Questions
Review Questions
Describe three structures or carvings made by past civilizations that show an understanding of astronomy.
How are constellations useful to astronomers? How many stars are not part of any constellation?
A fellow student tells you that only those stars in Figure 2-2b that are connected by blue lines are part of the constellation Orion. How would you respond?
Why is a particular star overhead at 10:00 p.m. on a given night rather than two hours later at midnight; how does this relate to Earth’s orbit? Why are different stars overhead at midnight on June 1 rather than at midnight on December 1?
What is the celestial sphere? Why is this ancient concept still useful today?Imagine that someone suggests sending a spacecraft to land on the surface of the celestial sphere. How would you respond to such a suggestion?
What is the celestial equator? How is it related to Earth’s equator? How are the north and south celestial poles related to Earth’s axis of rotation?
Where would you have to look to see your zenith? Where on Earth would you have to be for the celestial equator to pass through your zenith? Where on Earth would you have to be for the south celestial pole to be at your zenith?
How many degrees is the angle from the horizon to the zenith? Does your answer depend on what point on the horizon you choose?
Why can’t a person in Antarctica use the Big Dipper to find the north direction?
Is there any place on Earth where you could see the north celestial pole on the northern horizon? If so, where? Is there any place on Earth where you could see the north celestial pole on the western horizon? If so, where? Explain your answers.
How do the stars appear to move over the course of the night as seen from the north pole? As seen from the equator? Why are these two motions different?
Using a diagram, explain why the tilt of Earth’s axis relative to Earth’s orbit causes the seasons as we orbit the Sun.Give two reasons why it is warmer in summer than in winter.
What is the ecliptic plane? What is the ecliptic?
Why is the ecliptic tilted with respect to the celestial equator? Does the Sun appear to move along the ecliptic, the celestial equator, or neither? By about how many degrees does the Sun appear to move on the celestial sphere each day?
Where on Earth do you have to be in order to see the north celestial pole directly overhead? What is the maximum possible elevation of the Sun above the horizon at that location? On what date can this maximum elevation be observed?
What are the vernal and the autumnal equinoxes? What are the summer and winter solstices? How are these four points related to the ecliptic and the celestial equator?
At what point on the horizon does the vernal equinox rise? Where on the horizon does it set? (Hint: See Figure 2-16.)
How does the daily path of the Sun across the sky change with the seasons? Why does it change?
Where on Earth do you have to be in order to see the Sun at the zenith? As seen from such a location, will the Sun be at the zenith every day? Explain your reasoning.
What is precession of the equinoxes? What causes it? How long does it take for the vernal equinox to move 1° along the ecliptic?
What is the (fictitious) mean sun? What path does it follow on the celestial sphere? Why is it a better timekeeper than the actual Sun in the sky?
Why is it convenient to divide Earth into time zones?
Why is the time given by a sundial not necessarily the same as the time on your wristwatch?
What is the difference between the sidereal year and the tropical year? Why are these two kinds of year slightly different in length? Why are calendars based on the tropical year?
When is the next leap year? Was 2000 a leap year? Will 2100 be a leap year?
Advanced Questions
Questions preceded by an asterisk (*) are discussed in the Boxes.
Problem-solving tips and tools
To help you visualize the heavens, it is worth taking the time to become familiar with various types of star charts. These include the simple star charts at the end of this book, the monthly star charts published in such magazines as Sky & Telescope and Astronomy, and the more detailed maps of the heavens found in star atlases.
One of the best ways to understand the sky and its motions is to use the Starry Night™ computer program on the CD-ROM that accompanies certain printed copies of this book. This easy-to-use program allows you to view the sky on any date and at any time, as seen from any point on Earth, and to animate the sky to visualize its diurnal and annual motions.
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You may also find it useful to examine a planisphere, a device consisting of two rotatable disks. The bottom disk shows all the stars in the sky (for a particular latitude), and the top one is opaque with a transparent oval window through which only some of the stars can be seen. By rotating the top disk, you can immediately see which constellations are above the horizon at any time of the year. A planisphere is a convenient tool to carry with you when you are out observing the night sky.
