SUMMARY

The universe is the totality of all space, time, matter, and energy. Astronomy is the study of the universe. A widely used unit of distance in astronomy is the light-year, the distance traveled by a beam of light in one year.

Early observers grouped the thousands of stars visible to the naked eye into patterns called constellations. These patterns have no physical significance, although they are a useful means of labeling regions of the sky. The nightly motion of the stars across the sky is the result of Earth’s rotation on its axis. Early astronomers, however, imagined that the stars were attached to a vast celestial sphere centered on Earth and that the motions of the heavens were caused by the rotation of the celestial sphere about a fixed Earth. The points where Earth’s rotation axis intersects the celestial sphere are called the north and south celestial poles. The line where Earth’s equatorial plane cuts the celestial sphere is the celestial equator.

The time from one noon to the next is called a solar day. The time between successive risings of any given star is one sidereal day. Because Earth revolves around the Sun, the solar day is a few minutes longer than the sidereal day. Because Earth orbits the Sun, we see different constellations at different times of the year, and the Sun appears to move relative to the stars. The Sun’s yearly path around the celestial sphere, or equivalently, the plane of Earth’s orbit around the Sun, is called the ecliptic. The constellations lying along the ecliptic are collectively called the zodiac. Because Earth’s axis is inclined to the ecliptic plane, we experience seasons, depending on which hemisphere (Northern or Southern) happens to be "tipped" toward the Sun. At the summer solstice, the Sun is highest in the sky, and the length of the day is greatest. At the winter solstice, the Sun is lowest, and the day is shortest. At the vernal and autumnal equinoxes, Earth’s rotation axis is perpendicular to the line joining Earth to the Sun, so day and night are of equal length. The interval of time from one vernal equinox to the next is one tropical year.

The Moon emits no light of its own. It shines by reflected sunlight. As the Moon orbits Earth, we see lunar phases as the amount of the Moon’s sunlit face visible to us varies. At full Moon, we can see the entire illuminated side. At quarter Moon, only half the sunlit side can be seen. At new Moon, the sunlit face points away from us, and the Moon is nearly invisible from Earth. The time between successive full Moons is one synodic month. The amount of time for the Moon to return to the same position in the sky, relative to the stars, is one sidereal month. Because of Earth’s motion around the Sun, the synodic month is about two days longer than the sidereal month.

The time required for Earth to complete one orbit around the Sun, relative to the stars, is one sidereal year. In addition to its rotation about its axis and its revolution around the Sun, Earth has many other motions. One of the most important of these is precession, the slow "wobble" of Earth’s axis due to the influence of the Moon. As a result, the sidereal year is slightly longer than the tropical year, and the particular constellations that happen to be visible during any given season change over the course of thousands of years.

A lunar eclipse occurs when the Moon enters Earth’s shadow. The eclipse may be total, if the entire Moon is (temporarily) darkened, or partial, if only a portion of the Moon’s surface is affected. A solar eclipse occurs when the Moon passes between Earth and the Sun, so that a small part of Earth’s surface is plunged into shadow. For observers in the umbra, the entire Sun is obscured, and the solar eclipse is total. In the penumbra, a partial solar eclipse is seen. If the Moon happens to be too far from Earth for its disk to completely hide the Sun, an annular eclipse occurs. Because the Moon’s orbit around Earth is slightly inclined with respect to the ecliptic, solar and lunar eclipses do not occur every month, but only a few times per year.

Surveyors on Earth use triangulation to determine the distances to faraway objects. Astronomers use the same technique to measure the distances to planets and stars. The cosmic distance scale is the family of distance-measurement techniques by which astronomers chart the universe. Parallax is the apparent motion of a foreground object relative to a distant background as the observer’s position changes. The larger the baseline, the distance between the two observation points, the greater the parallax. The same basic geometric reasoning is used to determine the sizes of objects whose distances are known.

SELF-TEST: TRUE OR FALSE?

