.11 THE DAY. S it crosses the meridian at apparent noon. Before (ante) noon is thus a.m., while after (post) noon is p.m. FIGURE 7.

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1 Confirming Pages UNIT 7 PA RT I The Time of Day From before recorded history, people have used events in the heavens to mark the passage of time. The day was the time interval from sunrise to sunrise, and the time of day could be determined from how high the Sun was in the sky. As our ability to independently measure time has become more accurate, we have found that the apparent motions of the Sun across the sky are not as uniform as we once thought, and in this age of rapid travel and communications it no longer makes sense for each town to set its own time according to the Sun. With high-precision modern clocks we have even detected a gradual slowing of the Earth s spin! Each of these adjustments to our understanding of how to keep time provides an insight into the workings of astronomy. In this Unit we explore the motions of the Sun in detail. We use some basic ideas of day and night and celestial coordinates presented in Unit 5 and of the apparent motion of the Sun against the stars from Unit 6. If these ideas are unfamiliar, you may want to review those Units first. UNIT OUTLINE 7.1 The Day 7.2 Length of Daylight Hours 7.3 Time Zones 7.4 Daylight Saving Time 7.5 Leap Seconds THE DAY Meridian The length of the day is set by the Earth s rotation speed on its axis. One day is defined to be one rotation. However, we must be careful how we measure our planet s rotation. For example, we might use the time from one sunrise to the next to define a day. That, after all, is what sets the day night cycle around which we structure our activities. However, we would soon discover that the time from sunrise to sunrise changes steadily throughout the year as a result of the seasonal change in the number of daylight hours. A better time marker is the time it takes the Sun to move from its highest point in the sky on one day, what we technically call apparent noon, to its A.M. P.M. highest point in the sky on the next day a time interval that we call the solar day. Summer Local noon We often divide a day into a.m. and p.m., which stand for ante meridian and post meridian, respectively. Equinox The meridian is a line that divides the eastern and western halves of the sky. The meridian extends from the Winter point on the horizon due north to the point due south and passes directly through the zenith, the point exactly overhead. As the Sun moves across the sky (Figure 7.1), S it crosses the meridian at apparent noon. Before (ante) East West noon is thus a.m., while after (post) noon is p.m. FIGURE 7.1 Apparent solar time is what a sundial measures, and The Sun rises in the east, crosses the meridian at local noon, then sets in during the year this time may be ahead of or behind the west. This figure depicts the path of the Sun seen from the Northern clock time by as much as a quarter of an hour. This Hemisphere at the equinoxes and solstices. variation arises from the Earth s orbital characteristics 53 sch12133_ch07.indd 53

2 54 Part One The Cosmic Landscape Sun Day 1 Noon Sun and star are both overhead. North Pole To star Day 2 Noon Earth has now turned once with respect to the Sun but has made more than one full turn with respect to the star. Day 2 11:56 am Earth has turned once with respect to the star. Star is back overhead, but the Sun isn t. FIGURE 7.2 The length of the day measured with respect to the stars is not the same as the length m easured with respect to the Sun. The Earth s orbital motion around the Sun makes it necessary for the Earth to rotate slightly more before the Sun will be back overhead. (Motion is exaggerated for clarity.) (Unit 13). Although the Sun s position determines the day night cycle, it is not a stable reference for measuring Earth s spin. We can avoid most of the variation in the day s length if, instead of using the Sun, we use a star as our reference. For example, if we pick a star that crosses our meridian at a given moment and measure the time it takes for that same star to return to the meridian again, we will find that this time interval repeats quite precisely. However, this interval is not 24 hours, but about 23 hours, 56 minutes, and seconds. This day length, measured with respect to the stars, is called a sidereal day, which is divided into correspondingly shorter hours, minutes, and seconds of sidereal time. Astronomers find that a clock set to run at this speed is very useful. It is not just that the sidereal day is much more stable. Another reason is that, at a given location, any particular star will always rise at the same sidereal