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 very 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 sunrise to the next is called a solar day. The time between successive risings of any given star is one sidereal day. Because of Earth's revolution around the Sun, the solar day is a few minutes longer than the sidereal day.

The Sun's yearly path around the celestial sphere, or, equivalently, the plane of Earth's orbit around the Sun, is called the ecliptic. 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, and so day and night are of equal length. The interval of time from one vernal equinox to the next is one tropical year.

Because Earth orbits the Sun, we see different constellations at different times of the year. The constellations lying along the ecliptic are collectively called the zodiac. The time required for the same constellations to reappear at the same location in the sky, as viewed from a given point on Earth, 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 particular constellations that happen to be visible on any given night change over the course of many years.

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 all but invisible from Earth. The time between successive full Moons is one synodic month. The time taken 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 2 days longer than the sidereal month.

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 distant 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. Astronomers use parallax when measuring the distances to the planets by triangulation. The same geometric reasoning is used to determine the sizes of objects whose distances are known.


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

2. The number 2 106 is equal to 2 billion. HINT

3. The stars in a constellation are physically close to each other. HINT

4. Some constellations, at one time, were used as simple calendars. HINT

5. Constellations are no longer of any use to astronomers. HINT

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

7. The constellations lying immediately adjacent to the north celestial pole 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 fall. 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.

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


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

2. The light year is a unit of _____. 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.

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

13. To measure distances to nearby stars by parallax, a baseline equal to Earth's _____ is used.

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


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

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

3. What is a constellation? HINT

4. 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

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

6. Why are there seasons on Earth? HINT

7. Why do we see different stars in summer and in winter? HINT

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

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

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

11. Why aren't there lunar and solar eclipses every month? HINT

12. What is precession, and what is its cause? HINT

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

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

15. 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


1. (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) ÷ (5.97 1024); (3.16 107) (2.998 105). HINT

2. In 1 second, light leaving Los Angeles will reach approximately as far as (a) San Francisco (about 500 km), (b) London (roughly 10,000 km), (c) the Moon (400,000 km), (d) Venus (0.3 AU from Earth at closest approach), or (e) the nearest star (about 1 pc from Earth). Which is correct? HINT

3. How would the length of the solar day change if Earth's rotation were suddenly to reverse direction? HINT

4. What would be the length of the month if the Moon's sidereal orbital period were (a) 1 week (7 solar days)? (b) 1 (sidereal) year? HINT

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

6. Through how many degrees, arc minutes, or arc seconds does the Moon move in (a) 1 hour of time, (b) 1 minute, (c) 1 second? How long does it take for the Moon to move a distance equal to its own diameter? HINT

7. A surveyor wishes to measure the distance between two points on either side of a river, as illustrated in Figure 1.22. 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

8. 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

9. Given that the distance to the Moon is 384,000 km and its angular size is 0.5°, calculate the Moon's diameter. HINT

10. What angle would Eratosthenes have measured (see More Precisely 1-3) had Earth been flat?


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) location of these stars with respect to trees or buildings in the foreground. Do this every week or so for a couple of months. 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?