Time on Our Hands

Why did the ancients concern themselves about things moving in the sky when they were stuck here down on Earth? Chalk it up in part to human curiosity. But their interest also had even more basic motives.

You're walking down the street, and a passerby asks you for the time. What do you do?

You look at your watch and tell him the time. But what if you don't have a watch?

If you still want to be helpful, you might estimate the time, and you might even do this by noting the position of the sun in the sky.

The ancients had no wrist watches, and, for them, time—a dimension so critical to human activity—was measured by the movement of objects in the sky, chiefly the sun and the moon. What, then, could be more important than observing and explaining the movement of these bodies?

What Really Happens in a Day?

We define a day as a period of 24 hours—but not just any 24 hours. Usually, by a "day," most people, and certainly ancient cultures would have meant the period from one sunrise to the next.

But how long is a day, really? What do we mean when we say a day? It turns out that there are two different kinds of days: a day as measured by the rising of the sun (a solar day), and a day as measured by the rising of a star (a sidereal day). Let's think about this a bit.

Even casual observation of the night sky reveals that the position of the stars relative to the sun are not identical from one night to the next. Astute ancient skywatchers noticed that the celestial sphere shifted just a little each night over the course of days, weeks, and months. In fact, the aggregate result of this slight daily shift is the well-known fact that the constellations of summer and winter, for example, are different. We see Orion in the winter, and Leo in the spring.

Astronomers call the conventional 24-hour day (the time from one sunrise [or sunset] to the next) a solar day. They call a day that is measured by the span from star rise to star rise a sidereal day. The sidereal day is almost 4 minutes (3.9 minutes) shorter than the solar day. We'll see why in a moment.

It works like this: Relative to the rotating and orbiting Earth, we may imagine that the sun is essentially at rest at the center of the solar system. However, from any spot on Earth it looks as if the sun is rising, traveling across the sky, and setting. A solar day is not really the 24 hours from sunrise to sunrise, but the 24 hours it takes the earth to rotate one full turn.

While spinning on its axis, the earth is also orbiting the sun, with one complete revolution defining a year (we'll get into the details of years in a moment). Remember that a circle consists of 360 degrees; therefore, one complete circuit around the sun is a journey of 360 degrees. It takes the earth one year to make a complete circuit around the sun. And for the moment, let's say that a year consists of 365 days. To find out how far the earth travels through its orbit in one day, divide 360 degrees by 365 days. The result is about 1 degree.

A sidereal day is defined as the time between risings of a particular star (all of which are very distant relative to the distance to the sun). Since the earth is

constantly moving ahead in its orbit around the sun, we will see the same star rise again on the next day slightly sooner than we see the sun rise—precisely 3.9 minutes sooner each day. In one solar day, then, the earth has advanced in its orbit almost a degree, and it takes the earth 3.9 minutes to rotate through this one-degree angle and bring about another sunrise.

A Month of Moons

And then there is the moon. As we saw in Chapter 1, "Naked Sky, Naked Eye: Finding Your Way in the Dark," the words "moon" and "month" are closely related, and with good reason. The moon takes about a month (29^ days) to cycle through all its phases.

V The invisible (or almost invisible) new moon

V The waxing crescent (fully visible about four days after the new moon)

V The first quarter (the half moon, a week after the new)

V The waxing gibbous (75 percent of the moon visible, 10 days after new moon)

V The full moon (two weeks after new moon)

V The waning gibbous (75 percent, 18 days old)

V The third quarter (half a moon at 22 days old)

V The waning crescent (a sliver by the 26th day)

V New moon at day 29

What's going on here? Doubtless, many of our ancestors believed the moon changed shape, was consumed and reborn. The Greeks, however, surmised that the moon had no light of its own, but reflected the light of the sun—and therein lies the explanation for the phases of the moon.