time. To avoid the nuisance of a.m. and p.m., sidereal time is measured on a 24-hour basis. For example, the bright star Procyon in the constellation Canis Minor (small dog) rises at about 10 p.m. in November but at about 8 p.m. in December and 6 p.m. in January by solar time. However, on a clock keeping sidereal time, it always rises at the same time at a given location: about 01:30 by the sidereal clock. Why is the sidereal day shorter than the solar day? We can see the reason by looking at Figure 7.2, where we measure the interval between successive apparent noons a solar day. Let us imagine that at the same time as we are watching the Sun, we can also watch a star, and that we measure the time interval between its passages across the meridian a sidereal day. As we wait for the Sun and star to move back across the meridian, the Earth moves along its orbit. The distance the Earth moves in one day is so small compared with the star s distance that we see the star in essentially the same direction as on the previous day. However, we see the Sun in a measurably different direction, as Figure 7.2 illustrates. The Earth must rotate a bit more before the Sun is again on the meridian. That extra rotation, needed to compensate for the Earth s orbital motion, makes the solar day slightly longer than the sidereal day. It is easy to figure out how much longer, on the average, the solar day must be. Because it takes us 365¼ days to orbit the Sun and because there are 360 in a circle, the Earth moves approximately 1 per day in its orbit around the Sun. That means that for the Sun to reach its noon position, the Earth must rotate approximately 1 past its position on the previous day. Another way of thinking about this is that the Sun is slowly moving eastward across the sky through the stars at the same time as the Earth is rotating. Therefore, in a given day, the Earth must rotate a bit more to keep pace with the Sun than it would to keep pace with the stars. In 24 hours there are 1440 (24 60) minutes, and during this time the Earth rotates 360. Therefore, for the Earth to rotate about 1 extra so that the same side is facing the Sun again, takes about 1440/360 = 4 minutes. The solar day is therefore about 4 minutes longer than the sidereal day. 7.2 LENGTH OF DAYLIGHT HOURS Clarification Point Many people believe that the Sun is straight overhead every day at noon. Outside of the tropics (latitudes within 23.5 of the equator) the Sun is never straight overhead, and even within the tropics the Sun passes overhead around noon on only one or two days each year. Although each day lasts 24 hours, the number of hours of daylight, or the amount of time the Sun is above the horizon, changes dramatically throughout the year unless you are close to the equator. For example, in northern middle latitudes, including most of the United States, southern Canada, and Europe, summer has about 15 hours of daylight and only 9 hours of night. In the winter, the reverse is true. Just north of the Arctic Circle at a latitude of 66.5 ( ), the Sun remains above the horizon for 24 hours on the summer solstice (Figure 7.3) and below the horizon the entire day on the winter solstice. On the equator, day and night are each 12 hours every day. sch12133_ch07.indd 54

3 Unit 7 The Time of Day 55 FIGURE 7.3 Sequence of 24 pictures of the Sun taken from a spot close to the Arctic Circle near the summer solstice. The pictures were taken 1 hour apart and show the Sun circling the sky but never setting. ANIMATION Hours of daylight This variation in the number of daylight hours is caused by the Earth s tilted rotation axis. Remember that as the Earth moves around the Sun, its rotation axis points in very nearly a fixed direction in space. As a result, the Sun shines more directly on the Northern Hemisphere during its summer and at a more oblique angle during its winter. The result (as you can see in Figure 7.4) is that a large fraction of the Northern Hemisphere is illuminated by sunlight at any time in the summer, but a small fraction is illuminated in the winter. So as rotation carries us around the Earth s axis, only a relatively few hours of a summer day are unlit, but a relatively large number of winter hours are dark. On the first days of spring and autumn (the equinoxes), the hemispheres are equally lit, so that day and night are of equal length everywhere on Earth. If we change our perspective and look out from the Earth, we see that during the summer the Sun s path is high in the sky, so that the Sun spends a larger portion of the day above the horizon (Figure 7.1). This gives us not only more heat but also more hours of daylight. On the other hand, in winter the Sun s path across the sky