Extraterrestrial Civilizations - Isaac Asimov [60]
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