Astronomy Today, 8th Edition Solution Manual

Astronomy Today, 8th Edition (Solution Manual)

Chapter 1: Charting the Heavens The Foundations of Astronomy

Copyright © 2014 Pearson Education, Inc.

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Chapter 1: Charting the Heavens

The Foundations of Astronomy

Outline

1.1 Our Place in Space 1.2 Scientific Theory and the Scientific Method 1.3 The “Obvious” View 1.4 Earth’s Orbital Motion 1.5 The Motion of the Moon 1.6 The Measurement of Distance

Summary

Chapter 1 begins with a “Big Picture” overview of our place in the Universe. This is followed by a brief introduction to the science of Astronomy and the definition of “Universe.” Common units of measurement that are important to astronomers are introduced, along with the convention of scientific notation. Section 1.2 discusses the scientific method, giving the students an understanding of some of the differences between science and pseudoscience or non-science such as religion. Section 1.3 introduces constellations and the celestial sphere, which serve as a springboard to descriptions in Section 1.4 of the apparent daily and annual motion of celestial bodies such as the Sun, Moon, and stars. Most of this motion is actually illusory, caused by various motions of the Earth. Section 1.4 also explains the nature and cause of the Earth’s seasons. Section 1.5 deals with the relationship between the Earth and the Moon that causes the phases of the Moon as well as solar and lunar eclipses. Chapter 1 concludes with the concept of parallax and its use in performing measurements of distance and size.

Major Concepts

▪ The Big Picture—Our Place in the Universe ▪ Scientific Theories • Testable • Simple • Elegant ▪ Astronomy and the Scientific Method • Observation • Hypotheses/Explanation • Observation/Experimentation ▪ Constellations ▪ The Celestial Sphere ▪ Earth’s Motion • Rotation on its Axis (Daily Motion) • The Tilt of the Axis and the Seasons • Revolution around the Sun (Yearly Motion) and the Zodiac • Precession ▪ The Moon’s Orbit • Lunar Phases • Lunar Eclipses • Solar Eclipses 1 / 4

Astronomy Today, 8th Edition Instructor Guide

Chapter 1: Charting the Heavens The Foundations of Astronomy

Copyright © 2014 Pearson Education, Inc.

2 ▪ Distance • Triangulation and Parallax • Sizing Up the Earth

Teaching Suggestions and Demonstrations

One of the challenges of studying astronomy is developing the ability to view the universe from different perspectives. The biggest challenge is in shifting from the perspective we have from Earth, where we see the Sun and stars rise in the east and set in the west, to the perspective from “outside,” where we “see” Earth spinning on its axis and orbiting the Sun. Models and diagrams are essential to teaching this introductory material, to help your students practice shifting viewpoints. Many students have poorly developed visualization skills, so the more visual aids the better. This chapter contains lots of new vocabulary, so take the time to define new terms.This will likely be students’ first exposure to a formal class in astronomy. They will come to the class with some concrete knowledge, but also with a great deal of misinformation and misconceptions derived from years of exposure to multimedia sources. It is not unusual for people to believe some aspects of what they know as science fiction. Most students are still comfortable with Aristotelian thinking. This chapter provides your first opportunity to slowly move your students toward a new way of thinking—a new perspective. As listed below, the number of problem areas and misconceptions are numerous, especially in the early chapters of this text. This is to be expected. Students have few misconceptions about active galaxies because most have never heard of them.

Section 1.1

Students almost universally think of the light-year as a unit of time rather than distance. This confusion comes about simply because of the word “year.” Spend some time discussing a light-year by first introducing the speed of light. Tell them that light travels at a finite speed and therefore takes time to get to where it’s going. Students may be familiar with “lag time” in a long-distance cell-phone call or in a “live via satellite” interview on the television news; part of this is because the radio signals take time to travel up to the satellites and “bounce around” to their destination.Emphasize “distance” here. Since the speed of light is about 3  10 5

km/s, one light-second is a distance of 3  10 5

km. Next, describe a few examples, such as the fact that light travels fast enough to go around the Earth more than seven times in one second; therefore, one light-second is equivalent to a bit more than seven times the circumference of the Earth. Another example is that the Sun is about 8 light-minutes away. Students are usually intrigued by the idea that if the Sun were to burnout or explode right now, then we would have no way of learning that fact for another 8 minutes. Finally, use the distance to far away galaxies as another example. The galaxies are so distant that it takes millions of years for their light to reach us. Therefore, they are millions of light-years away.This is good conceptual foreshadowing for things to come later in the semester. When we look at distant objects, we see them as they were when their light left them. We see things not as they are “right now,” but as they were when the information—light—left them. The Sun appears to us as it was 8 minutes ago. Distant galaxies appear to us as they were millions of years ago. When we look at distant objects, we effectively are effectively looking back in time.