is much shorter, giving us less heat and fewer hours of light (also see Unit 6). Sun Night No daylight 10.3 hr daylight 12 hr daylight 13.7 hr daylight 24 hr daylight Sunlight 24 hr daylight 13.7 hr daylight 12 hr daylight 10.3 hr daylight No daylight December 21 June 21 FIGURE 7.4 The tilt of the Earth affects the number of daylight hours. Locations near the equator always receive about 12 hours of daylight, but locations toward the poles have more hours of darkness in winter than in summer. In fact, above latitudes 66.5 the Sun never sets for part of the year (the midnight sun phenomenon) and never rises for another part of the year. At the equinoxes, all parts of the Earth receive the same number of hours of light and dark. (Sizes and separation of the Earth and Sun are not to scale.) Equator Night sch12133_ch07.indd 55

4 Confirming Pages 56 Part One The Cosmic Landscape 7.3 TIME ZONES 7. Because the Sun is our basic timekeeping reference, most people like to measure time so that the Sun is highest in the sky at about noon. As a result, clocks in different parts of the world are set to different times so that the local clock time approximately reflects the position of the Sun in the sky. Because the Earth is round, the Sun can t be overhead everywhere at the same time, so it can t be noon everywhere at the same time. By the late 1800s, with the increasing speed of travel and communications, it became confusing for each city to maintain its own time according to the position of the Sun in the sky. By international agreement, the Earth was therefore divided into 24 major time zones, centered every 15 of longitude, in which the time differs by one hour from one zone to the next. With this system, clocks in a time zone all read the same, and they are at most a half hour ahead of or behind what they would be if the time were measured locally. Many regions use local geographic features or political borders to define the boundaries between time zones rather than strictly following the longitude limits (see Figure 7.5). Authorities in a few countries and regions did not adopt this agreement, choosing instead to maintain a time standard that was closer to local time. For example, Newfoundland, India, Nepal, and portions of Australia are offset by 30- or 15-minute differences from the international standard. Across the lower 48 United States, the time zones are, from east to west, Eastern, Central, Mountain, and Pacific. Within each zone the time is the same everywhere and is called standard time. In the eastern zone the time is denoted Eastern Standard Time (EST), in the central zone it is denoted Central Standard Time (CST), and so on. If you travel across the United States, you reset your watch as you cross from one time zone to another, adding one hour for each time zone as you go east, and subtracting one hour for each time zone as you go west. If you travel through many time zones, you may need to make such a large time correction that you shift your watch past midnight. For example, if you could In Figure 7.5 the international date line has a very complex shape. If you were sailing north through the 11h time zone, how would your time and date change? FIGURE 7.5 Time zones of the world and the international date line. Local time = universal time + numbers on top or bottom of chart h h 3h 1h h 9h 3h 8h Pacific 7h Mountain 5h Eastern h +1h h +2h +3h +4h +8h +9h +5h45m +5h +6h +13h +14h 11h +11h +13h 9h 5h 4h 10h +3h 45m sch12133_ch07.indd h +3h +4h 0h +9 +9h +5h +1h 1h 6h Central +5 +4h 4h International Date Line +4 +7h 9h 10h +3 Prime meridian Concept Question 1 3h +9h +8h +11h Locations where time differs by a fraction of an hour from standard

5 Confirming Pages Unit 7 The Time of Day Concept Question 2 In Jules Verne s story Around the World in 80 Days, the travelers discover that although they have experienced 80 days and nights, they still have one more day before 80 days will have passed in London. How can this be? 57 travel westward quickly enough that little time elapsed, setting your watch back each time you crossed a time zone, you could end up at your starting point with your watch turned backward by 24 hours. But you would not have traveled back in time! When you cross longitude 180 (roughly down the middle of the Pacific Ocean), you add a day to the calendar if you are traveling west and subtract a day if you are traveling east. For example, you could celebrate the New Year in Japan and take a flight after midnight to Hawaii, where it would still be the day before, so you could celebrate the New Year that night too! The precise location where the day shifts is called the international date line (Figure 7.5). It generally follows 180 longitude