Close Encounter

Wondering what the phase of the moon is right now? Too lazy to go outside and look for yourself? Then check out www.tycho.usno.navy./mil/vphase.html. This cool Web site allows you to see the moon phase for any day you choose.

The full disc of the moon is always present, but we see what we call the full moon only when the sun and the moon are located on opposite sides of the earth. When the moon comes between the sun and the earth, the side of the moon away from the earth is illuminated, so we see only its shadowed face as what we call the new moon. In the periods between these two phases (new and full), the sun's light reveals to us varying portions of the moon, depending upon the relative position of the earth, moon, and sun.

There is another observation that must have been made early on, which probably puzzled early sky watchers. The moon's face is irregular, marked with what we now know to be craters (holes and depressions left by meteor impacts) and other features (which we will investigate in Chapter 10, "The Moon: Our Closest Neighbor"). Even naked eye observations make it abundantly clear that the moon always presents this same, identifiable face to us, and that we never see its other side—a fact that has given rise to innumerable myths.

For generations, the far side of the moon, or the "dark side," has been the subject of wild speculation, including stories of mysterious civilizations hidden there. Humankind didn't get so much as a glimpse of it until a Soviet space probe radioed images back to Earth in 1959. As it turns out, the "far side" of the moon hid no mysterious civilizations, but did look rather different from the near side, with more craters and fewer large grey areas (seas). Those differences support certain theories of how the moon formed, as we'll see in Chapter 10.

Calling the face of the moon that we never see the "dark side" is a misnomer, since at new moon, the side of the moon that we do not see is fully illuminated by the sun and not dark at all. (We just don't see it.) "Far side" is a far better term.

Astro Byte

Calling the face of the moon that we never see the "dark side" is a misnomer, since at new moon, the side of the moon that we do not see is fully illuminated by the sun and not dark at all. (We just don't see it.) "Far side" is a far better term.

The Moon as you might see it through a telescope.

(Image from arttoday.com}

The Moon as you might see it through a telescope.

(Image from arttoday.com}

Close Encounter

Want a peek at the far side? A phenomenon called libration, a kind of swaying (or wobbling) motion to which the moon is subject, means that you can occasionally catch the smallest glimpse of the far side. Libration can reveal 59 percent of the lunar surface-though, of course, never more than 50 percent at once, since the swaying of part of the moon toward us means that the part opposite it must sway away from us. After you become an experienced lunar observer, look at the extreme northern and southern regions of the moon. With the help of a good lunar map, see if you can find features there that you never saw before and that later seem to disappear.

The explanation of why we never see the far side requires understanding a few more of the solar system's timing mechanisms. Like the earth, the moon rotates as well as orbits. It rotates once on its axis in 27.3 days, which is exactly the amount of time it takes for the moon to make one complete orbit around the earth. Synchronized in this way, the rotating and orbiting moon presents only one face to the earth at all times.

But hold the phone! Twenty-seven-and-one-third days to orbit the earth? Why, then, does it take 29.5 days for the moon to cycle through all of its phases? It seems as if the solar system is playing games with time again.

Close Encounter

Hold your hand out at arm's length with the back of your hand facing you. Imagine that your head is the earth, and the back of your hand (facing you) is the face of the moon. Now, move your arm in an arc from right to left, keeping the back of your hand facing you. This exercise should help you to appreciate that the moon (your hand) must rotate to keep the same side facing the earth (your head).

True enough. But given what we just discussed, the difference between a sidereal month (the 27.3 days it takes the moon to complete one revolution around the earth) and the synodic month (the 29.5 days required to cycle through the lunar phases) should now be easy to understand. The difference is explained by the same principle that accounts for the difference between the solar day and the sidereal day. Because the earth's position relative to the sun—the source of light that reveals the moon to us—changes as the earth travels in its orbit, the moon must actually complete slightly more than a full orbit around the earth to complete its cycle through all the phases. That is, the moon will have traveled through 360 degrees of its orbit around the earth after 27.3 days, but due to the earth's motion, the moon has to continue a little farther in its orbit before it will be full (or new) again.

