Extraterrestrial civiliz.., p.14
Extraterrestrial Civilizations, page 14
Next, suppose that Earth were 300,000 kilometers (186,000 miles) from the center of such a star and therefore circling it at a height of 150,000 kilometers (93,000 miles) above its surface. Earth would circle that star every 1.1 hours.
Earth would receive as much total energy from that very nearby midget star as the Earth now does from the Sun. The fact that the midget star would be barely red hot would be made up for by the fact that from the distance of the planet its apparent size would be 3,000 times that of the Sun as we see it from Earth.
To be sure, the nature of the energy received from the midget star would be different from that of the Sun. The midget star would deliver virtually no ultraviolet radiation and, in fact, very little visible light. Most of its energy would be in the form of infrared light.
This would be very inconvenient from our standpoint. To our own eyes, everything would seem very dim and unpleasantly deep red in color. We could imagine, however, that life on such a planet would have developed a sense of sight that would be sensitive to red and infrared, and perhaps see sections of it in different colors. To such life, the light might well appear white and sufficiently bright.
Red and infrared are less intensively energetic than the remainder of the visible light spectrum, and there would be many chemical reactions that yellow, green, or blue light could initiate that red and infrared could not. However, life is not based on photochemical reactions, except for photosynthesis and that is initiated by red light. No doubt we would not have to stretch matters intolerably to imagine life on such a world—so far.
Let us, however, take up a new issue:
The gravitational field of any object decreases in intensity with the square of the distance. If distance is doubled, the intensity falls to ¼ of what it was; if the distance is tripled, it falls to 1/9 and so on.
This affects the manner in which the Moon and the Earth attract each other.
The average distance between the center of the Moon and the center of the Earth is 384,390 kilometers (238,860 miles). This varies somewhat as the Moon moves about its orbit, but that doesn’t affect the line of argument.
Not all parts of the Earth are, however, at the same distance from the Moon. When the center of the Earth is at its average distance from the center of the Moon, the surface of the Earth that directly faces the Moon is 6,356 kilometers (3,950 miles) closer. The surface of the Earth that faces directly away from the Moon is 6,356 kilometers (3,950 miles) farther.
This means that while the surface of the Earth directly facing the Moon is at a distance of 378,034 kilometers (234,910 miles) from the Moon’s center, the surface of the Earth facing directly away from the Moon is at a distance of 390,746 kilometers (242,810 miles) from the Moon’s center.
If the distance of the Earth’s near side from the Moon’s center is set at one, the distance of the Earth’s far side is 1.0336. This difference, only 3.36 percent of the total distance from the Moon, does not seem like much. However, the gravitational pull of the Moon falls off over that small distance by an amount equal to 1/1.03362 and is only 0.936 at the far side as compared with 1.000 at the near side.
The result of this difference in the Moon’s pull at the near and far sides of the Earth is that the Earth is stretched in the direction of the Moon. The near surface is pulled toward the Moon more forcibly than the center is, and the center is pulled toward the Moon more forcibly than the far surface is. Both the near and far surface bulge, the former toward the Moon, the latter away from the Moon.
It is a matter of a small bulge only, half a meter or so. Still, as the Earth rotates, each part of its solid matter bulges up when it turns toward the side facing the Moon, reaching its greatest height when it passes under the Moon, then settling back. The solid matter bulges as it turns toward the side away from the Moon, reaching another peak when it is directly opposite the position of the Moon, then receding.
The water of the ocean bulges up also, to a greater extent than the solid land does. This means that as the Earth turns, the land surface passes through the higher bulge of water and, as it does so, the water creeps up the shore and then back down. It does so as it passes through both bulges of water, one on the side facing the Moon and one on the side away from it. This means the water rises and falls along the shore twice a day; or, we can say, there are two “tides” a day.
Because this difference in gravitational pull causes the tides, it is referred to as a tidal effect.
