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This lesson is the next step in setting the foundation for observations and for determining "how we know what we know." Here we cover the the coordinate system used by astronomers to locate objects on the celestial sphere.
After completing this lesson, you should be able to
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One of the reasons why many students of astronomy have difficulty with some of the concepts is the fact that a high level of abstract thinking is required. We need almost to approach an "out-of-body-experience" where we step back, assume a priviledged position (high above the North Pole, the solar system, or the Galaxy, for example) and then relate what we learn to how the phenomena actually look trapped here on Earth. View your journey through this chapter much like a road trip: you have your map showing the freeways, cities, rest stops, and roadside attractions. How often have you returned from a trip and related what you saw and the distances you traveled to how it looked on your map? Do you mark the places you have visited? Do you take lots of pictures so you don't forget what you saw and where?
The information in this chapter may seem a lot like that map. As you read it, try to relate it to what you have observed. For example, as the text goes through the reasons for the seasons, think about the long-summer versus short-winter days. How high does the Sun get in the sky in the middle of summer as opposed to the middle of winter? Think about where the Moon was in the sky when you observed it at various phases. Was the Sun up at the same time? Can you always see the Moon at the same time each day, weather permitting?
The most important part of this lesson is the mapping of the sky, and how astronomers go about locating objects in the sky and centering them in their telescopes. Work with using the terms right ascension and declination, and compare the use of these coordinates to the locations and sizes of the constellations within which the celestial objects lie. Recall, however, that although we may say that, for instance, the Crab Nebula is in the constellation of Taurus, the stars and other objects in this constellation are all at different distances. It is just from our perspective and the fact that we cannot tell their actual distances without sophisticated measuring techniques that they appear to lie on a celestial sphere. We locate objects on a world globe by their latitudes and longitudes; these coordinates give us no information as to the altitude of the object. Similarly, the celestial coordinates give us the location of objects on the celestial globe, but they give us no information as to how far away those objects are.
Before we move onto coordinate systems for the sky, let's make sure we are confident we understand the coordinate system on Earth. Read carefully through the section on locating places on Earth. With today's accurate global positioning devices, we can usually determine the latitude and longitude of where we are precisely (to within a few meters). As a way of refreshing your memory, find out what the latitude and longitude are for your city, out to three decimal places in degrees if possible. To help you in this search, the following Web page: http://geography.about.com/cs/latitudelongitude/index_2.htm, has a link called "Latitude and Longitude Look Up" that will find the latitude and longitude for major cities around the world. Study the next table that gives the latitudes for the Equator, North and South Poles, the Arctic and Antarctic Circles, and the Tropics of Cancer and Capricorn. Recall what the tilt of the Earth is from the plane of its orbit (23.5 degrees) and relate this amount to what you find for the latitudes. Do the values make sense (Hint: what is 90 – 23.5)?
| Equator | North Pole | South Pole | Arctic Circle | Antarctic Circle | Tropic of Cancer | Tropic of Capricorn |
| 0 | 90 N latitude | 90 S latitude | 66.5 N latitude | 66.5 S latitude | 23.5 N latitude | 23.5 S latitude |
Wouldn't it seem logical for the coordinates in the sky to be called "sky latitude" and "sky longitude"? No such luck; however, the sky coordinates do work much like latitude and longitude here on Earth, only they are called "declination" and "right ascension." The text explains this coordinate system (also called "equatorial coordinates"). The following figure shows the celestial sphere, with the vernal equinox and some of the declination coordinates indicated.
The coordinates in right ascension start at the vernal equinox: the location set in the celestial sphere where the celestial equator crosses the ecliptic, or where the Sun is located on or around March 21. The hours run from 0 to 24 hours. Subdivisions for these coordinates are also measured in time: minutes and seconds. Since there are 24 hours in a day, and 360 degrees in a circle, each hour of right ascension is equal to 15 degrees. Celestial objects appear to rise in the East and set in the West due to the Earth's rotation; so, the right ascension coordinates increase to the East. For example, you may have a star with a right ascension of 8 hours 30 minutes (8h 30m) on the meridian at the beginning of the night, and have a star with a right ascension of 20h 30m on the meridian at the end of the night.
