Figure 21. The extreme size range of habitable planets.
vo to zero and matter was lost from the planet, or when the shape of the surface became unstable and axial symmetry was lost.
Just what extremes of rotation rate are compatible with habitability is difficult to say. These extremes, however, might be estimated at, say, 96 hours (4 Earth days) per revolution at the lower end of the scale and 2 to 3 hours per revolution at the upper end, or at angular velocities where the shape becomes unstable because of the high rotation rate.
A special case, that in which the planet's sidereal day is precisely equal to its year, so that one side of the planet perpetually faces the primary while the other side is in perpetual darkness, might be thought to be compatible with habitability—that is, temperatures near the terminator (day-night line) might be in the desired range. In our solar system, Mercury fits into this category as far as rotation rate is concerned. Just what would happen to a planet's atmosphere under these circumstances is a somewhat debatable question. Would the atmospheric circulation be strong enough to prevent all the gases from condensing on the dark side? Or would all the water and carbon dioxide, at least, precipitate out in the extreme cold of the dark side? If it is assumed, as seems reasonable, that the day-equals-year situation did not come into being ab initio but was preceded by a long slowing-down period, then, during this time, all of the planet's water might well have been lost by photodecomposition with the subsequent escape of hydrogen. The day-equals-year case then may be ruled out as indicating either that all the water is precipitated out in solid form on the dark side or that the planet is completely dry. In any case, there would be no oceans of liquid water on the planet, and, consequently, it would not be habitable according to the present definition of the term.
Considering high rotation rates, it is apparent that the force of gravity becomes a function of latitude, being lowest at the equator and higher in high latitudes. For an Earth-like planet with a 3-hour period of rotation, for example, if it is assumed that the mean density is unchanged (5.52 grams per cubic centimeter), the oblateness would be about 0.24 and the force of gravity at the equator about 0.7 g. The gravitational field at other latitudes would be higher and would depend on the internal density distribution.
From this it may be seen that surface gravity depends on rate of rotation as well as on mass, and this dependence may affect previous statements about the upper limit of mass of a habitable planet. Based on data on planets of the solar system, however, it seems probable that the rate of rotation is a rough function of mass, as shown in Chapter 3. The correlation is not perfect, but the trend displayed is probably not due to chance alone. Also, it is reasonable to hypothesize that, during the process of planetary formation (by accretion), each captured particle of mass affected rotational energy unless it fell squarely dead-center on the planet's disk. The net effect of capturing many particles has been an increase in rotation rate with increasing mass. Since all the planets of our solar system except Uranus rotate in the same direction as their orbital motion, there was evidently a tendency for the incoming particles to impact so as to impart a direct spin to the planets. This hypothesis is illustrated in Figure 22.
Figure 22. Rotation of the Earth produced by impacting particles.
The very low rotation rates exhibited by Mercury, the Moon, and probably Venus (although its true rate of rotation is not yet known) are apparently due to tidal braking effects. This subject will be discussed later.
Age. A certain amount of time must elapse before a newly formed planet can have surface conditions suitable for life. The sequence of events for an Earth-like planet might proceed according to the thirteen steps listed below.
1. A planet is formed by the gradual accretion and capture of small particles.
2. After the accretion process has been terminated because of a lack of growth materials, the surface is airless, or very nearly so.
3. The interior of the planet is extremely hot as a result of gravitational compression. Internal hydrostatic readjustments are taking place; denser materials, such as iron, are flowing slowly downward and lighter materials, such as certain silicates, are flowing upward. Because of the high viscosities involved, the internal readjustments take place over a long period of time. They also produce movements in surface materials, with extensive volcanism, crustal movements, or earthquakes. Localized heating of crustal rocks by friction and the decay of radioactive materials in the mantle produce high temperatures, and absorbed gases are released.
4. The lighter gases escape and the heavier gases are retained. Gases such as methane and ammonia may begin to accumulate if their rate of evolution exceeds their rate of escape. Photodissociation of water vapor by solar radiation takes place, with the hydrogen escaping and the oxygen entering into chemical oxidation of surface materials.
5. Those stable gases that can be retained (nitrogen and carbon dioxide and, possibly, methane and ammonia) begin to accumulate and an atmosphere begins to form.
6. As the atmosphere becomes thicker and volcanic activity continues, a point is reached at which the rate of production of water vapor exceeds the rate of loss by photodissociation and traces of oxygen and ozone can appear in the atmosphere.
7. The oxygen and ozone absorb in the ultraviolet region of the solar spectrum (the wave lengths responsible for photodecomposition of water) and water vapor can now begin to accumulate more rapidly. The presence of even small amounts of ozone also produces a more stably stratified stratosphere, so that water vapor is unable to diffuse upward as rapidly. This is known as the atmospheric "cold trap" and is an important factor in the retention of water vapor.
8. When the concentration of water vapor in the atmosphere reaches the dew point or frost point, liquid water or frost condenses locally. When the atmospheric pressure has become high enough (greater than 6.3 millibars), the water condensed on the surface can appear as a liquid, provided that the temperature conditions are right (slightly above 0°C).
9. With continued volcanism, bodies of water appear on the planet and most of the carbon dioxide goes into solution, forming carbonic acid and reacting to form carbonate rocks. The ammonia also goes into solution and enters into reactions. Now the atmosphere consists mainly of nitrogen and methane, with water vapor as a variable constituent.
