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We now have about 1,500 years of the universe according to Ptolemy, before modern astronomers begin to straighten out his spaghetti. So, let's take this time to start becoming familiar with the sky.
The sky has changed little in the last 2,000 years. Few bright stars have sufficient proper motion (apparent shift in position against the background stars) to be noticeable without a telescope. Alpha Centauri has shifted about two degrees in 2,000 years. However, being too far south, Alpha Centauri was not cataloged by ancient Mediterranean astronomers. As for stars in the northern hemisphere bright enough to attract attention, Arcturus (Alpha Boötis) is the only one that has shifted notably—by about one degree. That is the only change in the constellations in thousands of years.
However, the alignment of the sky to the Earth has changed significantly. As mentioned above, the Earth precesses; it wobbles like a spinning top or gyroscope, taking 26,000 years to complete one precession cycle. Therefore, the alignment of the Earth's axis to the sky has shifted about 27 degrees to the west in the last 2,000 years.
Foremost on a list of tasks for early astronomers was to map the sky. Early astronomers are known for their star catalogs, which list useful data about stars, such as their brightness and location in the sky. To specify the location, astronomers needed a coordinate system.
On the Earth, we use a coordinate system of latitude and longitude. With any coordinate system, you need a starting point. For latitude, we chose the equator for a latitude of zero. We measure latitude in degrees north or south of the equator, with the poles at 90 degrees. Any particular distance from the equator forms an imaginary ring on the surface of the Earth (called a parallel) that is parallel to the equator. Since these rings are laid out on a sphere, they get smaller and smaller as we approach the poles. At the poles, they are infinitely small or just a dot.
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For longitude, we chose the meridian (the imaginary line that goes from pole to pole) passing through the Royal Observatory in Greenwich, England, as a longitude of zero. We then measure east and west in degrees. The meridian that passes through the Royal Observatory is called the prime meridian. Any point east or west of the prime meridian has a meridian of its own (previously, we mentioned Alexandria's meridian, noting that it is three degrees west of Syene).
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We can fix the position of any location on the earth with a north or south latitude and an east or west longitude. For example, at 31 degrees, 12 minutes, and 0 seconds North latitude and 29 degrees, 55 minutes, and 7 seconds East longitude (31°12'0" N, 29°55'07" E), you will find Ahmed Zewail Square in Alexandria, Egypt. Notice that fractions of degrees are specified in minutes of arc (1/60 of a degree) and seconds of arc (1/60 of a minute). Here are some other points of interest and their coordinates:
34°03'13" N, 118°14'33" W, Los Angeles City Hall
333°51'24" S, 151°12'55" E, Sydney Opera House in Sydney,
Australia
35°11'53" N, 101°04'55" W, Leaning water tower
of Groom, Texas.
Many ancient astronomers compiled star catalogs using various coordinate systems. Ptolemy used a system analogous to latitude and longitude where the ecliptic was the zero point for north and south measurements, and the vernal equinox was the zero point for east and west measurements. This inclined his measurements to the equator by 23.5 degrees. In the following text, we will use the system used by modern astronomers where the celestial equator is the zero point for north and south measurements, and the vernal equinox is the zero point for east and west measurements. However, for east and west measurements, we measure in hours, where each hour is 15 degrees, increasing to the east. This divides the sky into 24 equal hours. The East and West measurement is called right ascension. The north and south measurement is called declination. It is aligned with the Earth where the celestial equator (zero degrees declination) lies directly above the Earth's equator, and, for example, 45 degrees north declination is directly above the Earth at the 45th parallel or 45 degrees north latitude./p> /p>
As we often do with the Earth, we will map the sky on a globe. Regardless of the actual layout of the universe, we see the celestial bodies as if they were projected on a sphere, much like the dome of a planetarium. We see the celestial sphere from the inside at the sphere's center. However, Figure 32 shows this globe from the outside, looking in.
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In Figure 33, the blue circle represents the celestial sphere. The magenta line is the celestial equator—the imaginary line directly above the Earth's equator. The brown line is the ecliptic—the Sun's path among the stars as seen from the Earth. The ecliptic is shown inclined to the celestial equator by 23.5 degrees.