Naturally, the Earth also exerts a tidal effect on the Moon. Since the Moon is smaller than the Earth, the Moon’s diameter being 3,476 kilometers (2,160 miles) as compared with Earth’s diameter of 12,713 kilometers (7,900 miles), the drop in gravitational pull across the Moon is smaller than the drop across the Earth.
The width of the Moon is only 0.90 percent of the total distance between the Earth and the Moon, so that the gravitational pull on the far side is 98.2 percent of the force on the near side. The tidal effect on the Moon would be, in this respect, only 0.29 times what it is for the Earth, but the Earth’s gravitational field is 81 times that of the Moon, since the Earth is 81 times as massive as the Moon. If we multiply 0.29 by 81, we find that the tidal force of the Earth on the Moon is 23.5 times that of the Moon on the Earth.
Does this difference matter? Yes, it does.
As the Earth turns and bulges, the internal friction of the rock as it lifts up and settles down, and the friction of the water moving up the shore and back, consumes some of the energy of Earth’s rotation and turns it into heat. As a result, tidal action is slowing the Earth’s rotation. However, the Earth is so massive and the energy of its turning is so huge that the Earth’s rotation is slowing very slowly indeed. The length of the day is increasing by one second every 100,000 years.*This isn’t much on the human time scale, but if the Earth has been in existence for 5 billion years and this rate of day lengthening has been constant throughout, the day has lengthened a total of 50,000 seconds or nearly 14 hours. When the Earth was created, it may have been rotating on its axis in only 10 hours—or less, if the tides were more important in early geologic times than they are now, as they well might have been.
What about Earth’s tidal effect on the Moon?
The Moon has a smaller mass and therefore, very likely, a smaller rotational energy to begin with. Furthermore, the tidal effect on the Moon is 23.5 times that on the Earth. The stronger effect, working on the smaller mass, has a greater slowing effect. As a result, the Moon’s rotational period has slowed until it is now equal to exactly one revolution about the Earth. Under those conditions, the same side of the Moon always faces the Earth, the tidal bulge is always in the same spot on its surface, so that different parts of its body no longer have to heave up and settle back as it turns. There is no further slowing (at least as far as Earth’s tidal effect on the Moon is concerned) and the Moon’s rotational period is now stable.
As a result of tidal effect, small bodies would always be expected to turn only one face to the large bodies they circle. (This was first suggested by Kant in 1754.) Not only does the Moon turn only one face to the Earth, the two Martian satellites turn only one face to Mars, the five innermost satellites of Jupiter turn only one face to Jupiter, and so on.
In that case, though, why doesn’t the Earth turn only one side toward the Sun?
Consider what would happen if the Moon receded from the Earth. As it receded, Earth’s gravitational pull would decrease as the square of the distance. Also as it receded, the fraction of the total distance represented by the diameter of the Moon would decrease in proportion to the distance. The tidal effect would decrease for both reasons, and if both are taken into account it means that the tidal effect falls off as the cube of the distance.
The Sun is 27 million times as massive as the Moon. If both Sun and Moon were at an equal distance from the Earth, the Sun’s tidal effect upon the Earth would be 27 million times that of the Moon’s tidal effect upon the Earth.* The Sun, however, is 389 times as far from the Earth as the Moon is. The Sun’s tidal effect is weakened by an amount equal to 389 × 389 × 389, or 58,860,000. Divide 27 million by 58,860,000 and we find that the Sun’s tidal effect on Earth is only about 0.46 that of the Moon. If the Moon’s tidal effect has not sufficed to slow the Earth’s rotational period very much as yet, the Sun’s certainly would not.
Mercury is closer to the Sun than the Earth is, and that would be a factor that would tend to increase the tidal effect of the Sun. On the other hand, Mercury is smaller than the Earth, and that would tend to decrease it. Taking both factors into account, it turns out that the Sun’s tidal effect on Mercury is 3.77 times that of the Moon’s tidal effect on the Earth, and only 1/6 Earth’s tidal effect on the Moon.
