An Introduction To Ptolemys Theory Of Telescopes

Tuesday, December 7, 2021 5:16:15 AM

An Introduction To Ptolemys Theory Of Telescopes



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The Greeks not only knew Earth was round, but also they were able to measure its size. His method was a geometric one, based on observations of the Sun. The Sun is so distant from us that all the light rays that strike our planet approach us along essentially parallel lines. To see why, look at Figure 2. Take a source of light near Earth—say, at position A. Its rays strike different parts of Earth along diverging paths. From a light source at B, or at C which is still farther away , the angle between rays that strike opposite parts of Earth is smaller.

The more distant the source, the smaller the angle between the rays. For a source infinitely distant, the rays travel along parallel lines. Of course, the Sun is not infinitely far away, but given its distance of million kilometers, light rays striking Earth from a point on the Sun diverge from one another by an angle far too small to be observed with the unaided eye. As a consequence, if people all over Earth who could see the Sun were to point at it, their fingers would, essentially, all be parallel to one another.

The same is also true for the planets and stars—an idea we will use in our discussion of how telescopes work. Eratosthenes was told that on the first day of summer at Syene, Egypt near modern Aswan , sunlight struck the bottom of a vertical well at noon. This indicated that the Sun was directly over the well—meaning that Syene was on a direct line from the center of Earth to the Sun. And the measurement of the angle in Alexandria, he realized, allowed him to figure out the size of Earth. Alexandria had been measured to be stadia north of Syene. The stadium was a Greek unit of length, derived from the length of the racetrack in a stadium.

It is not possible to evaluate precisely the accuracy of Eratosthenes solution because there is doubt about which of the various kinds of Greek stadia he used as his unit of distance. Even if his measurement was not exact, his success at measuring the size of our planet by using only shadows, sunlight, and the power of human thought was one of the greatest intellectual achievements in history. Perhaps the greatest astronomer of antiquity was Hipparchus , born in Nicaea in what is present-day Turkey. He erected an observatory on the island of Rhodes around BCE, when the Roman Republic was expanding its influence throughout the Mediterranean region.

There he measured, as accurately as possible, the positions of objects in the sky, compiling a pioneering star catalog with about entries. He designated celestial coordinates for each star, specifying its position in the sky, just as we specify the position of a point on Earth by giving its latitude and longitude. He also divided the stars into apparent magnitudes according to their apparent brightness.

This rather arbitrary system, in modified form, still remains in use today although it is less and less useful for professional astronomers. By observing the stars and comparing his data with older observations, Hipparchus made one of his most remarkable discoveries: the position in the sky of the north celestial pole had altered over the previous century and a half.

Hipparchus deduced correctly that this had happened not only during the period covered by his observations, but was in fact happening all the time: the direction around which the sky appears to rotate changes slowly but continuously. If the north celestial pole is wobbling around, then Earth itself must be doing the wobbling. If you have ever watched a spinning top wobble, you observed a similar kind of motion.

Because our planet is not an exact sphere, but bulges a bit at the equator, the pulls of the Sun and Moon cause it to wobble like a top. As a result of this motion, the point where our axis points in the sky changes as time goes on. While Polaris is the star closest to the north celestial pole today it will reach its closest point around the year , the star Vega in the constellation of Lyra will be the North Star in 14, years. The last great astronomer of the Roman era was Claudius Ptolemy or Ptolemaeus , who flourished in Alexandria in about the year Today, it is our main source of information about the work of Hipparchus and other Greek astronomers.

Hipparchus, not having enough data on hand to solve the problem himself, had instead amassed observational material for posterity to use. Ptolemy supplemented this material with new observations of his own and produced a cosmological model that endured more than a thousand years, until the time of Copernicus. 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. Figure 2. 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. The planetary configurations simulator from Foothill AstroSims allows you to see the usual prograde and occasional retrograde motion of other planets. You can switch back and forth between viewing motion from Earth and Mars as well as other planets. Normally, planets move eastward in the sky over the weeks and months as they orbit the Sun, but from positions B to D in Figure 2. 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.

In his day, a complex universe centered on Earth was perfectly reasonable and, in its own way, quite beautiful. 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 Figure 2. When the planet is at position x in Figure 2. 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.

Use the Ptolemaic System simulator from Foothill AstroSims to explore how Ptolemy's system of deferents and epicycles explained the apparent motion of the planets. 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. As an Amazon Associate we earn from qualifying purchases. And for Pluto: a planet or dwarf planet? What is your Sign? Capricorn, Aquarius, Leo, Sagittarius, Ophiuchus? Astrologers claim you are born under the sign in which the Sun is in that constellation. For Earth this is a slow process— 26, years to complete one precession.

Privacy Policy. Skip to main content. Module 2: Historical Astronomy. Search for:. Astronomy and Astrology Historically Astronomy and Astrology went hand-in-hand, but is there scientific evidence to support this theory? Public Domain Image courtesy of Pixabay. Licenses and Attributions.

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