act one must go through to create worlds both credible and incredible simultaneously takes a good deal of work on the writer’s part, but is also part of the fun of the narrative.

The discussion in this chapter is strongly motivated by the wonderful essay “How to Build a Planet,” by Poul Anderson. The essay was originally published in the Science Fiction Writers of America bulletin in 1966 and later expanded into one of the famous Writers Chapbooks published by Pulphouse Press. My own copy of the essay is a badly worn Xerox copy of unknown origin. I don’t remember when I originally read the essay, only that I was about ten years old and that it was my first exposure to the scientific ideas in science fiction. If I hadn’t read the essay I wouldn’t have written this book. By necessity, this chapter and that essay cover much the same ground, though in different ways. I would recommend that readers who enjoy this book try to track down a copy of the essay.

14.1  ADLER’S MANTRA

I’m going to stick to a discussion of Earth-like worlds in this chapter. That means worlds that are capable of supporting life as it exists on Earth, sometimes referred to as “carbon-based life.” Speculations about non-carbon-based life abound, but since I am a physicist rather than a biologist or chemist, I plan to stick closer to what I know and review the physics of life as we know it. This is still a big issue, but more manageable than if we throw the subject open entirely.

Life as we know it on Earth requires two things at a bare minimum: an atmosphere with large quantities of oxygen in it and average planetary temperatures between the freezing and boiling points of water. The requirements for intelligent life are more restrictive, but we’ll deal with that later.

To start with, these two basic requirements probably dictate the type of planet we need to deal with. In our own Solar System there are two basic types of planets, terrestrial and gas planets.

•  The terrestrial or rocky planets are Mercury, Venus, Earth, and Mars. Some astronomers also include Earth’s Moon as a member of this class of planets. They are the small planets closest to the Sun, and are characterized by compositions that are mostly metals and rocks, with thin to nonexistent atmospheres. The zone of these planets more or less extends out to the asteroid belt, about 2–3 AU from the Sun, and is defined by the so-called “frost line,” the distance from the Sun where ices of various kinds form. Until recently it was thought that most solar systems would have the terrestrial planets closest to their sun because of this: as the Solar System was forming, heat from the Sun drove the volatile ices to the outer edge of the Solar System, where they formed the gas giants.

•  The gas giants are the four planets of the outer system, Jupiter, Saturn, Uranus, and Neptune. In general, they are characterized by their large sizes compared to the terrestrial planets, with masses ranging from 18 to 318 times the mass of Earth. They are also composed mostly of ice and liquids, with perhaps no solid surfaces.

Other bodies, too small to be called planets, also occur in our Solar System, including dwarf planets, such as Pluto, and over fifty moons, mostly circling the gas giants. Several of these moons might have conditions conducive to life. This has served as the basis of several science fiction stories, the most famous being 2010: Odyssey Two by Arthur C. Clarke, which centers on the discovery of life on Jupiter’s moon Europa [57]. The movie Avatar is also set on the habitable moon of a gas giant planet, but not one in our solar system. So is the rebel base in the movie Star Wars: A New Hope.

Until 1993, astronomers thought that the arrangement in our Solar System was typical. However, once scientists began discovering planets circling other stars, a third class of planets was discovered, called hot Jupiters, planets the size of gas giants but circling their stars at very close distances, sometimes so close that their orbital period is merely hours long! About 25% of all exoplanets discovered are hot Jupiters. To some extent this reflects instrumentation issues: it’s easier to discover large planets close to their stars. However, I think it safe to say that no astronomers would have predicted any of these odd giants before they were discovered.

This leads me to a mantra I tell all my astronomy students the very first day of class:

All stars are fundamentally the same; all planets are different from each other.

This doesn’t mean that all stars have exactly the same properties or behaviors, but all of the properties of a star stem from two basic data, the star’s mass and its composition at the time of its formation. This is known as the Russell-Vogt theorem in astrophysics. However, stars are almost identical in their initial composition (mostly hydrogen with a little helium and even less of everything else), so the big determinant of how stars behave, their luminosity, their surface temperature, and their lifetimes is the stellar mass.

On the other hand, planets are a chaotic mess. Although we can put the planets in our Solar System into two broad classes, individual differences among them are as great as their overall similarities. For example, Earth is unique among the terrestrial planets in having a large moon circling it. It is also the only known planet with plate tectonics. There are reasons to think that both these properties might be needed for life on Earth to thrive. Venus is very similar to Earth in size and overall composition, but it has a thick atmosphere with a runaway greenhouse effect, probably a result of being slightly closer to the Sun than Earth is. Mars has a long trench similar to the Grand Canyon but 3,000 miles long, and boasts the largest mountain in the Solar System, the extinct volcano Mons Olympus. Mercury has odd, extremely long cracks running along its surface called lobate scarps, which no other planet has. And so on. The differences result from the fact that many causes determine the characteristics of the planets, and it is not always possible to cleanly separate cause from characteristic.