On November 1 at 8:30 p.m. you look toward the eastern horizon and see the bright star Bellatrix (shown in Figure 2-2b) rising. At approximately what time will Bellatrix rise one week later, on November 8?
Figure 2-4 shows the situation on September 21, when Cygnus is highest in the sky at 8:00 p.m. local time and Andromeda is highest in the sky at midnight. But as Figure 2-5 shows, on July 21 Cygnus is highest in the sky at midnight. On July 21, at approximately what local time is Andromeda highest in the sky? Explain your reasoning.
Figure 2-5 shows which constellations are high in the sky (for observers in the northern hemisphere) in the months of July, September, and November. From this figure, would you be able to see Perseus at midnight on May 15? Draw a picture to justify your answer.
Figure 2-6 shows the appearance of Polaris, the Little Dipper, and the Big Dipper at 11 p.m. (daylight saving time) on August 1. Sketch how these objects would appear on this same date at (a) 8 p.m. and (b) 2 a.m. Include the horizon in your sketches, and indicate the north direction.
Figure 2-6 shows the appearance of the sky near the North Star at 11 p.m. (daylight saving time) on August 1. Explain why the sky has this same appearance at 1 a.m. on July 1 and at 9 p.m. on September 1.
The time-exposure photograph that opens this chapter shows the trails made by individual stars as the celestial sphere appears to rotate around Earth. (a) For approximately what length of time was the camera shutter left open to take this photograph? (b) The stars in this photograph (taken in Hawaii, at roughly 20° north latitude) appear to rotate around one of the celestial poles. Which celestial pole is it? As seen from this location, do the stars move clockwise or counterclockwise around this celestial pole? (c) If you were at 20° south latitude, which celestial pole could you see? In which direction would you look to see it? As seen from this location, do the stars move clockwise or counterclockwise around this celestial pole?
(a) Redraw Figure 2-10 for an observer at the north pole. (Hint: The north celestial pole is directly above this observer.) (b) Redraw Figure 2-10 for an observer at the equator. (Hint: The celestial equator passes through this observer’s zenith.) (c) Using Figure 2-10 and your drawings from (a) and (b), justify the following rule, long used by navigators: The latitude of an observer in the northern hemisphere is equal to the angle in the sky between that observer’s horizon and the north celestial pole. (d) State the rule that corresponds to (c) for an observer in the southern hemisphere.
The photograph that opens this chapter was taken next to the Gemini North Observatory atop Mauna Kea in Hawaii. The telescope is at longitude 155° 28' 09? west and latitude 19° 49' 26? north. (a) By making measurements on the photograph, find the approximate angular width and angular height of the photo. (b) How far (in degrees, arcminutes, and arcseconds) from the north celestial pole can a star be and still be circumpolar as seen from the Gemini North Observatory?
The Gemini North Observatory shown in the photograph that opens this chapter is located in Hawaii, roughly 20° north of the equator. Its near-twin, the Gemini South Observatory, is located roughly 30° south of the equator in Chile. Why is it useful to have telescopes in both the northern and southern hemispheres?
Is there any place on Earth where all the visible stars are circumpolar? If so, where? Is there any place on Earth where none of the visible stars is circumpolar? If so, where? Explain your answers.
This image of Earth was made by the Galileo spacecraft while en route to Jupiter. South America is at the center of the image and Antarctica is at the bottom of the image. (a) In which month of the year was this image made? Explain your reasoning. (b) When this image was made, was Earth relatively close to the Sun or relatively distant from the Sun? Explain your reasoning.
R I V U X G(NASA/JPL)Figure 2-16 shows the daily path of the Sun across the sky on March 21, June 21, September 22, and December 21 for an observer at 35° north latitude. Sketch drawings of this kind for (a) an observer at 35° south latitude; (b) an observer at the equator; and (c) an observer at the north pole.
Suppose that you live at a latitude of 40° N. What is the elevation (angle) of the Sun above the southern horizon at noon (a) at the time of the vernal equinox? (b) at the time of the winter solstice? Explain your reasoning. Include a drawing as part of your explanation.
In the northern hemisphere, houses are designed to have “southern exposure,” that is, with the largest windows on the southern side of the house. But in the southern hemisphere houses are designed to have “northern exposure.” Why are houses designed this way, and why is there a difference between the hemispheres?.
