Chapter 3: The Unexplained Motions of the Heavens

Chapter 3: The Unexplained Motions of the Heavens

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Chapter 3: The Unexplained Motions of the Heavens

In This Chapter

z How does celestial movement mark time?

z The discrepancy between the solar and sidereal day--and what it means

z The sidereal month versus the synodic month

z Understanding the tropical year and the sidereal year

z The reason for seasons

z The solar system according to Ptolemy

The next time you're outside doing yard work in the sun, put a stick in the ground, call it a gnomon, and watch the motion of its shadow. Believe it or not, you have made a simple sundial, which was one of the earliest ways that human beings kept track of time. In fact, keeping time was one of the two major reasons that early civilizations kept a close watch on the skies. The other reason, of course, was to use the motions of the planets through the constellations to predict the future for the benefit of kings and queens and empires. Well, the first practice (keeping track of time) has continued to this day. The U.S. Naval Observatory is charged with being the timekeeper for the nation, using technology a bit more advanced than a stick in the ground. The second practice (predicting the future) is also alive and well, but astronomers have turned those duties over to The Psychic Network0/00--at least for the time being.

In the days before movies, television, video games, and the Internet, the starry sky (untouched by city lights and automobile exhaust) was truly the greatest show on Earth. Generations of sky watchers looked and imagined and sought to explain. Common sense told many of these early watchers that they were on a kind of platform overarched by a rotating bowl or sphere that held the stars. We have seen that in various cultures, other explanations surfaced from time to time.

It doesn't matter right now whether these explanations were right or wrong (well, many of them were wrong). What matters is that the explanations were, to many astronomers, unsatisfying. None of the explanations could account for everything that happened in the sky. For example, if the stars were all fixed in this overarching bowl, how did the planets break free to wander among the stars? And they didn't wander randomly. The planets were only found in certain regions of the sky, close to the great circle on the sky called the ecliptic. Why was that? The sky is filled with thousands of bright points of light that move, and none of the ancient explanations adequately explained all of these movements.

In this chapter, we examine the sky in motion and how early astronomers came to be the keepers of the clock.

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.

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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.

Star Words

A solar day is measured from sunup to sunup (or noon to noon, or sunset to sunset). A sidereal day is measured from star rise to star rise, for example, the time between the star Betelgeuse rising above the horizon one day and the next. A solar day is 3.9 minutes longer than a sidereal day.

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, theaggregate 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.

Astro Byte

You can check out for yourself the difference between the solar day and the sidereal day by noting, over the course of a month, what constellations are directly overhead at 9 p.m. You should see that the constellations exhibit a slow drift. In what direction are they drifting? East or west? This drift is the cumulative effect of the 3.9 minute difference between the sidereal day and the solar day.

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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 (291/2 days) to cycle through all its phases.

z The invisible (or almost invisible) new moon

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

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

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

z The full moon (two weeks after new moon)

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

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

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

z 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

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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 . 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.

Figure 3.1 The Moon as you might see it through a telescope.

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.

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.

Close Encounter Want a peek at the far side? A phenomenon called libration, a kind of swaying (or

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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.

Star Words

A sidereal month is the period of 27.3 days it takes the moon to orbit once around the earth. A synodic month is the 29.5 days the moon requires to cycle through its phases, from new moon to new moon or full moon to full moon.

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