Here’s a short list of causes of planetary characteristics:

•  Type of star the planet circles;

•  Mean distance of the planet from the star and orbital eccentricity;

•  Planetary mass;

•  Planetary atmosphere;

•  Exact planetary composition; and

•  A history of impacts with other objects in the system (especially during formation).

In particular, the history is important. When Poul Anderson mentioned history in his essay, he was probably thinking of the history of the societies on these worlds. In a larger sense, the exact geological history of the planet, and especially the history of planetary impacts, is very important in determining the later features of the planet. If Earth hadn’t undergone an impact with a Mars-size object in exactly the right way during its formation, we wouldn’t have the Moon. Without the Moon it is very possible that life wouldn’t have developed on Earth.

14.2  TYPE OF STAR

Stars are simple objects: all of their properties are determined by mass and composition. The obvious question that arises is, what are those properties? There are really only four important ones:

•  Luminosity. Luminosity is how bright the star is and is usually measured relative to our Sun. Luminosities range from about 1/1,000 (10⁻³) of our Sun’s to about 1 million (10⁶) times greater than it.

•  The surface temperature of the star. The surface temperature runs from about 3,000 K to 30,000 K; our Sun is right in the middle, with a surface temperature of about 5,800 K. Surface temperature also determines the overall color of the star, which ranges from red for the cooler stars to blue-white for the hottest.

•  Main-sequence lifetime. About 90% of the stars in the sky burn hydrogen via fusion in their cores into helium. These are referred to as main-sequence stars. Our sun is a main-sequence star, and most stories feature planets orbiting main-sequence stars because post-main-sequence evolution probably ends up destroying life on the planets. Main-sequence lifetime is strongly determined by mass: bigger stars live shorter lives.

•  Old age and death. After the star eats up all the hydrogen in its core and leaves the main sequence, it evolves into a giant phase, followed by one of three possibilities. For stars with less than about eight times the mass of the sun, the star shrinks and becomes a white dwarf, while for stars between eight and twenty solar masses, the star supernovas, leaving a neutron star behind. The largest stars collapse into black holes.

Stellar modeling is essentially a solved subject. From the 1960s on astrophysicists have developed elaborate computer codes to model the stars, and these models have been extensively compared against observation. If any of my readers are interested in the subject I highly recommend the hefty textbook An Introduction to Modern Astrophysics by Bradley W. Carroll and Dale A. Ostlie; much of the information presented here is adapted from that book [47]. Main-sequence stars are divided into spectral classes. For historical reasons the classes are (listed from hottest stars to coolest): O, B, A, F, G, K, M, L, and T. Ignoring the two final classes, they can be remembered using the mnemonic “Oh, Be A Fine Girl/Guy, Kiss Me.” The classes run in that order from the hottest, brightest, most massive stars to the dimmest, coolest, and smallest. L and T are brown dwarf stars, which radiate light mainly in the infrared region of the spectrum and use different fusion processes in their interior; I’ll ignore them, although some science fiction stories have been set on worlds circling these stellar objects.

The representative properties of main-sequence stars are a useful way to start thinking about stars for science fiction stories. (The data in table 14.1 and referenced in the following discussion are from Carroll and Ostlie’s An Introduction to Modern Astrophysics [47, appendix G]).

L is the stellar luminosity (the rate at which the star emits energy in the form of light) in units where the Sun’s luminosity is 1; M and R are the mass and radius of the star, again measured with respect to the Sun. The variable τ is the main-sequence lifetime, the amount of time it spends as a middle-aged star, burning hydrogen in its core until all the hydrogen is used up. The numbers after each class represent different subclasses: the lower the subclass: the hotter and brighter the star is.

For any star, the following formula is very useful:

This is the Stefan-Boltzmann formula for a black body emitter in normalized units. We can turn it around and write the temperature in terms of radius and luminosity:

or write the radius in terms of temperature and luminosity:

The star’s light is emitted in a spectral range that depends on its surface temperature: this is described by the Wien displacement formula from chapter 1, which I’ll write in the following way:

where T is (as always) measured in Kelvin. The reason this is useful is as follows. The smallest stars have surface temperatures right around 2,900 K, so they will emit most of their light in the infrared region of the spectrum (i.e., with wavelengths around 1µm, longer than what the eye can see). Most of the visible light they emit is in the red end of the spectrum, making them red in appearance. Our Sun, however, has a temperature of 5,800 K, just about twice this, meaning that the light is emitted around a peak wavelength of 0.5 µm, right in the middle of the visible spectrum. The brightest stars have temperatures above 29,000 K, so their light will be concentrated at wavelengths of about 0.1 µm or shorter—that is, in the ultraviolet. Most of the visible light they emit will be at short wavelengths, making them appear blue or blue-white.