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The above and following illustrations are shown with the celestial equator horizontal and the ecliptic inclined. They are shown this way because that is the way we tend to see them in the sky since we naturally orient ourselves to the equator. However, the ecliptic is aligned with the Earth's orbital plane, and it is the Earth's rotational axis that is inclined. As the earth precesses, we tend to see the ecliptic and the rest of the sky precess around the equator. However, it is actually the ecliptic and the sky that are stationary, and it is the Earth, along with its equator and poles, that precesses, taking 26,000 years for one circuit.
Imagine a coin wobbling on a table, settling after being spun. Now, imagine the coin's edge as the celestial equator.
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This is what the Earth, along with the celestial equator, is doing, except it takes 26,000 years for each wobble.
2,000 years ago, the vernal equinox (where the sun crosses the equator on its way from the southern hemisphere to the northern hemisphere) occurred on the eastern edge of the constellation of Pisces.
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Over the last 2,000 years, the Earth, along with the celestial equator, has precessed about 27 degrees to the west. This moved the vernal equinox to the western edge of Pisces.
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Once we have decided on a coordinate system, we need to determine the initial points to measure from. This means that ancient astronomers needed to determine the locations of the celestial equator, the ecliptic, and the vernal equinox. None of these tasks were straightforward. The ecliptic is the path of the Sun among the stars, but you can't see the stars in the daytime to determine precisely where that is. Determining the location of the celestial equator would be simple if you could travel to the equator, assuming once you got there, you knew exactly where you were. Nevertheless, travel to the equator to determine the location of the celestial equator wasn't practical in ancient times.
Imagine the difficulty of making these determinations. To start with, where exactly is one's celestial meridian (the imaginary line directly over one's terrestrial meridian)? You can, of course, point up and imagine a line going from north to south, but you need much more precision to map the sky. You could use a gnomon, knowing that when the Sun reaches high noon the gnomon's shadow points directly to the north. You could also measure the direction of a star when it reaches culmination (the highest point above the southern horizon), knowing that at culmination a star Is due south. However, determining exactly when a star reaches culmination is much like Aristarchus's problem in determining exactly when the quarter moon occurred. It can be done, but it is a challenge. It may be easier to determine the exact location of the celestial pole by measuring the altitudes of circumpolar stars through the night and using those measurements to zero in on the pole. Nevertheless, ancient astronomers were able to determine their celestial meridians with remarkable accuracy.
Ancient astronomers had several tools to help them measure angles, which was essential to mapping the sky. Some of these were protractor-like instruments called quadrants, sextants, and octants. As their names imply, a quadrant can measure angles up to 90 degrees, a sextant can measure angles up to 60 degrees, and an octant can measure angles up to 45 degrees. These tools used by ancient astronomers were often quite large, especially those used by Tycho Brahe to make his precise measurements.
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In addition to the above instruments, they had cross-staffs.
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They also had dioptra, a tool for measuring angles along the horizon.
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With a celestial meridian established and instruments aligned to it, we are ready to determine the positions of the celestial equator, the ecliptic, and the vernal equinox.
The equator isn't difficult once the celestial north pole has been located; it's simply 90 degrees to the south.
The ecliptic is another matter. The ecliptic is the path of the Sun against the stars, but being unable to see stars in the daytime, it is problematic to determine the exact location of the ecliptic by direct observation. Lunar eclipses aided in determining the location of the ecliptic since the Earth's shadow centers on the ecliptic. They could also carefully determine when the summer and winter solstices occurred, which they were able to determine with an accuracy to within one day. In subsequent months (after the Sun moved out of that part of the sky), they could measure where that point was among the stars. With careful measurements, they could determine the location of the solstice to within one or two degrees. Subsequent measurements could improve the accuracy.
Another way to locate the ecliptic would be to observe the azimuth (angle along the horizon) of the Sun at sunrise, knowing that two weeks later, that point in the sky would rise 55 minutes and 4 seconds earlier than the Sun. Ancient astronomers had adequate instruments and clocks to locate the ecliptic with this method. After enough measurements, the entire ecliptic could be located among the stars.
Once both the celestial equator and the ecliptic were mapped, the equinoxes could be located, being the intersections of the equator with the ecliptic. However, I'm getting the cart before the horse here, as the locations of the equinoxes could be mapped directly using the above methods (starting by measuring the azimuth of the sunrise on the day of the equinox). Therefore, locating the equinoxes aided with mapping the whole ecliptic, not the other way around. With the celestial equator, the ecliptic, and the vernal equinox mapped, we have a coordinate system ready to map the sky. However, there is still that little problem of precession.
