Extraterrestrial Civilizations - Isaac Asimov [53]
Or—the loss of angular momentum to the planets may take time and as we shall see, the really massive stars are all young stars. It may be that they haven’t yet had time to transfer the angular momentum.
From the data on stellar rotation, then, it seems fair to conclude that at least 93 percent—and possibly 100 percent—of stars have planetary systems.
THE WOBBLING STARS
So far, so good, but we must admit that stars may be fast-rotators or slow-rotators for reasons that have nothing to do with planets. Some stars may simply form from clouds that have more angular momentum to begin with—or less.
Can we therefore look for other types of evidence?
We can, if we stop to consider that when two bodies attract each other gravitationally, the attraction is two-way. The Sun attracts Jupiter, but Jupiter also attracts the Sun.
If two bodies, attracting each other gravitationally, were exactly equal in mass, neither would rotate about the other, properly speaking. Contributing equally to the gravitational interaction, they would each circle around a point exactly midway between the two. This point around which they would circle is the “center of gravity.”
If the two bodies were unequal in mass, the more massive body would be less affected by the attraction and would move less. If the more massive body is twice the mass of the less massive, the center of gravity would be twice as close to the center of the more massive body as to the center of the less massive body. Suppose we consider the Moon and the Earth. The Moon is usually considered as revolving about the Earth, but it doesn’t revolve about the Earth’s center. Both it and the Earth revolve about a center of gravity that always lies between Earth’s center and the Moon’s center.
As it happens, the Earth is 81 times as massive as the Moon, so the center of gravity has to be 81 times as close to the center of the Earth as to the center of the Moon. The center of gravity of the Earth-Moon system is 4,750 kilometers (2,950 miles) from the Earth’s center. It is 348,750 kilometers (239,000 miles), 81 times as far, from the Moon’s center.
The center of gravity of the Earth-Moon system is so close to the Earth’s center that it is 1,600 kilometers (1,000 miles) under the Earth’s surface. Under the circumstances, it is certainly reasonable to consider the Moon as revolving about the Earth; it is, after all, revolving about a point inside the Earth.
The center of the Earth also moves in a small circle about that center of gravity once every 27⅓ days. If the Moon weren’t there, the Earth would move around the Sun in a smooth path. Because of the presence of the Moon, the Earth makes a small wave 27⅓ days long in its path about the Sun—twelve and a fraction of these waves through each complete turn. The wobble of the Earth’s could, in theory, be measured from out in space, and from it the presence of the Moon and perhaps its distance and size could be worked out even if, for some reason, it could not be directly seen.
This is true of Jupiter and the Sun, too. The Sun is 1,050 times as massive as Jupiter, so the center of gravity of the Sun-Jupiter system should be 1,050 times as close to the Sun’s center as it is to Jupiter’s center. Knowing the distance between the two centers, it turns out that the center of gravity is 740,000 kilometers (460,000 miles) from the center of the Sun. This means that the center of gravity is 45,000 kilometers (28,000 miles) outside the Sun’s surface.
The center of the Sun circles this center of gravity every 12 years. The Sun, in its smooth progress about the center of the Galaxy, wobbles slightly, moving first to one side of its path, then to the other.
If only the Sun and Jupiter existed, an observer from a post in space, from which it was too far to see Jupiter directly, might deduce the presence of Jupiter from the Sun’s wobble.
Actually, the Sun also