Section 1.2

Since many of your students are likely to have had minimal exposure to science, this section is worth focusing on for class discussions. In introducing the scientific method, refer to Figure 1.6 now as well as throughout the semester. Remind the students that science is a process rather than some fixed set of ideas or laws. Furthermore, it is an iterative process that really has no end, as theories are constantly being re-tested and improved. Therefore, scientific theories are always subject to challenge and change. In fact, it is a good thing when a theory is challenged, because it may be an opportunity to enhance our understanding. This is a strength, not a weakness, of science. Ask the students to provide examples of ideas in their own minds that had changed once additional pieces 2 / 4

Astronomy Today, 8th Edition Instructor Guide

Chapter 1: Charting the Heavens The Foundations of Astronomy

Copyright © 2014 Pearson Education, Inc.

3 of data or knowledge were made available to them. The foundation of science rests on the fact that it does not rely on the authority of political or religious systems or on the interpretation of text, ancient or otherwise. It relies on a constant process of improvement.It is important in this section to distinguish between facts, the things we observe and measure, and theory, our explanations for those observations. Emphasize that no matter how good, useful, or thorough a theory is, it can never be a fact. The fact is that apples fall from trees; the theory that explains how and why they fall is the theory of gravity. Theories should never be given too much credit, and they should not be sold short. Theories are not just guesses or statements of belief. Theories are our best possible explanations for the things we see happening around us, backed up by data and the hard work of men and women who are striving to understand the universe more completely. To use the phrase “just a theory” is to demean that hard work. Theories are powerful things, even if they are not facts. Students appreciate it when instructors are candid about the strengths -- and limitations -- of scientific theories, so don’t be afraid to be honest about the nature of science.

Section 1.3

Your students will all have heard of constellations and will probably be able to name at least a few, usually signs of the Zodiac or “big names” like Orion. Emphasize that the stars in a given constellation are probably not physically close to each other in space; they just appear close to each other as seen from Earth. Compare Figure 1.8 to Figure 1.9. Use an analogy with how close buildings may appear to each other when observing a large city from a distance.The stars in the northern part of the sky were grouped together by observers in ancient times, and we continue to use nearly the same groupings (mostly from Eastern Mediterranean cultures) today. You can pass out or project a sky chart without constellations drawn in and challenge students to make up their own. You could even create a writing project in which students research an ancient culture—I usually disallow the Greeks and the Romans to make it challenging—and come up with constellations for that culture.Students may be surprised to find that there are 88 constellations, and that constellations are used to divide the sky into sections, the way that county, state, and national boundaries are used on Earth. It is also interesting to compare names of northern and southern constellations. The northern constellations are mostly traditional, typically named for animals and mythological characters, such as Cygnus (the Swan), Cassiopeia (the Queen), and Orion (the Hunter). The Southern Hemisphere sky includes more modern constellation names such as Telescopium (the Telescope), Microscopium (the Microscope), and Antlia (the Air Pump). Ask your students if they can explain why there is a difference. The constellation names we have inherited today derive from northern- sky observers, mostly in ancient Greece. The northern constellation names, therefore, date from ancient times, but the names from the southern sky date from the travels made by northern explorers to the Southern Hemisphere in more recent times.I find that mythological stories not only give students time to “rest their hands,” but can also help refocus their attention and see the connections to the past. The story of Cassiopeia, Cepheus, Andromeda, Cetus, and Perseus is a nice way to show the connections among a “family” of constellations. I also use the myth of Orion and Scorpius to explain the different appearances of the summer and winter skies, as shown in Figure 1.14. The two mortal enemies, placed on opposite ends of the sky, continuously chase each other around. Their “guardians”—Taurus for Orion and Sagittarius for Scorpius—insure that they don’t “cheat” and take a shortcut over the Earth. These are all constellations your students can find in the night sky, depending on the time of year in which you are teaching the course. Provide star charts and encourage your students to find major constellations in the night sky throughout the course.The concept of the celestial sphere is an important one. We are missing depth perception when we look out at the night sky, and so we perceive the 3-dimensional Universe as a 2-dimensional sphere.