The city of Mumbai (formerly Bombay) in India is 19° north of the equator. On how many days of the year, if any, is the Sun at the zenith at midday as seen from Mumbai? Explain your answer.
Ancient records show that 2000 years ago, the stars of the constellation Crux (the Southern Cross) were visible in the southern sky from Greece. Today, however, these stars cannot be seen from Greece. What accounts for this change?
The Great Pyramid at Giza has a tunnel that points toward the north celestial pole. At the time the pyramid was built, around 2600 b.c.e., toward which star did it point? Toward which star does this same tunnel point today? (See Figure 2-20.)
The photo shows a statue of the Greek god Atlas. The globe that Atlas is holding represents the celestial sphere, with depictions of several important constellations and the celestial equator. Although the statue dates from around 150 c.e., it has been proposed that the arrangement of constellations depicts the sky as it was mapped in an early star atlas that dates from 129 b.c.e. Explain the reasoning that could lead to such a proposal.
R I V U X G(Scala/Art Resource, NY)Unlike western Europe, Imperial Russia did not use the revised calendar instituted by Pope Gregory XIII. Explain why the Russian Revolution, which started on November 7, 1917, according to the modern calendar, is called the October Revolution in Russia. What was this date according to the Russian calendar at the time? Explain your answer.
*What is the right ascension of a star that is on the meridian at midnight at the time of the autumnal equinox? Explain your answer.
*The coordinates on the celestial sphere of the summer solstice are R.A. = 6h 0m 0s, Decl. = + 23° 27'. What are the right ascension and declination of the winter solstice? Explain your answer.
*Because 24 hours of right ascension takes you all the way around the celestial equator, 24h = 360°, what is the angle in the sky (measured in degrees) between a star with R.A. = 8h 0m 0s, Decl. = 0° 0' 0? and a second star with R.A. = 11h 20m 0s, Decl. = 0° 0' 0?? Explain your answer.
*On a certain night, the first star in Advanced Question 49 passes through the zenith at 12:30 a.m. local time. At what time will the second star pass through the zenith? Explain your answer.
*At local noon on March 21, when the Sun is at the vernal equinox, a sidereal clock will say that it is midnight. Explain why.
*(a) What is the sidereal time when the vernal equinox rises? (b) On what date is the sidereal time nearly equal to the solar time? Explain your answer.
*How would the sidereal and solar days change (a) if Earth’s rate of rotation increased, (b) if Earth’s rate of rotation decreased, and (c) if Earth’s rotation were retrograde (that is, if Earth rotated about its axis opposite to the direction in which it revolves about the Sun)?
Discussion Questions
Examine a list of the 88 constellations. Are there any constellations whose names obviously date from modern times? Where are these constellations located? Why do you suppose they do not have archaic names?
Describe how the seasons would be different if Earth’s axis of rotation, rather than having its present 23½° tilt, were tilted (a) by 0° or (b) by 90°.
In William Shakespeare’s Julius Caesar (act 3, scene 1), Caesar says:
But I am constant as the northern star,
Of whose true-fix’d and resting quality
There is no fellow in the firmament.
Translate Caesar’s statement about the “northern star” into modern astronomical language. Is the northern star truly “constant”? Was the northern star the same in Shakespeare’s time (1564–1616) as it is today?
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Web/eBook Questions
Search the World Wide Web for information about the national flags of Australia, New Zealand, and Brazil and the state flag of Alaska. Which stars are depicted on these flags? Explain any similarities or differences among these flags.
Some people say that on the date that the Sun is at the vernal equinox, and only on this date, you can stand a raw egg on end. Others say that there is nothing special about the vernal equinox, and that with patience you can stand a raw egg on end on any day of the year. Search the World Wide Web for information about this story and for hints about how to stand an egg on end. Use these hints to try the experiment yourself on a day when the Sun is not at the vernal equinox. What do you conclude about the connection between eggs and equinoxes?
Use the U.S. Naval Observatory Web site to find the times of sunset and sunrise on (a) your next birthday and (b) the date this assignment is due. (c) Are the times the same for the two dates? Explain why or why not.