For main-sequence stars only, the following relation holds:

That is, luminosity increases rapidly with mass, essentially increasing as mass cubed. The power law is an approximation to the true behavior; for very low-mass stars the exponent is somewhat lower, for very high-mass stars the exponent is higher. The fact that luminosity increases so rapidly is why large stars have short lifetimes: a star’s main-sequence lifetime is determined by the ratio of the amount of fuel it has to burn (its mass) and the rate at which it is burning it (its luminosity):

This is an approximate formula. In particular, it doesn’t work well for very low-mass stars. One other thing can be worked out: in these units, along the main sequence,

This isn’t a coincidence. It stems from the fact that the proton-proton cycle operating at the core of the star doesn’t “turn on” until the core reaches a temperature of about 10⁷ K [170].

To convert everything to metric units we need only remember a few numbers. The sun radiates energy at a rate of 3.84×10²⁶ W, so

L_metric = 3.84 × 10²⁶ W × L.

Similarly,

R_metric = 6.95 × 10⁸ m × R,

and

M_metric = 1.99 × 10³⁰ kg × M.

With these formulas we can do a lot. In particular, life emerged on Earth only about 700 million years after the Earth formed. As a wild guess, if we assume that it takes life everywhere in the universe about that long to evolve on a given Earth-like planet, we need to pick a star whose main-sequence lifetime will be longer than about 700 million years, meaning that the O- and B-class stars won’t work, and possibly not A-class stars either. This doesn’t eliminate a lot of them: there are many more smaller, cooler, dimmer, longer-lived stars than there are bigger, brighter, hotter stars. But it gives a point to start from. The smallest class M stars also may not work too well because planets in the zone of life will have to orbit so closely that tidal effects will lock one side of the planet into permanently facing the star, in the same way that the Moon presents only one face to the Earth, making one side much hotter than the other.

Other fun formulas: if the planet is located d astronomical units away from the star, the angular size of the star as seen from the planet is

If the planet has a moon, its angular size as seen from the planet is

where R_m is the radius of the planet’s moon relative to the radius of Earth’s Moon (= 1,737 km) and a_m is the average distance of the moon from the planet, again relative to the distance of Earth’s Moon from the center of Earth (384,000 km). Kepler’s third law tells us that the length of a year on the planet (i.e., the rotational period around the star) is

where Y is measured in years.

14.3  PLANETARY DISTANCE FROM ITS STAR

Now that we have the star, where do we put the planet? Carbon-based life requires oxygen in the atmosphere and liquid water on the planet’s surface. If the planet is too close to its star, it gets too hot, and water will boil on its surface; too far, and water will freeze. In the Solar System there are only three planetary candidates for Earth-like life based on this criterion, Earth, Venus, and Mars.

A planet both absorbs energy from its star and radiates energy on its own. This fact can be used to figure out the temperature of the planet. There are a few ideas that go into this:

1. Radiation from a star spreads out in all directions; the total amount of light the star radiates away is spread out over a sphere centered on the star. If a planet is at distance r away from its star, the total amount of power emitted by the star is spread over a sphere whose surface area is 4πr².

2. Some of the light from its star will be absorbed by the planet and some will be reflected away, because of the planetary makeup and the atmosphere of the planet. The total amount of light absorbed will be proportional to the area of the planet.

3. The key point is that the total power absorbed by the planet must equal the total power radiated away (on average); if this weren’t true, the planet wouldn’t maintain an even temperature. Planetary temperature stays relatively constant because if it radiated away less light than it absorbed, its temperature would increase until it radiated away exactly as much as it absorbed. If it radiated away more light, the temperature would decrease until this happened.

We also have to define a concept called the average albedo of the planet. The albedo is the fraction of sunlight that is reflected without being absorbed. Earth’s albedo is about 0.3, meaning that about 30% of the light from the Sun isn’t absorbed by Earth’s surface. This is an average between the oceans (which are relatively absorptive) and the ground and cloud cover (which are relatively reflective), and also changes from point to point and from time to time as well. Our definition is one that is averaged over the surface of the Earth and over time—say, over several years. I’m also assuming that the orbit is essentially circular. With these definitions, for a planet without an atmosphere,

What this means is that there is a zone of life around the star. As a very rough cut, the zone is the region where the mean temperature ranges from 273 K (on the outer edge), that is, where water freezes, to 373 K, where water boils, on the inner edge. The zone doesn’t have hard-and-fast edges because planets have different albedos, and atmosphere plays a role as well. Three points are relevant here:

1. The luminosity of most stars isn’t very near that of our Sun. The range of luminosities goes from about 10⁻³ to 10⁶—a range over a factor of one billion. This means that the distance of the “zones of life” for different stars will have different values;

2. I call the temperature “T₀” because this is the temperature of the planet if it had no atmosphere. Atmosphere plays a major role in determining planetary temperatures; we’ll introduce a simple model for the effect of the atmosphere later in the chapter.