10. The bodies of water increase in size and join to form oceans. Rainfall becomes more prevalent; weathering begins to become significant; soluble minerals are washed into the oceans.
11. More complicated chemical compounds begin to accumulate in the oceans. Lightning discharges form small quantities of the oxides of nitrogen; these dissolve to form nitric acid and nitrates. Sulfur dioxide from volcanoes dissolves to form sulfuric acid and sulfates.
12. At some point, life appears, and eventually photosynthesis is established; free oxygen begins to accumulate in the atmosphere. [So much has been written in recent years about the origin of life on the Earth and elsewhere that no attempt will be made here to review these ideas.* It is significant that life, in the opinions of those who have studied the subject intensively (Edsall and Wyman, 1958; Henderson, 1958; Sidgwick, 1950),
* The interested reader is referred to Calvin (1955, 1959, 1961); Haldane (1928, 1954); Horowitz (1956, 1958); Oparin (1938, 1957, 1961); Tax (1960); and Wald (1954).
implies life based on the compounds of carbon. Sidgwick has summed up unequivocally, "Carbon is unique among the elements in the number and variety of the compounds which it can form. Over a quarter of a million compounds have already been isolated and described, but this gives a very imperfect idea of its powers, since it is the basis for all forms of living matter. Moreover, it is the only element which could occupy such a position. We know enough now to be sure that the idea of a world in which silicon should take the place of carbon as the basis for life is impossible; the silicon compounds have not the stability of those of carbon, and in particular it is not possible to form stable compounds with long chains of silicon atoms."]
13. After a long period of time, during which the prevalence of plants (or living forms carrying on photosynthesis) increases, the oxygen concentration of the atmosphere reaches the minimum value required by human beings; the volcanic activity level has slowed down, the meteorite-infall rate has diminished, and the planet may be considered habitable.
How long does this entire process take ? One billion, 2 billion, 3 billion years? It is not possible to say with much accuracy, but the amount of time is surely of this order of magnitude. Thus, even though a planet has all the other essential attributes from an astronomical point of view, it must also be of a certain age before it can be considered habitable.
From the evolutionary point of view, or from the above sketchy chronological sequence, it may be seen that several factors could interfere with the development of suitable conditions on the surface of a planet. If the planetary mass were only slightly too small, the rate of juvenile water production by volcanic activity would be too low to balance the loss rate by photodissociation, and water would never accumulate on the surface. If the mean surface temperature were too high, water would never condense on the surface; instead, all of it would remain in the atmosphere, where it would continue to be lost by photodecomposition. No oceans would form, and carbon dioxide would become a major constituent of the atmosphere.
In general, it is probably safe to say that a planet must have existed for 2 or 3 billion years, under fairly steady conditions of solar radiation, before it has matured enough to be habitable.
Distance from Primary and Inclination of the Equator. The two parameters, distance and inclination, must be considered together because habitability depends on the two in combination, rather than on each independently. Orbital eccentricity is also interrelated with these parameters in determining habitability. As will be indicated later, however, the eccentricity requirements seem to be somewhat less restrictive than those of distance and inclination. In the present discussion it will be assumed that the orbital eccentricity is zero (the orbit being a circle centered on the primary).
Actually the radiation received by a planet from a particular star with given luminosity L may be expressed either in terms of the distance r or the illuminance E, because E = Ljr2. Illuminance is the term more generally useful in discussing the habitability of planets, so it will be employed in the remainder of this section. The terms are defined so that if r is in astronomical units and L is in terms of the Sun's luminosity, then E is in terms of the solar constant above the Earth's atmosphere at 1 astronomical unit (solar constant = 1.94 g cal/cm2 min, or 1.35 X 106 erg/cm2 sec).
In this connection, it is useful to introduce the term "ecosphere" (from the Greek, oikos, house, with the combining form oiko- denoting habitat or environment), a word apparently first used by Strughold (1955). For present purposes, ecosphere will be used to mean a region in space, in the vicinity of a star, in which suitable planets can have surface conditions compatible with the origin, evolution to complex forms, and continuous existence of land life and surface conditions suitable for human beings, along with the ecological complex on which they depend. The ecosphere lies between two spherical shells centered on the star. Inside the inner shell, illuminance levels are too high; outside the outer shell, they are too low.
Now it is a difficult problem to predict temperatures at a particular location on the surface of a planet as functions of illuminance and equatorial inclination. The problem becomes extremely complicated when a planet has atmospheric circulation and irregularly shaped ocean and dryland areas. We do not even have acceptable theories about the causes of the glacial periods and of the dependence of climatic changes on the distribution of land and sea and the inclination of the equator. Attempts to calculate even mean annual temperatures on the Earth's surface on theoretical grounds have not been highly successful (Milankovitch, 1930). For this reason it was decided to use empirical methods here for the determination of planetary surface temperatures, using the Earth as a standard.
The empirical method employed assumed Earth-like planets with optically thin atmospheres and a cloud cover of approximately 45 per cent. Theoretical temperatures were calculated at various latitudes and seasons for rapidly rotating, nonconducting, black spheres (of various axial inclinations) that were half-illuminated by a distant point source. A relationship was then found between these theoretical temperatures and the actual observed temperatures on the Earth's surface (Figure 23), and this relationship was used as a basis for predicting mean surface temperatures on planets of any inclination at any latitude and at summer solstice, winter solstice, and the equinoxes.
Finally, habitability figures were computed by applying the rules that a region is habitable only if the mean annual temperature lies between
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