The Sun, therefore, slows Mercury’s rotation more effectively than the Moon slows Earth’s, but less effectively than the Earth slows the Moon’s. We might suspect, then, that Mercury rotates slowly but not so slowly as to face one side only to the Sun.
In 1890, Schiaparelli (who reported the canals on Mars thirteen years before) undertook the task of observing Mercury’s surface. This is a very difficult thing to do, since Mercury is farther from us than Mars, usually; since Mercury shows only a crescent phase, usually, whereas Mars is always full or nearly full; and since Mercury, unlike Mars, is usually close enough to the brightness of the Sun to make comfortable viewing unlikely. Nevertheless, from what faint spots Schiaparelli could make out on the surface of Mercury, he decided that it rotated only once in each revolution of 88 days, and that it faced only one side to the Sun.
In 1965, however, radar waves that were emitted from Earth were bounced off Mercury’s surface. The echo, received on Earth, told a different story. The length of the radar waves changes if they strike a rotating body, and the change varies with the speed of rotation. From the nature of the reflected radar waves, it turns out that Mercury’s period of rotation is 59 days, or just ⅔ of its period of revolution. This is a comparatively stable situation, not as stable as having its rotation equal to its period of revolution, but stable enough to resist further change through the Sun’s insufficiently strong tidal effect.
Now we can return to the imaginary situation of our midget star, with Earth circling it at a distance of 300,000 kilometers (186,000 miles) from its center. This distance is only 1/500 that of our Earth from the Sun, and even allowing for the fact that the midget star had only 1/16 the mass of the Sun, its tidal effect on Earth would be 150,000 times that of the Earth’s tidal effect on the Moon.
There is no question, then, but that if Earth were close enough to a midget star to be within its ecosphere, the powerful tidal effect of the star would slow its rotation, and quite early in its lifetime cause it to face one side forever toward the star and one side forever away.
On the side facing always toward the star, the temperature would go up past the boiling point of water. On the side facing always away from the star, the temperature would drop far below the freezing point of water. There would be no liquid water on either side.
One could imagine that there might be a “twilight zone” on the boundary between the forever-lit and the forever-dark hemispheres, in which the conditions would be mild. This would be so only if the orbit of the planet were nearly circular. Even then, the temperature on the hot side might be hot enough to result in the slow loss of the atmosphere, so that the planet would be airless and the twilight zone no more habitable than any other part.
As we imagine a larger and larger star, the ecosphere would be farther and farther from it. A planet within the ecosphere would be subjected to a smaller and smaller tidal effect. Eventually, if the star were large enough, the tidal effect will no longer be large enough to render the planet unfit for life as we know it.
We might estimate that a star should have at least ⅓ the mass of the Sun (which means it would have to be of spectral class M2 at least) before a planet in its ecosphere would be suitable for life.
Nor is the matter of tidal effect the only problem with midget stars. The width of an ecosphere depends on how much energy a star is radiating. A massive, luminous star has an ecosphere far out in space and one that is very deep; deeper than the entire width of our Solar system. A midget star has an ecosphere that is close in on itself and is very shallow. The chance of a planet’s happening to form within so shallow an ecosphere is vanishingly small.
Finally, stars smaller than spectral class M2 are very often “flare stars.” That is, flares of unusually bright and hot gas periodically burst out on its surface. This happens on all stars, even on our Sun, for instance. On the Sun, however, such a flare would only add a small and bearable fraction to the ordinary Solar output of light and heat. The same flare on a dim midget star would increase its light and heat output by up to 50 percent. A planet receiving a proper amount of energy from the midget star would receive far too much under flare conditions. The star’s role as incubator would be carried out in too irregular a fashion to be compatible with life.
Between tidal effects, shallowness of ecosphere, and periodic flares, the exclusion of midget stars from further consideration in connection with extraterrestrial intelligence is triply justified.