3. This is simply the mean temperature for the planet. The actual temperature will vary quite a bit over time and from point to point on the planet’s surface.

We can rework this to find the inner and outer edges of the zone of life for a given planetary albedo and stellar luminosity. Let d_i and d_o be the inner and outer edges of the zone for planets (ignoring the effects of atmosphere):

Again, these are very rough cuts. Because we didn’t include the effects of planetary atmosphere we find that Earth is actually outside the zone, too far from the Sun, in this naive model. However, it serves as a starting point.

The only candidate planets in our solar system potentially within the zone are Venus, Earth, and Mars. In the late 1800s the astronomers Giovanni Schiaparelli and Percival Lowell wondered whether they had detected signs of life on Mars after seeing an intricate network of canals on its surface; Lowell felt the canals could have been the products of an advanced civilization. This work was the inspiration for innumerable works of science fiction, from H. G. Wells’s War of the Worlds to Robert Heinlein’s Red Planet and Stranger in a Strange Land [108][115][248]. However, almost from the beginning critics pointed out that Mars was probably too cold and too arid for life of this kind. The Nobel laureate chemist Svante Arrhenius was one of the first to go over the scientific evidence and conclude that Mars was an unlikely abode for life. He was right. The “canals” were merely the product of low telescope resolution and eye strain. But what Arrhenius took with one hand he gave back with the other; in his book, The Destinies of the Stars (written with Jones Elias Fries), he predicted that the surface of Venus was wet and misty, with conditions similar to Earth’s during its Jurassic period [25]. This prediction led to many a science fiction novel set in the jungles of Venus where dinosaur-like monsters hunted humans through the mud. Heinlein’s novel Podkayne of Mars is perhaps archetypal of these, although S. M. Stirling has written a new alternate-universe series based on this idea. In these novels, Mars and Venus were seeded with life by an unknown alien race. The feel of them is similar to Burroughs’ Barsoom novels [118][229].

But these ideas disappeared from serious science in the 1960s and 1970s with the advent of unmanned probes that flew by and landed on Mars and Venus. They found Mars a desert with average temperatures around that of Antarctica, which was not very surprising, and Venus a hell whose surface temperatures reached 750 K—hot enough to melt lead! The difference in the temperature of Venus from our ideal model has everything to do with its atmosphere.

14.4  THE GREENHOUSE EFFECT

Certain gases in the atmospheres of planets tend to trap infrared radiation, which is heat radiated away by planetary surfaces; these gases include carbon dioxide (CO₂), which makes up 380 parts per million in Earth’s atmosphere and a whopping 98% of the atmosphere of Venus, and methane, which is found in trace amounts in our atmosphere. The most important greenhouse gas, however, is water vapor, which accounts for about 90% of the total for Earth.

The idea behind the green house effect is pretty straightforward: light from the sun is mostly visible light, which the atmosphere is transparent to; about 70% of it reaches the Earth’s surface. However, the Earth radiates away light in the infrared region of the spectrum, so most of it is trapped near the surface. We can see this by considering equation (14.2): because the average temperature of the Earth is about 290, most of the light reradiated from the Earth is at wavelengths near 10 µm, in the infrared region of the spectrum. This is strongly absorbed by the atmosphere, and much of it is reradiated back to the ground. In “building planets,” as Anderson puts it, it is vital to include somehow the effects of the atmosphere in our calculations. Computer models to calculate the temperature typically divide up the atmosphere into vertical layers with different amounts of infrared absorbance in each layer; they also grid the world into cells based on the terrain the cells overlie. However, one can get some good insight into what is going on using a simple model.

Greenhouse gases act as a blanket, so that heat from the planet takes longer to escape into space, leading to an increase in the average temperature not predicted by equation (14.7). Mars has a very thin atmosphere, much thinner than the atmosphere at the top of Earth’s highest mountains, so this greenhouse effect increases its average temperature by only a small amount. Earth has a moderately thick atmosphere, so the greenhouse effect raises its temperature by about 30 K. Venus has a thick atmosphere mostly composed of CO₂; it has a runaway greenhouse effect, which raises its surface temperature by over 500 K.

