PLANETS IN ANCIENT TIMES
Five planets were known to the ancient Greeks: Mercury, Venus, Mars, Jupiter, and Saturn. It was not recognized that earth was a planet that orbitted the sun. In the night sky they did not look different from the many thousands of stars that were visible at that time. (Today, especially in cities, we see many fewer stars because their light is masked by the artificial lights of human society.) How did they distinguish these special five (and give them names corresponding to gods)? The word planet means "wanderer," and the planets differed from the stars in their motions across the sky. Our object is to discuss that motion.
ANGULAR MOTION
First keep in mind that by motion we do not mean motion in three-dimensional space, such as the motion of a baseball across a field or a car along a road. The stars and planets appear as points of light in the sky, and we have no direct way of knowing how far away they are. We can specify their position by giving angles that define a direction -- the direction for pointing to them. Motion means moving from one angular position to another, and the amount that the object moves is given as an angle. The "speed" of the motion is how fast its angular position changes. It would be given in degrees per second (or per year).
[If somebody was in front of you and then moved to the right side of you, his angular position would have changed by 90 degrees. If this took place in 5 seconds, the angular speed would be 90/5 = 18 degrees per second.]
DIURNAL MOTION
When you go out and look at the stars at night, if you watch for an hour or so you will see that they move. You can't actually see the motion becuase it's too slow. but after an hour (or probably less) you will notice that they have not stayed in the same postion relative to, say, the horizon, or trees or tall buildings. They will move about 15 degree in an hour. We'd say the angular speed 15 degrees per hour. What's most important is that all the objects in the sky, stars, planets (even the moon) undergo the same motion. Objects move across the sky from east to west, just as the sun does. You might see one star low above the eastern horizon early in the evening and another star directly overhead. As time went on, in one hour, the eastern star would move 15 degrees higher above the horizon, and the overhead star would begin to sink toward the western horizon. Figure 1 shows how you might imagine the stars' motion in space above you. If there is a pattern of stars (a constellation), as indicated by the group toward the west in the figure, those stars stay together and the pattern remains.
The second important fact about this motion is that it repeats the next night. If you go out at the same time you will see the same two stars, one in the east and one overhead, in (almost) the same position -- and the constellation in the west. Some insightful people thousands of years ago deduced that the earth was probably round, and the stars were going around the earth in a complete circle in a day (Figure 2), and so arriving at the same position 24 hours later.
This is called diurnal motion, meaning "daily."
To explain this motion the ancient Greeks imagined the stars embedded in a large sphere, with the earth at the center. The sphere rotated once every 24 hours.
ROTATION OF THE EARTH
Today we understand that the earth rotates every 24 hours and the stars are fixed. Figure 3 shows a view from a point above the earth's north pole.
From this viewpoint the earth rotates counter-clockwise as shown. North America, with New York on the eastern end and Los Angeles in the west is shown. Suppose you're looking from New York at a pair of stars. The arrow indicates the direction directly overhead; the dotted line indicates the direction you look to see the stars. In picture A you have to look toward the east over the Atlantic ocean to see them. In picture B (a few hours later) you look directly overhead to see them. In picture C you cannot see them at all, even if you look straight to the west (dotted line); they have set below the western horizon.
Note also that whether or not you see these stars depends on where the sun is, i.e. whether it's day or night. We haven't considered that question. It might be that the sun is up during all, part, or none of this star motion. The stars are still there and moving, but you can't see them because the sky is too bright.
ANNUAL MOTION
The positions of the stars are almost the same after 24 hours, but there is a small difference. If you have an accurate measurement of the time, and you look exactly 24 hours later, you will find that the stars have moved (the word "drifted" is often used) a small amount toward the west compared to the previous night. Casually looking at the sky you wouldn't notice this, but this east to west drift continues night after night, and after a few weeks you would notice it. In a month the motion would be about 30 degrees. At some time during the year the group of stars you are watching might disappear below the western horizon. At some time later they would reappear above the eastern horizon. And after exactly one year the stars would appear at the same point where they started. This is called annual motion. After one year the motion repeats.
The speed of annual motion is about 1 degree per day.
PERSPECTIVE FROM OUTER SPACE
Today we know that the earth orbits the sun in exactly one year. The annual motion of stars is therefore really a consequence of the earth's orbit, and the fact that we observe the stars from a moving platform. Figure 4 shows how this works.
It's a view of the earth and its solar orbit from above the north pole, and the orbit is in the counter-clockwise direction. We want to show an observer looking at the sky at the same time every night. So in the diagram each picture of the earth is at a time when the observer (in New York) is in the dark; he's facing directly away from the sun and it is midnight. The stars are not moving; they are in a fixed position shown toward the right of the diagram.
In picture A the observer has to look toward the east to see the stars. (If he looks directly overhead (arrow) he doesn't see them.) Picture B is about 4 months later, about one-third of the way around the orbit. Here he has to look west to see the stars. So the apparent motion is that they have drifted from east to west. Picture C is another 4 months later, and the observer at midnight, whether he looks straight up or to the east or west, can't see the stars. When a full year goes by he's back at position A and again sees the stars in the east.
Note also in position C, that if the observer waits 12 hours till the earth rotates on its axis half-way around, then he's at point P as shown on the diagram. Here he could see the stars if the sun weren't there. But the sun is there, it is daytime -- noon in fact -- and he can't see any stars because the sky is bright.
Since there is not any real motion of the stars, all the stars undergo the same motion as the earth moves around on its orbit. If there is a constellation, showing a few stars depicting a certain shape, that constellation stays together. It drifts east to west and goes below the western horizon, and will be seen as exactly the same constellation, in the same place, one year later.
To be correct it should be added that not all the stars undergo this kind of annual motion. There are some stars that move in circles in the sky and that are visible only to people in the northern hemisphere (and others are visible only in the southern hemisphere). Looking at Figure 4, these would be stars that are not near the plane in which the earth's orbit occurs, but are located up -- that is above the page on which the diagram is drawn -- or down.
THE PLANETS
The stars all move together in annual motion, except: The Greeks noticed that certain stars did not. Imagine that Figure 5 (picture A) represents a constellation of five stars in the positions shown. (The dotted lines are just to guide your eye.)
A week later the constellation has drifted toward the west, but it looks like picture B. One star has moved a little differently. Its position is displaced by an amount that might be a few degrees. It's not difficult to notice. If you wait a year, the other four stars are found in exactly the same position, but the one "wandering" star is in an entirely different place. It might be below the horizon where it can't be seen at all. It might be in the west when the other four stars are in the east.
It is easy to see how this happen from today's perspective. The wandering star is really a planet that orbits the sun. Its period (time it takes to go around the sun) is not at all the same as the earth's. It's much nearer to the sun than to the stars. Figure 6 shows the earth and Mars on Jan. 1, 2009, when Mars is in the same direction as a group of three stars, and it may appear as part of a constellation with those stars. The observer on earth at midnight sees them directly overhead. A year later the earth is at the same place, but Mars has gone part way around the sun and is in position P. The observer sees the three overhead, but cannot see Mars at all.