JUST RIGHT
If the stars with too much mass to serve as adequate incubators for life, those more massive than spectral class F2, make up a small fraction of all the stars, this is not the case for the stars that are less massive than spectral class M2 and also don’t serve as adequate incubators for life. Midget stars are very common. More than two-thirds of the stars in our Galaxy, and presumably in any galaxy, are too small to be suitable for life.
Between spectral classes F2 and M2 are the stars that range in mass from 1.4 times that of the Sun to 0.33 times that of the Sun. At the upper end of this range, the lifetime of the stars is barely enough to give intelligence a fair chance to evolve. At the lower end of this range, a planet barely escapes tidal effects of too serious a nature.
Within the range, though, are the “Sunlike stars,” which, all other things being equal, are suitable incubators for life. While these Sunlike stars do not make up a majority of the stars in the sky, they are not really few in number, either. Perhaps 25 percent of all the stars in the Galaxy are sufficiently Sunlike in character to serve as adequate incubators of life.
That gives us our third figure:
3—The number of planetary systems in our Galaxy that circle Sunlike stars = 75,000,000,000.
* A very massive star may radiate so much of its energy in the invisible ultraviolet region that it will seem less luminous (to the human eye) than one might expect it to be.
* Eco- is from the Greek for home or habitat.
* For details on all this, see my book, The Collapsing Universe.
† The Sun will gradually grow warmer as it ages and by its final billion years on the main sequence, life may not be possible on Earth. When the Sun expands to a red giant, it will engulf the orbits of Mercury and Venus, and though Earth will probably remain outside the Sun’s swollen sphere, it will at best be a red-hot ball of rock.
*The slowing of the rotation means a loss of angular momentum that by the law of conservation of angular momentum can’t really be lost. What happens is that the Moon is slowly moving farther away from the Earth and so is the center of gravity of the Earth-Moon system. What the Earth loses in the angular momentum of rotation, it gains in the angular momentum of a larger swing about a more distant center of gravity.
* This is a hypothetical case only, for if the center of the Sun were as close to the Earth as the center of the Moon is, the Earth would be far beneath the surface of the Sun
CHAPTER 8
Earthlike Planets
BINARY STARS
A star may be Sunlike and yet still not be a suitable incubator for life. It may have properties, other than its mass and luminosity, that make it impossible for an Earthlike planet to circle it.
A star may be like the Sun in every apparent respect, for instance, and yet have as a companion not a planet or a group of planets, but another star. The presence of two stars in close association may conceivably ruin the chances for an Earthlike planet to circle either one.
The possibility of multiple stars did not dawn on astronomers until about two centuries ago. After all, our Sun is a star without stellar companions and that made it seem a natural condition. When the stars were recognized to be other suns, they, too, were assumed to be single. To be sure, there are stars that are close together in the sky. For instance, Mizar, the middle star in the handle of the Big Dipper, has a fainter star, Alcor, very near it. Such “double stars” were taken, however, to be single stars lying nearly in the same direction from the Earth but at radically different distances. In the case of Mizar and Alcor, this turned out to be true.
In the 1780s, William Herschel began to make a systematic study of double stars in the hope that the brighter (and presumably closer) one might move slightly and systematically with reference to the dimmer (and presumably more distant) one. This motion might reflect the motion of the Earth about the Sun and be the star’s “parallax.” From this, the star’s distance could be determined, something that had not yet been done.
Herschel did find motions among such stars, but never of the kind that would indicate the presence of a parallax. Instead, he found some double stars to be circling about a mutual center of gravity. These were true double stars, bound to each other gravitationally, and were called binary stars, from a Latin word meaning in pairs.
By 1802, Herschel was able to announce the existence of many such binary stars, and they are now known to be very common among the stars of the Universe. Among the bright and familiar stars, for instance, Sirius, Capella, Procyon, Castor, Spica, Antares, and Alpha Centauri are all binaries.