Let’s assume that the atmosphere can be modeled as one layer, not divided up either horizontally or vertically. We can use a simple model developed in Daniel J. Jacob’s book Atmospheric Chemistry to calculate the effect of greenhouse warming on Earth. [129, pp. 128–131]. We assume that the planet has an effective albedo a in the visible region of the spectrum and that the atmosphere as a whole traps a fraction f of the light emitted by the surface in the infrared part of the spectrum. Using this model, the temperature of the surface is given by

As f goes up, T goes up: the more radiation that is trapped by the atmosphere, the warmer the planet will be. Unfortunately, this is as far as we can go using a simple model; predicting f from the atmospheric constituents is a very difficult task. For Earth’s mean temperature of 288 K we need a value f = 0.77 with this model. One can use that as a guide when writing science fiction stories set on other worlds.

The temperature of the atmospheric layer can also be found in this model:

The model is OK for planets with relatively thin atmospheres, like Earth, but breaks down completely for planets with very absorptive atmospheres, like Venus, where we have to use a multilayer model to come close to the truth. The model also ignores convection and the horizontal transport of energy, both important effects when calculating the real temperature.

For the value of f given above, the mean temperature of Earth will remain between freezing and boiling anywhere within 0.6 to 1.1 AU from the sun. This is not to say, however, that the real zone of life is this wide. While planetary temperature depends on atmospheric composition, atmospheric composition also depends on planetary temperature. Venus in many respects is a sister planet to Earth, having about 85% of Earth’s mass and being about 90% of its size, but the surface conditions rival hell’s. Most astronomers think that Venus became the way it is because of a positive feedback effect. Venus started out with a slightly higher insolation than Earth’s, which caused more CO₂ to be liberated from the surface of the planet. This led to more warming, leading to more CO₂ being liberated, and so on [134]. Earth, being about three-tenths of an astronomical unit farther from the Sun, escaped this fate.

Habitable zones also change over time because of changes in planetary atmospheres and solar irradiance. Over time, the Sun’s luminosity has increased gradually. Shortly after the formation of the Solar System its luminosity was only 70% of what it is now, and it will be about 10% higher than now in about a billion years [47, fig. 11.1]. From this, Kasting, Whitmire, and Reynolds calculated that over the history of the Solar System from 4.5 billion years ago until today, the habitable zone for Earth-like life extended only from 0.95 to 1.15 AU [136].

It is very unlikely that there was ever any Earth-like life on Venus, given conditions there, but Mars is another story. Mars had a thicker atmosphere once, although it didn’t keep it. There is very good geological evidence that liquid water once flowed on the surface of Mars, presumably billions of years ago when its atmosphere was thicker and hence the surface temperature was higher. Where the water is now is anyone’s guess; it may be locked in permafrost beneath the surface of the planet. However, conditions once may have permitted Earth-like life on Mars’s surface, probably at the bacterial level.

Recent science fiction novels have used this idea, notably Greg Bear’s novel Moving Mars [33]. In the novel, a terraforming project to make Mars habitable for humans leads to a rebirth of the older life forms on Mars, which became dormant when conditions on the planet became too inhospitable.

The Kepler mission has just begun finding evidence of planets in habitable zones. As of December 2011, the Kepler mission had identified 54 planet candidates within habitable zones, with one candidate, Kepler 22-b, potentially Earth-like (about 2.4 times Earth’s radius) [1]. The BBC web report is in the form of a press release; one can find a preprint of a paper concerning this planet submitted for publication at the Cornell preprint server [39]. The writers make it very clear that they do not know that the planet is an Earth-like world. The mass could be up to 124 times the mass of the Earth, and it isn’t clear that it is a terrestrial/rocky planet at all. If it is, however, they estimated a value of T₀ (as defined above) of 262 K, assuming an albedo of 0.29 (the same as Earth’s), and a temperature of about 295 K if it has an atmosphere with the same properties as Earth’s, which they also state is very unlikely.

14.5  ORBITAL ECCENTRICITY

The habitable zone is a spherical shell surrounding a given star. Its borders are fuzzy because it depends on planetary albedo and atmosphere. Unfortunately, planetary orbits aren’t circular; they are characterized by orbital eccentricities. Even if the average distance from the star, d, is within the zone, a highly eccentric orbit will take a planet out of the zone for large periods of time as it orbits its star.