but bends around extreme eastern Siberia and some island groups to ensure that they keep the same calendar time as their neighbors. The nuisance of having different times at different locations can be avoided by using universal time, abbreviated as UT. Universal time is the time kept in the time zone containing the longitude zero, which passes through Greenwich, England. By using UT, which is based on a 24-hour system to avoid confusion between a.m. and p.m., two astronomers at remote locations can make a measurement at the same time without worrying about what time zones they are in. 7.4 DAYLIGHT SAVING TIME 7. International Date Line Prime meridian FIGURE 7.6 Regions where daylight saving time is observed for some portion of the year. In many parts of the world, people set clocks ahead of standard time during the summer months and then back again to standard time during the winter months (Figure 7.6). This has the effect of shifting sunrise and sunset to later hours during the day, thereby creating more hours of daylight during the time when most people are awake. Time kept in this fashion is called daylight saving time in the United States. In some other parts of the world it is called Summer Time. Locations where northern summer daylight saving time is observed Locations where southern summer daylight saving time is observed sch12133_ch07.indd 57

6 58 Part One The Cosmic Landscape Concept Question 3 If daylight saving time saves energy, why not just have people come to work earlier when the Sun rises earlier and later when it rises later? Daylight saving time was originally established during World War I as a way to save energy. By setting clocks ahead, less artificial light was needed in the evening hours. In effect, it is a method to get everyone to wake up and go to work an hour earlier than they would normally and take advantage of the earlier rising of the Sun. Clocks are not set ahead permanently because in some parts of the country the winter sunrise is so late that daylight saving time would require people to wake and go to work in the dark. In the United States daylight saving time runs from the second Sunday in March to the first Sunday in November. In Europe it runs from the last Sunday in March to the last Sunday in October, whereas in Australia it runs from October to April. Many other countries, and even some states within the United States, follow different rules, while most tropical countries keep their clocks fixed on standard time. 7.5 LEAP SECONDS The strong earthquake in Chile in March 2010 sped up the Earth s rotation slightly, shortening the day by about 1 millionth of a second. Note that atomic clocks are not radioactive. They use an internal vibration frequency of cesium atoms to determine precise time intervals. Highly accurate time measurements have now allowed us to detect a gradual slowing of the Earth s spin. The second was defined as 1 part in 86,400 ( ) of a day, based on astronomical measurements made more than a century ago. With modern atomic clocks it has been determined that the length of the mean solar day is now about 86, seconds, and it is increasing by about second each century. Over a year the second add up to most of a second: second each year. This means that an accurate clock set at midnight on New Year s Eve would signal the beginning of the next new year almost 1 second too early. By the year 2100, an accurate clock will be off by 1.2 seconds after a year. This time change might sound insignificant, but over long periods its effects accumulate. Fossil records from corals that put down visible layers each day indicate that 400 million years ago the Earth s year had about 400 days. The Earth took the same amount of time to orbit the Sun, but the Earth took only about 22 hours to spin on its axis. With the precise timing needed today for technological uses such as the Global Positioning System (GPS), even millisecond errors are critical. To keep our clocks in agreement with the Sun and stars, we now adjust atomic clocks with a leap second every year or two. This is coordinated worldwide so that clocks everywhere remain in agreement. The slowing of the Earth is a consequence of the interaction of the spinning Earth with ocean tides, which are held relatively stationary by the Moon s gravity. In effect, the eastern coasts of the continents run into high tide as the solid Earth spins beneath the tide, and this creates a tidal braking force that is slowing the Earth. Tides are discussed further in Unit 19. KEY POINTS The Earth s spin is very regular with respect to the stars, taking about 23 hours 56 minutes to complete one sidereal day. Because of Earth s orbital motion, the rotation relative to the Sun