1. The light-year is a measure of distance. HINT

2. The number 2 10⁹ is equal to two billion. HINT

3. The stars in a constellation are physically close to one another. HINT

4. The star Polaris always lies precisely at the north celestial pole. HINT

5. Constellations are no longer used by astronomers. HINT

6. The solar day is longer than the sidereal day. HINT

7. The constellations lying along the ecliptic are collectively referred to as the zodiac. HINT

8. The seasons are caused by the precession of Earth’s axis. HINT

9. The vernal equinox marks the beginning of spring. HINT

10. The new phase of the Moon cannot be seen because it always occurs during the daytime. HINT

11. A lunar eclipse can occur only during the full phase. HINT

12. Solar eclipses are possible during any phase of the Moon. HINT

13. An annular eclipse is a type of eclipse that occurs every year. HINT

14. Eclipses can occur only during winter and summer months. HINT

15. The parallax of an object is inversely proportional to its distance. HINT

SELF-TEST: FILL IN THE BLANK

1. A _____ is a glowing ball of gas held together by gravity. HINT

2. A _____ is a collection of hundreds of billions of stars. HINT

3. Rotation is the term used to describe the motion of a body around some _____. HINT

4. To explain the daily and yearly motions of the heavens, ancient astronomers imagined that the Sun, Moon, stars, and planets were attached to a rotating _____. HINT

5. The solar day is measured relative to the Sun; the sidereal day is measured relative to the _____. HINT

6. The apparent path of the Sun across the sky is known as the _____. HINT

7. On December 21, known as the _____, the Sun is at its _____ point on the celestial sphere. HINT

8. Declination measures the position of an object north or south of the _____. HINT

9. An arc second is _____ (give the fraction) of an arc minute. HINT

10. When the Sun, Earth, and Moon are positioned to form a right angle at Earth, the Moon is seen in the _____ phase. HINT

11. A _____ eclipse can be seen by about half of Earth at once. HINT

12. As seen from Earth, the Sun and the Moon have roughly the same _____. HINT

13. The distance to an object can be determined, for a known baseline, by measuring its _____. HINT

14. The size of an object can be determined, if we know its distance, by measuring its _____. HINT

15. The radius of _____ was first measured by Eratosthenes in 200 B.C. HINT

REVIEW AND DISCUSSION

1. Compare the size of Earth with that of the Sun, the Milky Way Galaxy, and the entire universe. HINT

2. What does an astronomer mean by "the universe?" HINT

3. How big is a light-year? HINT

4. What is a constellation? HINT

5. Why are constellations useful for mapping the sky? HINT

6. Why does the Sun rise in the east and set in the west each day? Does the Moon also rise in the east and set in the west? Why? Do stars do the same? Why? HINT

7. How and why does a day measured by the Sun differ from a day measured by the stars? HINT

8. How many times in your life have you orbited the Sun? HINT

9. Why do we see different stars at different times of the year? HINT

10. Why are there seasons on Earth? HINT

11. What is an equinox? HINT

12. What is precession, and what causes it? HINT

13. If one complete hemisphere of the Moon is always lit by the sun, why do we see different phases of the Moon? HINT

14. What causes a lunar eclipse? A solar eclipse? HINT

15. Why aren’t there lunar and solar eclipses every month? HINT

16. Do you think an observer on another planet might see eclipses? Why or why not? HINT

17. What is parallax? Give an everyday example. HINT

18. Why is it necessary to have a long baseline when using triangulation to measure the distances to objects in space? HINT

19. What two pieces of information are needed to determine the diameter of a faraway object? HINT

20. If you traveled to the outermost planet in our solar system, do you think the constellations would appear to change their shapes? What would happen if you traveled to the next-nearest star? If you traveled to the center of our Galaxy, could you still see the familiar constellations found in Earth’s night sky? HINT

PROBLEMS

Algorithmic versions of these questions are available in the Practice Problems Module of the Companion Website.

The number of squares preceding each problem indicates the approximate level of difficulty.

1. In one second, light leaving Los Angeles reaches approximately as far as (a) San Francisco, about 500 km; (b) London, roughly 10,000 km; (c) the Moon, 384,000 km; (d) Venus, 45,000,000 km from Earth at closest approach; or (e) the nearest star, about three light-years from Earth. Which is correct? HINT

2. (a) Write the following numbers in scientific notation (see Appendix 1 if you are unfamiliar with this notation): 1000; 0.000001; 1001; 1,000,000,000,000,000; 123,000; 0.000456. (b) Write the following numbers in "normal" numerical form: 3.16 10⁷; 2.998 10⁵; 6.67 10^-11; 2 10⁰. (c) Calculate: (2 10³) + 10^-2; (1.99 10³⁰) / (5.98 10²⁴); (3.16 10⁷) (2.998 10⁵). HINT

3. How, and by roughly how much, would the length of the solar day change if Earth’s rotation were suddenly to reverse direction? HINT

4. The vernal equinox is now just entering the constellation Aquarius. In what constellation will it lie in the year A.D. 10,000? HINT

5. What would be the length of the synodic month if the Moon’s sidereal orbital period were (a) one week (seven solar days); (b) one (sidereal) year? HINT