Let’s say that a planet orbits at an average distance d that is right in the middle of the habitable zone. This “average distance” is really the semi major axis of the planetary ellipse. If the orbit has eccentricity e, then the perihelion and aphelion distances are

If the width of the zone is Δz, then the perihelion and aphelion distances should lie within the zone, meaning that

or,

Earth’s orbital eccentricity is only 0.0167, whereas Δz/d for Earth is approximately 0.2, meaning that the eccentricity is well within the bounds set by this limit: Earth remains well inside the habitable zone for the entirety of its orbit. Other planets have larger eccentricities: Mars’s eccentricity, the largest in the Solar System, is 0.0934. The values for all the planets in the Solar System are relatively small, but eccentricities for exoplanets can be very large, raising the question of whether our Solar System is typical or atypical in this regard. Ursula K. Le Guin set her novel The Left Hand of Darkness on the ice world of Gethen; owing to a combination of relatively large distance and high orbital eccentricity, the world was frozen for most of its long rotational period [145]. It’s not entirely clear that life could evolve on such a world, although in the story humans have been settled on Gethen from elsewhere.

Exoplanet data show that most exoplanets have average eccentricities higher than those of the planets in the Solar System; it is not clear whether there is a reason for this or whether it is accidental that our system’s planets have low eccentricities. I estimate about 10% of all exoplanets found to date have eccentricities below 0.1. This is ignoring data for hot Jupiters, as tidal friction lowers the eccentricity of their orbits.

14.6  PLANETARY SIZE AND ATMOSPHERIC RETENTION

One other requisite for life (as far as we know) is an atmosphere. It’s interesting to compare Earth, Venus, and Mars in this respect. Mars has a very thin atmosphere that is mostly CO₂ (94%, with trace amounts of other gases); Earth has a moderate atmosphere that is 74% N₂, 24 % O₂, and 2% trace elements; and Venus has a horribly thick atmosphere that is almost entirely CO₂.

Mars’s atmosphere was thicker in the past.¹ This undoubtedly warmed Mars through to an enhanced greenhouse effect, but the planet lost its atmosphere over several billion years. There are lots of mechanisms by which planets can lose their atmospheres over the course of time. Following are just a few:

•  Thermal loss. Molecules in a gas at room temperature or above move with average speeds of a few hundred meters per second, which is about an order of magnitude less than the escape velocity for an Earth-sized planet. However, because this speed represents an average, some of the molecules move a lot faster. In the upper atmosphere, where collisions between molecules are few and far between, molecules moving faster than the escape velocity of the planet can be lost from the atmosphere. This is called the Jeans escape mechanism, after the astrophysicist who first described it. There are other non thermal loss mechanisms, including the fact that chemical reactions in the upper atmosphere can provide the reactants with enough energy to escape into space. Generally speaking, larger planets lose their atmospheres more slowly through this mechanism than do smaller ones.

•  Impacts. Here is where history becomes important. Impacts of planets with large objects (asteroids or comets) can push a lot of the atmosphere into space. Mars’s atmosphere may be thin partly because the planet is close to the asteroid belt and suffered collisions from asteroids over geological time spans.

•  Solar wind. Stellar winds, streams of charged particles from the sun, can strip away planetary atmospheres, particularly for small worlds close to their stars. This may have affected Mars’s atmosphere and almost certainly is responsible for stripping away what little atmosphere Mercury may once have had. In fact, all of the atmospheres of the inner planets are secondary ones, as the primary atmospheres that formed when the planets formed were stripped away by the strong solar winds from the young Sun.

•  Chemical sequestration. The atmospheres can become chemically bonded to the crust of the planet. This is where most of Earth’s carbon is: if all the carbon in the Earth’s crust were liberated into the atmosphere, Earth would have a worse greenhouse effect than Venus.

The formation of atmospheres is just as complicated, and harder to discuss in detail, as it is due to vulcanism, cometary impacts during the planet’s early history, and, for Earth, the presence of life on the planet (leading to the presence of significant amounts of O₂ in the atmosphere).

14.6.1 Thermal Loss Mechanisms

The average (rms) speed of a molecule of molar mass m in grams per mole in a gas at temperature T is given by

whereas the escape velocity of a planet is given by

where M_p is the mass of the planet measured relative to the mass of the Earth and R_p is the radius, again measured with respect to the Earth’s radius. A rule of thumb derivable from the Jeans escape formula that is used by planetary scientists is that if the rms molecular speed is greater than about one-sixth the escape velocity, thermal loss mechanisms will deplete the atmosphere of that particular molecule over geological periods of time [46, p. 103].

Table 14.2 shows some comparisons for Mars and Earth. The temperatures were chosen as typical of the top of each planet’s atmosphere. Earth is at a relatively high temperature because of the ozone layer. The absorption of UV light from the Sun puts energy into the atmosphere at that height, while Mars doesn’t have a similar protective layer.

There are a few points we can glean from table 14.2:

1. Neither hydrogen nor helium should be present in either atmosphere in appreciable quantities because their average molecular speeds are too high.

