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.

For instance, I said that the solar day is 1440 minutes long but actually thafs a He. Because the Earth's axis is tipped to the plane of its orbit and because the Earth is sometimes closer to the Sun and sometimes farther (so that it moves now faster, now slower in its orbit), the solar day is sometimes a little longer than 1440 minutes and sometimes a little shorter. If you mark off "noons" that are exactly 1440 minutes apart all through the year, there will be times during the year when the Sun will pass over head fully 16 minutes ahead of schedule, and other times when it will pass overhead fully 16 minutes behind schedule. Fortunately, the Fffors cancel out and by the end of the year all is even agmn.

For that reason it is not the solar day itself that is 1440 minutes Ion amp; but the average length of all the solar days of the year; this average is the "mean solar day." And at noon of all but four days a year, it is not the real Sun that crosses the overhead point but a fictitious body called the "mean Sun." The mean Sun is located where the real Sun would be if the real Sun moved perfectly evenly.

The lunar day is even more uneven than the solar day, but the sidereal day is a really steady affair. A particular star passes overhead every 1436 minutes virtually on the dot.

If we7re going to measure time, then, it seems obvious that the sidereal day is the most useful, since it is the most constant. Where the sidereal day is used as the basis for checking the clocks of the world by the passage of a star across the hairline of a telescope eyepiece, then the Earth itself, as it rotates with respect to the stars, is serving as the reference clocl The second can then be defined as 1/1436.09 of a sidereal day. (Actually, the length of the year is even more constant than that of the sidereal day, which is why the second is now officially defined as a frac tion of the tropical year.)

The solar day, uneven as it is, carries one important advantage. It is based on the position of the Sun, and the position of the Sun determines whether a particular por tion of the Earth is in light or in shadow. In short, the solar day is equal to one period of light (daytime) plus one period of darkness (night). The average man through out history has managed to remain unmoved by the posi tion of the stars, and couldn't have cared less when one of them moved overhead; but he certainly couldn't help noticing, and even being deeply concerned, by the fact that it might be day or night at a particular moment; surmise or sunset; noon or twilight.

It is the solar day, therefore, which is by far the most useful and important day of all. It was the original basis of time measurement and it is divided into exactly 24 hours, each of which is divided into 60 minutes (and 24 times 60 is 1440, the number of minutes in a solar day).

On this basis, the sidereal day is 23 hours 56 minutes long and the lunar day is 24 hours 50 minutes long.

So useful is the solar day, in fact, that mankind has become accustomed to thinking of it as the day, and of thinking that the Earth "really" rotates in exactly 24 hours, where actually this is only its apparent rotation with re spect to the Sun, no more "real" or "unreal" than its ap parent rotation with respect to any other body. It is no more "real" or "unreal," in fact, than the apparent rota tion of the Earth with respect to an observer on the Earth - that is, to the apparent lack of rotation altogether.

The lunar day has its uses, too. If we adjusted our watches to lose 2 minutes 5 seconds every hour, it would then be running on a lunar day basis. In that case, we would find that high tide (or low tide) came exactly twice a day and at the same times every day-indeed, at twelve hour intervals (with minor variations).

And extremely useful is the frame of reference of the Earth itself; to wit, the assumption that the Earth is not rotating at all. In judging a billiard shot, in throwing a baseball, in planning a trip cross-country, we never take into account any rotation of the Earth. We always assume the Earth is standing still.

Now we can pass on to the Moon. For the viewer from the Earth, as I said earlier, it does not rotate at all so that its "terrestrial day" is of infinite length. Nevertheless, we can maintain that the Moon rotates if we shift our frame of reference (-usually without warning or explana' tion so that the reader has trouble following). As a matter of fact, we can shift our plane of reference to either the Sun or the stars so that not only can the-Moon be con sidered to rotate but to do so in either of two periods.

With respect to the stars, the period of the Moon's rota tion is 27 days, 7 hours, 43 minutes, 11.5 seconds, or 27.3217 days (where the day referred to is the 24-hour mean solar day). This is the Moon's sidereal day. It is also the period (with respect to the stars) of its revolu tion about the Earth, so it is almost invariably called the "sidereal month."

In one sidereal month, the Moon moves about 1/1.1 of the length of its orbit about the Sun, and to an observer on the Sun the change in angle of viewpoint is consider able. The Moon must rotate for over two more days to make up for it. The period of rotation of the Moon with respect to the Sun is the same as its perio,d of revolution about the Earth with respect to the Sun, and this may be called the Moon's solar day or, better still, the solar month. (As a matter of fact, as I shall shortly point out, it is called neither.) The solar month is 29 days, 12 hours, 44 minutes, 2.8 seconds long, or 29.5306 days long.

Of these two months, the solar month is far more useful to mankind because the phases of the Moon depend on the relative positions of Moon and -Sun. It is therefore 29-5306 days, or one solar month, from new Moon to new Moon, or from full Moon to full Moon. In ancient times, when the phases of the Moon were used to mark off the seasons, the solar month became the most iinpor tant unit of time.

Indeed, great pains were taken to detect the exact day on which successive new Moons appeared in order that the calendar be accurately kept (see Chapter 1). It was the place of the priestly caste to take care of this, and the very word "calendar," for instance, comes from the Latin word meaning "to proclaim," because the beginning of each month was proclaimed with much ceremony. An assembly of priestly officials, such as those that, in ancient times, might have proclaimed the beginning of each month, is called a "synod." Consequently, what I have been calling the solar month (the logical name) is, actually, called the synodic month."

The farther a planet is from the Sun and the faster it turns with respect to the stars, the smaller the discrepancy between its sidereal day and solar day. For the planets beyond Earth, the discrepancy can be ignored.

For the two planets closer to the Sun than the Earth the discrepancy is very great. Both Mercury and Venus turn one face eternally to the Sun and have no solar day. They turn with respect to the stars, however, and have a sidereal day which @ out to be as long as the period of their revolution about the Sun (again with respect to the stars).