Declination is easier because it is similar to latitude on Earth: objects on the celestial equator have a declination of 0 degrees; objects near the celestial north pole have declinations near +90 degrees (south celestial pole, near –90 degrees). Subdivisions for declination are measured in minutes of arc and seconds of arc. There are 60 seconds of arc in a minute of arc, and 60 minutes of arc in 1 degree. One degree is equal to 3600 seconds of arc (remember this when we start talking about parallax of stars). Finishing this calculation, there are 1,296,000 seconds of arc in a full 360 degrees—that's how small a second of arc is—really, really, really small.
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The sky map on the right shows an example of a small region of the night sky with the right ascension and declination coordinates given. Find the celestial equator and the marked hours. Also find the declination scale along the right-hand side. After you've taken a few moments to study the coordinate grid and the stars, constellations, and other objects marked there, figure out the right ascension and declination for the "yellow-highlighted" stars: Betelgeuse, Capella, Rigel, Hamal, and the Pleiades. Check your answers when finished.
Answers
Lists of the right ascensions and declinations of stars or other celestial objects must also include the date for the coordinates. Although these coordinates change by only a very small amount over time, they do change. This is because of something called the "precession of the Earth's axis." Picture a top spinning. The top itself is rotating rapidly, but you will also notice that it is wobbling on its axis, tracing out a larger circle. The Earth wobbles, causing the poles of the axes of rotation to trace out a large circle against the background stars. In 2700 BC, Thuban, a star in the constellation of Draco, was the "north star." The north celestial pole will move slightly closer to Polaris before moving away. In a few thousand years, another star may take its place; it will be 26,000 years before the north celestial pole returns to Polaris' location on the celestial sphere.
There are additional coordinate systems for locating objects in the sky. The other two most commonly used are the altitude-azimuth and galactic coordinate systems. The alt-azimuth system (as it is more commonly called) is the basis for the movement of the less expensive telescopes. Altitude relates to the height, in degrees, of an object above a spot on the horizon. Azimuth relates to the angle around the horizon, measured from true north clockwise, to that spot. Galactic coordinates relate to the plane and center of our galaxy, and are measured in latitude (angle above or below the plane of the Galaxy) and longitude (angle away from the center of the Galaxy). We won't be concerning ourselves with these systems.
We notice the Moon in the sky throughout the months. We most often notice it when it is full and thus at its brightest and most prominent, prominent because it rises at dusk and sets at dawn, and thus is noticeable the whole night through. We lose track of it around new moon because it is in the sky during the day, somewhere close to being between us and the Sun. When the Moon is new, it rises and sets with the Sun. Then, as the Moon moves towards first quarter, we pick it up again in the western sky just after sunset. When the Moon is at first quarter, it rises in the East at noon and follows behind the Sun by 90 degrees. After the Moon passes through its full phase, it moves towards third quarter and leads the Sun in the sky. At third quarter, it is ahead of the Sun by 90 degrees and thus sets in the west at noon.
The assignment for this lesson is an lab on the phases of the Moon. It includes questions about observations that we're sure you will think, "I should know the answer to this!" These questions, however, are ones we usually don't think about, ever. We take our moon for granted. It's certainly nice to have a full moon on a warm summer evening, or a new moon when wanting to see a meteor shower. But, otherwise, we rarely think about the Moon, even if we do happen to notice it in the sky. Let's take an initial look at the questions. See if you can answer some of them before reading Section 3.5 in the text, or you may need to reread this section after reviewing these questions. Not all of them can be answered from the reading material, but they all should become clear after you finish the lab.
Clearing up a misconception: is there a dark side of the Moon? Is it the side we never, ever see? Answer: there is a dark side of the Moon—it is the side that is facing away from the Sun. The side we never see (because the Moon keeps the same side towards the Earth during its orbit) is called the far side or the back side of the Moon. Take a look at this drawing and notice that there is a phase when the dark side and the far side are the same side (during a full moon) and a phase where we are seeing the dark side of the Moon (during a new moon, although we can't see it because it is dark, and because it happens to occur during daylight).
Here is a short tutorial for why we see the Moon pass through phases. The images are as seen from the northern hemisphere, and are idealized in the sense that often the waxing or waning moon will seem slightly tilted with respect to the horizon on Earth.
Read through the section on eclipses; you will be expected to know the basic circumstances needed for a lunar or a solar eclipse to occur.
From the textbook:
Relating pictures of the phases of the Moon that are shown in textbooks to the actual phases that are seen in the sky seems to be one of the most difficult of the abstract concepts in astronomy for students.