takes about 4 minutes longer and is less regular. The Sun crosses your meridian at local noon, but at clock times that may vary by over a quarter hour at different times of year. The time from sunrise to sunset varies depending on latitude and season, with more extremes farther from the equator. In the tropics, the Sun can pass overhead one or two days each year; in polar regions, the Sun is sometimes above the horizon for 24 hours, and below the horizon for 24 hours six months later. Time zones help standardize times to the closest hour, although these are often modified for local reasons or to save daylight. The Earth s spin is gradually slowing, causing days to grow longer by about 1 thousandth of a second in the last century. sch12133_ch07.indd 58

7 Unit 7 The Time of Day 59 KEY TERMS a.m. (ante meridian), 53 sidereal day, 54 apparent noon, 53 sidereal time, 54 Arctic Circle, 54 solar day, 53 daylight saving time, 57 standard time, 56 international date line, 57 tidal braking, 58 leap second, 58 time zone, 56 meridian, 53 universal time (UT), 57 p.m. (post meridian), 53 CONCEPT QUESTIONS Concept Questions on the following topics are located in the margins. They invite thinking and discussion beyond the text. 1. The international date line. (p. 56) 2. Days passed when circling the globe. (p. 57) 3. Why use daylight saving time. (p. 58) REVIEW QUESTIONS 4. Where is the meridian located? 5. How is the sidereal day defined? Why do the sidereal and solar days differ in length? 6. What is universal time? 7. What are the advantages and disadvantages of time zones? 8. How does time shift across the international date line? 9. Why are leap seconds added to our clocks every few years? QUANTITATIVE PROBLEMS 10. Your friend lives in a town at a longitude 5 to the east of you. Both of you define noon as when the Sun reaches its highest point in the sky. How do your clocks differ from each other? 11. If Russia had all clocks set to Moscow time (time zone +3 in Figure 7.4) instead of using many time zones, what time would the Sun rise at the easternmost tip of Siberia on the equinoxes? Examining Figure 7.4, what places in the world have the Sun crossing the meridian earliest according to local time? What places have it latest? 12. One city is at a longitude of 78 E. A second city is at 95 W. How many hours apart will a star cross the meridian in the first city and then in the second? If the time zone of each city is based on the closest longitude that is a multiple of 15, and the star passes overhead in the first city exactly at midnight, at what time (by the clock) will it pass over the second city? 13. Suppose the Earth s spin slowed down until there were just 180 days in a year. Compare the length of a sidereal and a solar day in this new situation. (Do not redefine units of time just express them in terms of our current hours, minutes, and seconds.) 14. It is thought that the angle of the Earth s axis varies by a few degrees over tens of thousands of years. If the angle were 20 instead of 23.5, what would be the angle of the noontime Sun from the horizon at your own latitude on the solstices? 15. What is your longitude, and what is the longitude of the center of your time zone? (This should be a multiple of 15.) Calculate the time at which the Sun should, on average, cross your own meridian, assuming that the Sun crosses the meridian at exactly 12:00 at the center of your time zone. TEST YOURSELF 16. What effect does the Earth s orbit around the Sun have on stars rising? a. They rise only once a year. b. They rise several minutes earlier each night. c. They rise a little farther south or north each night, depending on the season. d. Nothing only the Sun rises, not stars. e. Nothing they rise the same time every night. 17. In which of the following locations can the length of daylight range from zero to 24 hours? a. Only on the equator b. At latitudes closer than 23.5 to the equator c. At latitudes between 23.5 and 66.5 north or south d. At latitudes greater than 66.5 north or south e. Nowhere on Earth 18. In which of the following locations is the length of daylight 12 hours throughout the year? a. Only on the equator b. At latitudes closer than 23.5 to the equator c. At latitudes between 23.5 and 66.5 north or south d. At latitudes greater than 66.5 north or south e. Nowhere on Earth 19. Daylight saving time a. shifts daylight from summer days into the winter. b. corrects clocks for errors caused by the Earth s tilted axis. c. results in the Sun crossing the meridian around 1 p.m. d. puts clocks in agreement with the Sun s position in the sky. e. All of the above sch12133_ch07.indd 59 11/26/10 3:12 PM

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