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The complicating factor in explaining the motions of the planets is that their apparent wandering in the sky results from the combination of their own motions with Earth’s orbital revolution. As we watch the planets from our vantage point on the moving Earth, it is a little like watching a car race while you are competing in it. Sometimes opponents’ cars pass you, but at other times you pass them, making them appear to move backward for a while with respect to you.

[link] shows the motion of Earth and a planet farther from the Sun—in this case, Mars . Earth travels around the Sun in the same direction as the other planet and in nearly the same plane, but its orbital speed is faster. As a result, it overtakes the planet periodically, like a faster race car on the inside track. The figure shows where we see the planet in the sky at different times. The path of the planet among the stars is illustrated in the star field on the right side of the figure.

Retrograde motion of a planet beyond earth’s orbit.

Retrograde Motion of an Outer Planet. This diagram has two parts. The portion at right illustrates the apparent motion of Mars projected against the fixed background stars. The portion at left shows the Sun surrounded by two blue circles. The innermost circle represents the orbit of the Earth, the outermost the orbit of Mars. The Earth is shown as a blue dot in 5 positions, labeled A through E, along its orbit. Likewise, Mars is shown as a yellow dot in 5 positions, labeled A through E, along its orbit. Since the Earth travels faster than Mars, the 5 points for Earth are spread evenly around the circle of its orbit. As Mars moves more slowly, its 5 dots are all plotted close together on the right-hand side of its orbit. Beginning with Earth at point A on the lower left side of Earth’s orbit, an arrow connects with Mars at its point A at the lower right side of its orbit. This arrow continues and connects with Mars at point A near the bottom of its projected path of motion in the illustration at right. As Earth moves counter-clockwise along its orbit, it travels to point B at lower right, and Mars moves slightly upward on its orbit to its point B. An arrow points from Earth through Mars and continues on to connect with Mars at the third point B, which is above center on the projected path of motion. Thus, Mars has moved upward as seen from Earth in this figure. Earth then moves to point C at center-right on its orbit as does Mars. An arrow connects Earth through Mars to point C at the center of the projected path of motion. Mars has moved slightly downward as seen from Earth. Earth moves to point D at the upper right of its orbit and Mars moves upward to its point D. An arrow connects Earth through Mars and on to point D, which is below center on the projected path of motion. Mars has moved downward as seen from Earth. Finally, Earth moves to point E at the upper left of its orbit and Mars moves upward to its point E. An arrow connects Earth through Mars and on to point E near the top of its projected path of motion. Mars has moved upward as seen from Earth. In total, Mars has made a sideways “Z” shape in the sky as seen from Earth in this illustration.
The letters on the diagram show where Earth and Mars are at different times. By following the lines from each Earth position through each corresponding Mars position, you can see how the retrograde path of Mars looks against the background stars.

Normally, planets move eastward in the sky over the weeks and months as they orbit the Sun, but from positions B to D in [link] , as Earth passes the planets in our example, it appears to drift backward, moving west in the sky. Even though it is actually moving to the east, the faster-moving Earth has overtaken it and seems, from our perspective, to be leaving it behind. As Earth rounds its orbit toward position E, the planet again takes up its apparent eastward motion in the sky. The temporary apparent westward motion of a planet as Earth swings between it and the Sun is called retrograde motion    . Such backward motion is much easier for us to understand today, now that we know Earth is one of the moving planets and not the unmoving center of all creation. But Ptolemy was faced with the far more complex problem of explaining such motion while assuming a stationary Earth.

Furthermore, because the Greeks believed that celestial motions had to be circles, Ptolemy had to construct his model using circles alone. To do it, he needed dozens of circles, some moving around other circles, in a complex structure that makes a modern viewer dizzy. But we must not let our modern judgment cloud our admiration for Ptolemy’s achievement. In his day, a complex universe centered on Earth was perfectly reasonable and, in its own way, quite beautiful. However, as Alfonso X, the King of Castile, was reported to have said after having the Ptolemaic system of planet motions explained to him, “If the Lord Almighty had consulted me before embarking upon Creation, I should have recommended something simpler.”

Ptolemy solved the problem of explaining the observed motions of planets by having each planet revolve in a small orbit called an epicycle    . The center of the epicycle then revolved about Earth on a circle called a deferent ( [link] ). When the planet is at position x in [link] on the epicycle orbit, it is moving in the same direction as the center of the epicycle; from Earth, the planet appears to be moving eastward. When the planet is at y , however, its motion is in the direction opposite to the motion of the epicycle’s center around Earth. By choosing the right combination of speeds and distances, Ptolemy succeeded in having the planet moving westward at the correct speed and for the correct interval of time, thus replicating retrograde motion with his model.

Ptolemy’s complicated cosmological system.

Ptolemy’s epicycles. A yellow dot labeled “Center” lies at the center of a blue circle which represents the orbit of a planet as seen from Earth. The large blue circle is labeled “Deferent” and has an arrowhead pointing counterclockwise. The Earth is drawn as a blue dot just to the left of center. To the right of center is a yellow dot labeled “Equant point”. An arrow labeled “y” is drawn from the equant to a point on the deferent, where a small arrow is then drawn pointing to another yellow dot. This yellow dot is the planet being observed. Centered on the point where the arrow from the equant meets the deferent, a circular arrow is drawn counterclockwise and is labeled “Epicycle”. The yellow dot of the planet lies on the epicycle.
Each planet orbits around a small circle called an epicycle . Each epicycle orbits on a larger circle called the deferent . This system is not centered exactly on Earth but on an offset point called the equant . The Greeks needed all this complexity to explain the actual motions in the sky because they believed that Earth was stationary and that all sky motions had to be circular.

However, we shall see in Orbits and Gravity that the planets, like Earth, travel about the Sun in orbits that are ellipses, not circles. Their actual behavior cannot be represented accurately by a scheme of uniform circular motions. In order to match the observed motions of the planets, Ptolemy had to center the deferent circles, not on Earth, but at points some distance from Earth. In addition, he introduced uniform circular motion around yet another axis, called the equant point . All of these considerably complicated his scheme.

It is a tribute to the genius of Ptolemy as a mathematician that he was able to develop such a complex system to account successfully for the observations of planets. It may be that Ptolemy did not intend for his cosmological model to describe reality, but merely to serve as a mathematical representation that allowed him to predict the positions of the planets at any time. Whatever his thinking, his model, with some modifications, was eventually accepted as authoritative in the Muslim world and (later) in Christian Europe.

Ancient Greeks such as Aristotle recognized that Earth and the Moon are spheres, and understood the phases of the Moon, but because of their inability to detect stellar parallax, they rejected the idea that Earth moves. Eratosthenes measured the size of Earth with surprising precision. Hipparchus carried out many astronomical observations, making a star catalog, defining the system of stellar magnitudes, and discovering precession from the apparent shift in the position of the north celestial pole. Ptolemy of Alexandria summarized classic astronomy in his Almagest ; he explained planetary motions, including retrograde motion, with remarkably good accuracy using a model centered on Earth. This geocentric model, based on combinations of uniform circular motion using epicycles, was accepted as authority for more than a thousand years.

Practice Key Terms 6

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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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