6. Round And Round And…
Any-one who writes a book on astronomy for the general public eventually comes up against the problem of trying to explain that the Moon always presents one face to the earth, but is nevertheless rotating.
To the average reader who has not come up against this problem before and who is inpatient with involved subtleties, this is a clear contradiction in terms. It is easy to accept the fact that the Moon always presents one face to the Earth because even to the naked eye, the shadowy blotches on the MooWs surface are always found in the same position. But in that case it seems clear that the Moon is not rotating, for if it were rotating we would, bit by bit, see every portion of its surface.
Now it is no use sm.Uing gently at the lack of sophistica tion of the average reader, because he happens to be right.
The Moon is not rotating with respect to the observer on the Earth's surface. When the astronomer says that the Moon is rotating, he means with respect to other observers altogether.
For instance, if one watches the Moon over a period of time, one can see that the line marking off the sunlight from the shadow progresses steadily around the Moon; the Sun shines on every portion of the Moon in steady pro gression. This means that to an observer on the surface of the Sun (and there are very few of those), the Moon would seem to be rotating, for the observer would, little by little'see every portion of the Moon's surface as it turned to be exposed to the suiidight.
But our average reader may reason to himself as fol lows: "I see only one face of the Moon and I say it is not rotating. An observer on the Sun sees all parts of the Moon and he says it is rotating. Clearly, I am more im portant than the Sun observer since, firstly, I exist and be doesn't, and, secondly, even if he existed, I am me and he isn't. Therefore, I insist on having it my way. The Moon does not rotate!"
There has to be a way out of this confusion, so let's think things through a little more systematically. And to do so, let's start with the rotation of the Earth itself, since that is a point nearer to all our hearts.
One thing we can admit to begin with: To an observer on the Earth,,the Earth is not rotating. If you stay in one place from now till doomsday, you will see but one portion of the Earth's surface and no other. As far as you are concerned, the planet is standing still. Indeed, through most of civilized human history, even the wisest of men insisted that "reality" (whatever that may be) exactly matched the appearance and that the Earth "really" did not rotate. As late as 1633, Galileo found himself in a spot of trouble for maintaining otherwise.
But suppose we had an observer on a star situated (for simplicity's sake) in the plane of the EartWs equator; or, to put it another way, on the celestial equator (see Chapter 3). Let us further suppose that the observer was equipped with a device that made it possible for Mm to study the Earth's surface in detail. To him, it would seem that the Earth rotated, for little by little he would see every part of its surface pass before his eyes. By taking note of some particular small feature (for example, you and I standing on some point on the equator) and timing its return, he could even determine the exact period of the Earth's rotation-that is, as far as he is concerned.
We can duplicate his feat, for when the observer on the star sees us exactly in the center of that part of Earth's surface visible to himself, we in turn see. the observer's star directly overhead. And just as he would time the periodic return of ourselves to that centrally located position, so we could time the return of his star to the overhead point.
The period determined wiU be the same in either case.
(Let's measure this time in minutes, by the way. A minute can be defined as 60 seconds, where I second is equal to 1/31,556,925.9747 of the tropical year.)
The period of Earth's rotation with respect to the star is just about 1436 minutes. It doesn't matter which star we use, for the apparent motion of the stars with respect to one another, ii viewed from the Earth, is so vanishingly small that the constellations can be considered as moving all in one piece.
The period of 1436 minutes is called Earth's "sidereal day." The word "sidereal" comes from a Latin word for "star," and the phrase therefore means, roughly speaking, "the star-based day."
Suppose, though, that we were considering an observer on the Sun. If he were watching the Earth, he, too, would observe it rotating, but the period of rotation would not seem the same to him as to the observer on the star. Our solar observer would be much closer to the Earth; close enough, in fact, for Earth's motion about the Sun to intro duce a new factor. In the course of a single rotation of the Earth (judging by the star's observer), the Earth would have moved an appreciable distance through space, and the solar observer would find himself viewing the planet from a different angle. The Earth would have to turn for four more minutes before it adjusted itself to the new angle of view.
We could interpret these results from the point of view of an observer on the Earth. To duplicate the measure ments of the solar observer, we on Earth would have to measure the period of time from one passage of the Sun overhead to the next (from noon to noon, in other words).
Because of the revolution of the Earth about the Sun, the Sun seems to move from west to east against the back ground of the stars. After the passage of one sidereal day, a particular star would have returned to the overhead posi tion, but the Sun would have drifted eastward to a point where four more minutes would be required to make it pass overhead. The solar day is therefore 1440 minutes long, 4 ' ates longer than the sidereal day.
Next, suppose we have an observer on the Moon. He is even closer to the @h and the apparent motion of the Earth against the stars is some thirteen times greater for him than for an observer on the Sun. Therefore, the dis crepancy between what he sees and what the star observer sees is about thirteen times greater than is the Sun/star discrepancy.
If we consi er this same si tion from t. ie Earth, we would be measuring the time between successive passages of the Moon exactly overhead. The Moon drifts eastward against the starry background at thirteen times the rate the Sun does. After one sidereal day is completed, we have to wait a total of 54 additional minutes for the Moon to pass overhead again. The Earth's "lunar day" is therefore 1490 minutes long.
We could also figure out the periods of Earth's rotation with respect to an ob 'server on Venus, on Jupiter, on Halley's Comet, on an artificial satellite, and so on, but I shall have mercy and refrain. We can instead summarize the little we do have as follows: sidereal day 1436 minutes solar day 1440 minutes lunar day 1490 minutes By now it may seem reasonable to ask: But which is the day? The real day?
The answer to that question is that the question is not a reasonable one at all, but quite unreasonable; and that there is no real day, no real period of rotation. There are only different apparent periods, the lengths of which de pend upon the position of the observer. To use a prettier sounding phrase, the length of the period of the Earth's rotation depends on the frame of reference, and all frames of reference are equally valid.
But if all frames of reference are equally valid, are we left nowhere?
Not at all! Frames of reference may be equally valid, but they are usually not equally useful. In one respect, a particular frame of reference may be most useful; in an other respect, another frame of reference may be most useful. We are free to pick and choose, using now one, now another, exactly as suits our dear little hearts.