DEMO—If available, bring in a transparent model of the celestial sphere with Earth inside and point out the north and south celestial poles and the celestial equator. Emphasize that this is not an accurate model of the universe, but a good illustration of the geocentric model. This is a good time to discuss Polaris and clear up any 3 / 4

Astronomy Today, 8th Edition Instructor Guide

Chapter 1: Charting the Heavens The Foundations of Astronomy

Copyright © 2014 Pearson Education, Inc.

4 misconceptions; often, introductory astronomy students believe the North Star must be the brightest star in the sky. The ancient Chinese saw Polaris as the Celestial Emperor, and while the Emperor may not be the brightest person in the kingdom, everyone still has to do what he says! Introduce students to right ascension and declination by comparing these to latitude and longitude. Compare the grid lines on the transparent sphere to the grid on the central Earth. Emphasize that the celestial coordinates are attached to the sky. Over the course of a night, stars move from east to west and the coordinate system moves with them. Look up the coordinates of a few well- known stars (including Polaris) and help students determine their positions on the transparent sphere. Ask students to compare the two different methods of describing star locations, by coordinates and by constellation, and discuss the advantages of each.

Section 1.4

Students usually know the terms “rotation” and “revolution” but often confuse them. For this reason, I try to avoid their use in class, and encourage students to do the same. It is much simpler and clearer to use “spin” and “orbit,” so try to get yourself in the habit of using these terms. Remember: students will be more impressed by someone who is clear than by someone who “sounds scientific!” Likewise, they will probably know that Earth takes a day to turn on its axis and a year to orbit the Sun, but will not know the difference between a solar day and a sidereal day, or a tropical year and a sidereal year. Use many diagrams, such as Figure 1.13, to help explain. Models also help.

DEMO—Demonstrate rotation and revolution with globes, or bring students to the front of the class to model Earth’s motions. For instance, one student can spin around (slowly) while orbiting another. Ask the class to concentrate on one point on the Earth, say, the spinning student’s nose, and imagine when it is lit and when it is dark. Use this model to explain day and night, sidereal vs. solar days, and why different constellations are visible in the night sky during different months.Figures 1.15 and 1.16 are very important and particularly insightful when used in conjunction with one another. Make sure students understand that Figure 1.16 shows the apparent path of the sun on the celestial sphere, and that this path passes through the constellations of the zodiac, as can be seen by taking the “Earth perspective” in Figure 1.15. If you ask students how many constellations are along the Sun’s path in the zodiac, the common answer will be 12. Although this is true of the “astrological zodiac,” students are usually surprised to learn that there are actually 13 zodiacal constellations, including Ophiuchus. Ask students to use Figure 1.15 to determine what constellation the Sun appears to be in at a certain time of year. Then ask students if they notice any “errors” in those dates. There may be several students who mention that their birthdays are not within the dates shown for their astrological “sign.” This usually serves as a perfect lead-in to the history of the modern calendar, including the concept of precession.

DEMO—A gyroscope or top in motion on a table or desk makes a good demonstration of precession. By changing the direction that Earth’s axis is pointing, precession is responsible for the fact that the zodiac constellations no longer correspond to their astrological dates. Another example, the heliacal rising of Sirius— Sirius rising right next to the Sun—was an important date in the ancient Egyptian agricultural calendar, since it signaled the flooding of the Nile. Thanks to precession, this no longer occurs on the same date today.

My experience has shown that few students have a good understanding of the cause of the seasons. After presenting a mythological explanation for the seasons—the Greek myth of Pluto and Persephone—I ask students to write a brief paragraph explaining why it is cold in winter and hot in summer. This would also make a good “clicker” question. Many students, especially those who have not yet read the text, will say the cause is the varying distance between the Earth and the Sun. I then present four pieces of information demonstrating why this can’t be so.

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