2. However, oxygen shouldn’t be lost because of thermal effects in either atmosphere. In the case of Mars, the low escape velocity is offset by the low atmospheric temperature compared to Earth’s.

The ratio of the average molecular speeds to the escape velocity is just about the same for molecules in the atmospheres of each planet. We therefore cannot attribute differences in atmospheric composition in either planet to purely thermal effects.

There is almost no oxygen in the Martian atmosphere because it is bound up in the Martian soil in the form of Fe₂O₃—rust. Oxygen is so highly reactive that chemical sequestration will bind it unless there is a continual source of it from somewhere else. In the case of Earth, the source of oxygen is the respiration cycle, that is, it is due to life on Earth. Similarly, there is almost no water on Mars because UV light dissociated the water vapor into hydrogen and oxygen; the oxygen was sequestered in the soil, while the hydrogen escaped into space. This shows how complicated atmospheres can be. That Mars has a much more rarified atmosphere than Earth doesn’t seem to owe principally to its mass and size but to a number of complicated factors.

14.6.2 Impacts

The total mass of Earth’s atmosphere is roughly 4×10¹⁸ kg. If we wanted to get 1% of the total mass of the atmosphere to escape velocity we would need to supply it with an energy of about 2.5×10²⁴ J. Comets or asteroids typically hit Earth at speeds of about 30,000 m/s, that is, at about the orbital speed of Earth. A collision of this energy would require an impact of an object with mass about 5×10¹⁵ kg, or, assuming an average density of 5,000 kg/m³, a volume of about 10¹² m—the equivalent volume of a cube 10 km on a side.

This is a very large impactor, about the size of the comet that wiped out the dinosaurs. Such impacts happen to Earth only about once every hundred million years or so. Because of this, we are pretty safe in ignoring this atmospheric loss mechanism for Earth, at least under present Solar System conditions. Comparing Mars to Earth in this manner is interesting. Mars is less massive than Earth, meaning it has a lower escape velocity, and it is closer to the asteroid belt, meaning it will sustain more frequent impacts. Both factors favor atmospheric loss from impacts for Mars over Earth.

14.6.3 What Is the Range of Sizes for a Habitable Planet?

From all of this it seems that are no easy criteria with which to establish a lower bound on the size of a planet capable of supporting life. If Mars had an ozone layer, would it have kept its water vapor, leading to higher planetary temperatures from greenhouse warming, or would it have lost its atmosphere faster because it would have developed a thermosphere similar to Earth’s? If we put Mars in Earth’s orbit, would it have kept an atmosphere longer because it didn’t suffer from as many impacts? As a guess, I would say that Mars is close to the lower bound on the mass or radius for a habitable world, as it seems that conditions there are right on the cusp of allowing life. This speculation must be taken with a large grain of salt: because of the interrelation of all of these variables it is hard to give definitive answers.

How about the upper limit on a habitable planet’s mass? This is similarly hard to estimate. One upper bound is that if a planet retains lighter gases in its atmosphere, it will likely turn into a gas giant planet. However, this depends both on the planetary mass and on its position in the Solar System, as all the gas giant planets formed beyond the “frost line,” outside the orbit of Mars. Perhaps more to the point, all the gas giant planets are thought to have solid cores of about ten times the mass of the Earth; maybe this core mass represents an upper limit. Or maybe not.

14.7  THE ANNA KARENINA PRINCIPLE AND HABITABLE PLANETS

All happy families are fundamentally the same; each unhappy family is unhappy in its own way.

—LEO TOLSTOY, ANNA KARENINA

Thus reads the famous opening line of Tolstoy’s Anna Karenina novel. Jared Diamond in Guns, Germs, and Steel introduced what he referred to as the “Anna Karenina” principle when reflecting on why, out of all possible animal species on the planet, only a handful had been domesticated by humans. He found that all animals domesticated for food had a number of features in common: they were all herbivores, matured quickly, bred in captivity, and had a few other similarities.

To quote Diamond,

To be domesticated, a candidate species must possess many different characteristics. Lack of any single required characteristic dooms efforts at domestication, just as it dooms efforts at building a happy marriage.

As he put it, “For most important things … success actually requires avoiding many separate causes of failure” [65, p. 157].

Above I introduced Adler’s mantra: “All stars are fundamentally the same; all planets are different from each other.” For planets, I will rephrase slightly:

Each lifeless planet is different from the others in its own way; all planets with Earth-like life on them will be fundamentally the same.