A few minutes here, a few days there. The progress of science, of coming to a greater understanding of reality, is often measured in small differences and discrepancies. These slight differences are akin to the apparently inconsequential "accounting error" that reveals to the careful auditor some vast scheme of financial manipulation.

Another Wrinkle in Time

Measured from equinox to equinox, a year is 365.242 days long. This length of time is called a tropical year. Yet the time it actually takes the earth to complete one circuit around the sun is twenty minutes longer: 365.256 days—a sidereal year.

Well, here we go again! More wrinkles in how we measure time. The slight discrepancy between the sidereal year and the tropical year is due to the fact that the earth's rotational axis slowly changes direction over long periods of time. Astronomers call this phenomenon precession. If you spin an old-fashioned top, you will notice that the toy spins rapidly on its own tilted axis and that, as the top starts to slow down, the axis itself slowly revolves around the vertical, the handle of the top tracing out a circle. The earth, subject to gravitational pull from sun and moon, behaves much like a toy top, spinning rapidly on its axis, even as that axis gradually rotates.

How gradually does the earth's axis precess? This is astronomy we're talking about, and things take a long time. A complete cycle of precession takes about 26,000 years. In practical terms, this means that, whereas Polaris is the pole star today—the star almost directly above the North Pole—a star called Thuban was the pole star in 3000 b.c.e., and Vega will be the pole star in c.e. 14000. Moreover, if we linked our calendars to the sidereal year instead of the tropical year, February would be a midsummer month in the northern hemisphere some 13,000 years from now. The effect on the celestial sphere is that points in the sky are not exactly fixed, but ever so slowly drift. The "zero mark" of right ascension (called the vernal equinox) is where the ecliptic and the celestial equator cross on the celestial sphere. That point in the sky is currently in the constellation Virgo. But it won't always be. The vernal equinox will drift through the constellations as the earth slowly precesses.

We don't think that our distant ancestors were aware of the causes of precession, but they did have a good deal of trouble coming up with accurate calendars, and making calendars was often a subject of intense debate. Hipparchos, in the second century b.c.e., was the first astronomer to explain the difference in length between the sidereal year and the tropical year as being due to the "precession of the equinoxes."

Close Encounter

Close Encounter

The slow drift of the earth makes it important to know the reference time, or epoch of your coordinates. Since the coordinates slowly drift, astronomers have to know whether they are talking about where objects were in the coordinate system as it was in 1950, or in the year 2000, or are exactly at this moment. To observe a source in the sky, of course, you want to know the coordinates at that particular moment. However, in order to compare their results, most astronomers convert their coordinates to what are called J2000 coordinates—the positions of sources in the sky in the year 2000. Not that there is anything special about the year 2000, it just serves (for now) as a common reference time to compare coordinates.

To Everything a Season

Both authors of this book remember learning how to drive a car with a stick shift. One of us (the bearded one) was once in line at a New Jersey Turnpike toll booth, waiting to pay. The car behind gently nudged him each time the line of cars inched forward. Not once, not twice, but several times. Finally, enough was enough. He got out of his car to give the other driver a piece of his mind. That fellow, however, rolled down his window first: "Why do you keep rolling back into me?"

That's when this author realized that he needed more practice coordinating the clutch with the shift. But until that rude awakening, it seemed to him that the other person's car was moving, and that he was standing still.

So it was for thousands of years with the people on Earth. As the earth orbits the sun, it appears (to an earthbound observer) that the sun gradually moves across the sky, relative to the position of the stars, in the course of a year. Early astronomers charted what was apparently the sun's path across the celestial sphere and found that it described a great circle inclined at 23!4 degrees relative to the celestial equator. This apparent path of the sun is called (as we have seen) the ecliptic. Like the odd pieces of time that are apparently lost or gained in the course of a day or a month, this curious angle can actually tell us a lot about how the solar system works, and why summer follows spring each year.