In the following diagrams, we can see how the celestial equator has shifted among the stars along the ecliptic.
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Precession raises a question: if the starting point for our coordinate system is moving, doesn't that change the coordinates of stars, etc., over time? It does. Astronomers update celestial catalogs every 50 years to align with the changing location of the vernal equinox. You might think they could have chosen a system that doesn't change so much. However, they didn't, so astronomers realign the coordinate system every 50 years to keep up with precession.
Now that we have a coordinate system with a, albeit moving, starting point, let's cover a couple more things to help us create useful charts and catalogs. Again, we will do this using modern systems.
One last thing we need to do before mapping the sky is to develop a system to specify the brightness of stars. The modern system was first popularized by Ptolemy and refined over time. The scale originally listed stars in six magnitudes, the brightest stars being of the first magnitude and those just visible to the unaided eye the sixth magnitude. The modern scale assigns a decimal fraction value to a star's brightness based on its electronically or photographically measured brightness on a logarithmic scale. Therefore, a star's brightness is now specified in decimal fractions of magnitude, such as 1.98 for Polaris. The modern scale has been extended so that the faintest stars visible to the unaided eye under good conditions have a magnitude of 6.5, and the brightest stars have negative magnitudes. Thus, Sirius, the visually brightest star (after the Sun), has a magnitude of -1.46. All of the planets visible to the unaided eye also have negative magnitudes, the brightest being Venus, which reaches -4.92 at its brightest.
The following table lists some stars we discuss throughout this text with their magnitudes. You can look at these stars to familiarize yourself with how bright stars of various magnitudes appear.
| Magnitude | Star |
| -1 | Sirius (-1.46) |
| 0 | Arcturus, Capella, Rigel, Vega |
| 1 | Aldebaran, Antares, Spica |
| 2 | Kochab, Mizar, Polaris, Saiph |
| 3 | Gamma (γ) Ursae Minoris |
| 4 | Epsilon (ε) Ursae Minoris, Alcor |
| 5 | Eta (η) Ursae Minoris, Epsilon Lyrae |
| 6 | HD 152303 (in Ursa Minor, see Figure 42) |
Ursa Minor (the little dipper) is often used by amateur astronomers to estimate seeing conditions. Ursa Minor has stars ranging from second to sixth magnitude in a part of the sky that is always visible from most northern latitudes.
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Under clear skies but poor conditions (due to haze, smoke, high cirrus clouds, or light pollution), you may see only three of Ursa Minor's stars. If the seeing is particularly dreadful, you may only see Polaris and Kochab. To estimate the current limiting magnitude, look at Ursa Minor and note the faintest star you can see, then look at Figure 42. The faintest of the labeled stars that is visible indicates the current limiting magnitude for the unaided eye.
One more last thing to look at are the lower-case Greek letters scattered around the star maps below.
In 1603, German astronomer Johann Bayer published a sky atlas including designations of stars based on their brightness. Using the Greek alphabet, the brightest star in a constellation was designated as alpha (α), using subsequent letters through omega (ω) if needed. Occasionally, Bayer used criteria other than brightness to choose the alphabetic order. His alternate criteria were based on the star's position in the constellation, historical or mythological importance, position in artistic figures, etc. Perhaps the most extreme example is Sagittarius. Alpha Sagittarii is an inconspicuous fourth-magnitude star relatively far from the asterism (a pictorial pattern of stars that may or may not represent an official constellation) most people see as Sagittarius. The brightest star, Kaus Australis, is designated as Epsilon Sagittarii. Nevertheless, most constellations follow the Greek alphabet in the stellar brightness hierarchy.
Asterism
Azimuth
Bayer designation
Celestial meridian
Circumpolar
Culmination
Declination
Limiting magnitude
Meridian (lines of longitude)
Stellar magnitude
Minutes of arc
Orbital plane
Parallel (lines of latitude)
Prime Meridian
Proper motion
Right ascension
Seconds of arc
Seeing
Transit (crossing the meridian)
Vernal Equinox
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