This is an extension of the Anna Karenina principle as applied to habitable worlds: all Earth-like planets have a number of similar characteristics, the most obvious being that they fall within a “zone of life,” not too far from or too near their star. The realization of this point has solved a conundrum that has faced scientists for a very long time: if the Earth is an average planet circling an average star in an average galaxy, with nothing special about it, then why haven’t we found life elsewhere in the cosmos yet? Why isn’t the universe teeming with life? Why haven’t the aliens made contact?

Since the 1960s, two ideas have gradually developed due to advances in planetary science:

1. The conditions on the different planets are far more diverse than was realized before. Planetary formation seems very chaotic, and planetary history (among other factors) plays a larger role in determining the geological and climatological features of the terrestrial planets than anyone realized.

2. The conditions required for Earth-like life on a planet are far more restrictive than was thought in the 1960s.

These two realizations severely reduce the number of possible planets with Earth-like life. Although Earth is in some sense no more special than any other planet, it is special in other ways as a cosmic lottery winner: it got everything right for life to appear on it. The point is that while it is improbable for any one particular person to win the lottery, someone almost always wins it.

Probability estimates of the number of worlds with life on them, in the fashion of the Drake equation, are meaningless, as we simply don’t have enough data. The criteria I have given so far are pretty solid for any planets with Earth-like life, but in the next section I’ll list a number of criteria for which there is less solid evidence.

14.8  IMPONDERABLES

One complication concerning Mars has been discovered by numerical simulations of its rotation. One of the characteristics of Earth’s climate is its long-term stability. This results in part from the fact that the rotational axis of the Earth more or less points in the same direction for long periods of time and doesn’t change dramatically.² However, because of Mars’s elongated orbit and its lack of a large moon to stabilize it, the orientation of the rotation axis of Mars can change dramatically and chaotically over the course of millions of years. It is believed that this has dramatically changed the characteristics of seasonal change on Mars [135][144]. It isn’t clear whether a stable rotational axis is needed for the evolution of life on a planet, but a stable climate certainly helps, in which case having a large moon might be a requirement for planetary life.

Another issue is that Earth is currently the only known planet that experiences plate tectonics, a result of both its size and its composition (radioactive decay in the Earth’s core keeps the mantle plastic). Some scientists have speculated that plate movement contributes to evolution because it allows the broad dissemination of plant and animal species, making it harder for individual species to be wiped out by a local catastrophe. Who knows? I am not aware of any science fiction stories that have incorporated the relationship between plate tectonics and evolution thematically; it would be interesting to see if it could be done in any reasonable way.

Other issues: Most exoplanets are found around stars with high metallicities, that is, around stars that contain more metals than average. (To an astronomer, a metal is any element that is not hydrogen or helium.) It may be that stars with higher metallicity simply contain more of the stuff that planets form from, although the exact details are not entirely clear [100]. More than half of all stars found so far with exoplanets have even higher metallicities than the Sun. What is interesting, however, is that high-metallicity stars are relatively young (population I) stars because the metals were mostly created by higher-order fusion processes in the hearts of the stars; the oldest stars formed at a time when these elements simply didn’t exist [130, pp. 495–497]. Because the higher elements are distributed by supernova explosions, which are more common toward the center of the galaxy than in the spiral arms, there may be a higher occurrence of stars with planets toward the centers of galaxies. However, the higher incidence of supernovas and radiation from supernovas may sterilize life emerging on these planets at distances too close to the galactic center. Thus there may also be a “galactic habitable zone” where life may form, an annulus neither too close to nor too far from the center of the galaxy [100].

Giant planets on highly eccentric orbits may perturb Earth-like planets out of the life zone because of their gravitational interactions with them, but large planets in the outer system may serve to screen planets from asteroid impacts like the one that eradicated the dinosaurs [247]. Hot Jupiters are thought to form in the outer system but migrate by various processes to close orbits around the star; the migration may disrupt the formation of planets in the zone. So the presence of hot Jupiters (found in over 10% of all exoplanet systems to date) may preclude life from developing, but cold Jupiters on nearly circular orbits in the outer system may be needed for life.

There is an almost infinite list of considerations which one can go into, especially when we add the question of intelligent life to the mix. I consider this subject in a later chapter. For anyone interested in exploring these ideas further, Brownlee’s book Rare Earth is a good place to start, but there has been a lot of research in this area since the book was published in 2000 [247].

We have now listed the criteria for a planet to support Earth-like life. In the next chapter I take up the issue of actually finding it out there.

NOTES

1. In a prescient piece of writing, Edgar Rice Burroughs in A Princess of Mars wrote that the Martian civilization built an atmosphere plant to combat atmospheric loss from their world. The means by which the atmosphere was replenished (the “ninth ray”) are not particularly scientific, however [43].

2. Dante Alighieri in 1300 CE understood this, though in a somewhat different way than we do now.