We now know that the sun doesn't travel across the celestial sphere in a course that is inclined at 23!4 degrees with respect to the celestial equator. In fact, as we all know, the earth orbits the sun while also rotating around its own north-south axis. The earth's rotational axis, however, is tilted at 23!/2 degrees relative to an axis perpendicular to its orbital plane. Think of it this way: The earth is not standing up straight in the plane of the solar system, but is tipped over on its side by an angle of 23!/2 degrees. It is this inclination in the earth's axis that makes it appear that the sun is traveling an inclined course across the sky. If the earth were not "tipped," then the sun would move directly along the celestial equator.

The earth's inclination has a profound effect on us all. When the sun appears to be at its northernmost point above the celestial equator, we have the summer solstice (June 2!). As the earth rotates on this date, locations north of the earth's equator enjoy the longest day of the year, because these locations spend the greatest portion of their time exposed to the sunlight. In the southern hemisphere, this day is the shortest of them all, because that portion of the earth is tilted away from the sun. Six months after the summer solstice comes the winter solstice (on December 2!). On this day, the situations of the northern and southern hemispheres are reversed: The sun is low in the sky in the northern hemisphere, making it the shortest day of the year, and the southern hemisphere has the sun high in the sky.

Between the two solstices come the equinoxes. On these dates— September 2! for the autumnal equinox, and March 2! for the vernal equinox—day and night are of equal

Star Words

The ecliptic traces the apparent path of the sun against the background stars of the celestial sphere. This "great circle" is inclined at 23'/2 degrees relative to the celestial equator, which is the projection of the earth's equator onto the celestial sphere.

Star Words

The ecliptic traces the apparent path of the sun against the background stars of the celestial sphere. This "great circle" is inclined at 23'/2 degrees relative to the celestial equator, which is the projection of the earth's equator onto the celestial sphere.

duration; the sun's apparent course (one great circle on the celestial sphere) intersects the celestial equator (another great circle) at these points, as it passes into the northern hemisphere of the celestial sphere.

In the Northern Hemisphere, the summer solstice marks the beginning of summer, the autumnal equinox the beginning of fall, the winter solstice is the first day of winter, and the vernal equinox is the start of spring.

The seasons as a function of the earth's orbit around the sun.

(Image from the authors' collection)

The equinoxes are more than just a matter of marking time. Because of the earth's tilt, the summer sun is high in the sky and the days are long, which means the weather tends to be warm. In the winter, the sun is low in the sky, the days are short, and the weather is cold. As the height of the sun in the sky changes, the area of the earth's surface over which the sun's energy is distributed also changes: a larger area in winter (when the sun is low in the sky) and a smaller area in summer (when the sun is more overhead). The effect is that the earth absorbs less energy per unit area in the winter (cooler temperatures), and more energy per unit area in the summer (warmer temperatures). The combination of this change in energy absorbed and the length of the day due to the position of the sun creates what we know as seasons.

Close Encounter

Close Encounter

In ancient times, sky watchers paid special attention to the 12 constellations grouped along the ecliptic, the apparent path of the sun. These constellations are known as the zodiac and are, accordingly, associated with certain seasons. For example, the earth squarely faces Gemini at about the time of the winter solstice, Virgo at the vernal equinox, Sagittarius and Capricorn at the summer solstice, and Pisces during the autumnal equinox. Our ancestors believed that the constellations of the zodiac exerted a special influence on events and human traits and character relative to the time of year and other factors. Of particular importance to early astrologer-astronomers was the interplay between the positions of planets and the constellations. Thus the pseudoscience of astrology came into being as an attempt to correlate seasonal, celestial, and earthly events. The precession of the earth has shifted the zodiac since Babylonian times. Your "true" astrological sign is (generally) shifted one sign earlier in the year. And you thought you were a Capricorn!

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