6. Through how many degrees, arc minutes, or arc seconds does the Moon move in (a) one hour of time; (b) one minute; (c) one second? How long does it take for the Moon to move a distance equal to its own diameter? HINT

7. Given the data presented in the text, estimate the speed (in km/s) at which the Moon moves in its orbit around Earth. HINT

8. A surveyor wishes to measure the distance between two points on either side of a river, as illustrated in Figure 1.23. She measures the distance AB to be 250 m and the angle at B to be 30°. What is the distance between the two points? HINT

9. At what distance is an object if its parallax, as measured from either end of a 1000-km baseline, is (a) 1°; (b) 1´; (c) 1´´? HINT

10. Given that the angular size of Venus is 55" when the planet is 45,000,000 km from Earth, calculate Venus’s diameter (in kilometers). HINT

11. Calculate the parallax, using Earth’s diameter as a baseline, of the Sun’s nearest neighbor, Proxima Centauri, which lies 4.3 light-years from Earth. HINT

12. Estimate the angular diameter of your thumb, held at arm’s length. HINT

13. The Moon lies roughly 384,000 km from Earth and the Sun lies 150,000,000 km away. If both have the same angular size, as seen from Earth, how many times larger than the Moon is the Sun? HINT

14. Given that the distance from Earth to the Sun is 150,000,000 km, through what distance does Earth move in (a) a second, (b) an hour, (c) a day? HINT

15. What angle would Eratosthenes have measured (see Discovery 1-1) had Earth been flat? HINT

COLLABORATIVE EXERCISES

1. Chasing Solar Eclipses. Consider the text figure showing solar eclipse paths over a world map. As a group, write a description of which eclipse your group would most like to observe together, where and when you would go to observe it, and fully explain why you selected the date and site you did.

2. Measuring Diameters from the Surface. Eratosthenes used simple geometric reasoning to calculate Earth’s size using shadows. As a group, create a sketch and an accompanying written description showing exactly how his measurements would lead to a different result using one of Jupiter’s moons.

3. Parallax Measurements. If the angular width of your thumb at arm’s length is about 1/2 of a degree, determine the angular size of four different objects in the room selected by your group members. Provide a sketch with an organized data table.

4. Astrophotographs from Distant Planets. Consider the semi-circular star trails shown in the time-lapse photograph (Fig. 1.9) of the northern sky. What was the exposure time used for the photograph? How long would you need to take a similar picture from a different planet of your group’s choosing? Fully explain your answer.

RESEARCHING ON THE WEB

To complete the following exercises, go to the online Destinations module for Chapter 1 on the Companion Website for Astronomy Today 4/e.

2. Access the "Moon Phase" page and determine what will be the illuminated fraction and age in days of the Moon on your next two birthdays. Include a sketch of the Moon’s appearance.

3. Access the "Solar Eclipse Path Predictions" page and determine the maximum duration of totality for the next total solar eclipse and write a rationale for where the best location to observe the eclipse would be.

4. Access the "List of Constellation Facts and Figures" page and describe the Messier objects that are located in your constellation most closely associated with your horoscope birth-sign.

PROJECTS

1. Go to a country location on a clear dark night. Imagine patterns among the stars, and name the patterns yourself. Note (or better yet, draw) the locations of these stars with respect to trees or buildings in the foreground. Do this every week or so for a couple of months, and be sure to look at the same time every night. What happens?

2. Find the star Polaris, also known as the North Star, in the evening sky. Identify any separate pattern of stars in the same general vicinity of the sky. Wait several hours, at least until after midnight, and then locate Polaris again. Has Polaris moved? What has happened to the nearby pattern of stars? Why?

3. Hold your little finger out at arm’s length. Can you cover the disk of the Moon? The Moon projects an angular size of 30´ (half a degree); your finger should more than cover it. How can you apply this fact in making sky measurements?

SKYCHART III PROJECTS

The SkyChart III Student Version planetarium program on which these exercises are based is included as a separately executable program on the CD in the back of this text.

1. Familiarity with the night sky starts with learning how to recognize significant constellations. SkyChart III can be very helpful in this endeavor. Set the COMPUTATION/Location for your area and set a convenient date and time for you to observe the stars. Do not attempt initially to learn all of the constellations, but start with the prominent ones currently visible. Concentrate your attention on the constellations depicted in the star charts on pages 7–10 of your text.

Make a careful sketch of the night sky that faithfully represents the size, shape and relative locations of the constellations. Prepare the sketch so you can carry it with you to the field when you view the stars. In your sketch, include the circumpolar constellations and asterisms that are always visible in the Northern Hemisphere. While the hand sketch is important in helping you appreciate the location and size of the various star groupings; it is also helpful to have a printed copy of the screen. To print out a copy of the screen, select FILE/Print Setup and select Landscape under Orientation. When FILE/Print is selected, accept the recommendation to not print colors and to print black lines on a white background.

The Big Dipper (an asterism) is a good place to start when attempting to find your way around the stars. Orient the display with north up, and carefully note the orientation of Polaris with respect to the pointer stars of the Big Dipper. Then note how you can project off the Big Dipper in the opposite direction to find Leo. You will find also that there are other useful projections that lead from the Big Dipper to objects of interest. When the Moon is visible, it will be in a different position each evening, providing a reference point that can be useful. A dark sky is not necessary to view constellations. In fact, the constellations typically are composed of the brightest stars, actually making it easier to see them from areas with moderate light pollution. In a dark sky, so many stars are visible that making out even familiar constellations can sometimes present a challenge.

2. Set up and print observation charts for a viewing session. Use the COMPUTATION menu to choose the Location and Date & Time. If it is not preset, you will need to enter the Longitude, Latitude, and Altitude of your location. Identify on your charts the brightest stars and most recognizable constellations. Identify galaxies, nebulae, and clusters.

3. Figure 1.12 illustrates the zodiac. Set up charts identifying which constellation of the zodiac marks the beginning of each season. Draw the Ecliptic:VIEW/Coordinates/Ecliptic; VIEW/Center Planet/Sun. Use the ANIMATION menu, with an appropriate Time Step, to observe the changing of the Zodiac. Keep track of time in the bottom left corner.

4. The constellations as we see them are not only unique to our culture but also unique to our point of reference. Use the COMPUTATION menu to View From the star Sirius, a star in the neighboring constellation of Canis Major. Can you explain the distortions seen in both Orion and Canis Major?

5. Simulate the total solar eclipse that will cross the central United States in 2017. Select COMPUTATION/Location and configure SkyChart III for St. Louis at longitude -90 30 00 and latitude +38 45 00. Under COMPUTATION/Date & Time set the Local date and time to 2017/08/21 and 11:30:00 with Time zone to -6.0. Select VIEW/Center Planet/Sun to center on the Sun. The Sun will now remain in the center of the screen as time and zoom are changed. Zoom in with Pg Up on the keyboard until you have a field of view of approximately 5º. You should see the Moon poised near the Sun. Animate the scene with one-minute time steps to observe motion of the Moon with respect to the Sun during this total solar eclipse.

6. Observe the August 21, 2017 solar eclipse as seen from a vantage point on the Sun. Configure SkyChart III by opening COMPUTATION/Location and selecting View from Object. Click on Select and Search for Sun. Turn off the horizon mask with DRAW/Horizon Mask. Center on Earth with VIEW/Center/Planet/Earth. Since you are viewing the Moon from the distance of the Sun, it will be necessary to use a more powerful telescope than is necessary to view the Moon from Earth. Zoom in until the field is approximately 1/60°. With time set for approximately 11:30 a.m., the Moon will be seen poised between Earth and the Sun. Animate the scene with time steps of one minute and watch the Moon advance across the surface of Earth. It should be obvious why the eclipse is visible only in certain locations on Earth at any one time.

7. Simulate the precession of Earth’s axis with SkyChart III by centering on Polaris and using animation to step through time in 100-year increments. Under the pull-down menu DRAW select Stars, Constellations, Chart Legend, Object Labels, and Grid Lines. Lock Polaris in the center of the screen by selecting VIEW/Center Object, typing in Polaris and clicking on Find. When Polaris is located, click on Select. Choose VIEW/180° Field. Select ANIMATION/100 Years and start Animation Forward. You can also run the animation backward to observe how difficult it might have been for navigation in the Dark Ages when there was no distinct North Star. When was Vega our North Star and when will it be again? Turn on DRAW/Mouse Coordinates to measure the angular separation of objects. Determine how close Polaris is to being true north today by pointing the cursor to true north and while holding the left button down, move the cursor over to Polaris. The angular separation is provided in a set of numbers in the upper left corner of the screen. How close Polaris was to being the North Star when Columbus made his famous voyage in 1492?

In addition to the Practice Problems and Destinations modules, the Companion Website at http://www.prenhall.com/chaisson provides for each chapter an additional true-false, multiple choice, and labeling quiz, as well as additional annotated images, animations, and links to related Websites.