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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
77.1
.11 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
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Part One The Cosmic Landscape
To star
Sun
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.
North
Pole
Day 1—Noon
Sun and star
are both
overhead.
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
measured 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 4.0905 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
7.
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.
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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° (90° − 23.5°), 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.
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Unit 7 The Time of Day
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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.
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).
A N I M AT I O N
Hours of daylight
Sun
No daylight
10.3 hr daylight
24 hr daylight
12 hr daylight
Night
13.7 hr daylight
Sunlight
13.7 hr daylight
r
ato
Equ
Night
12 hr daylight
24 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.)
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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.
+11
+12 – –11
–10
–9
–8
–7
–6
–5
–4
–4h
–3
–2
–1
0h
–3h
–1h
+12h
0
+1
+2
+3h
–9h
–3h30m
–8h
Pacific
–7h
Mountain
–5h
Eastern
+6
+7
+8
–10h
+1h
+10
+11h
+2h
+3h
+4h
+8h
+9h
+5h45m
+5h
30m
+6h30m
+10h
+12h
+13h +14h
–11h
+11h
30m +13h
–9h30m
–5h
–4h
–10h
+3h
+12h45m
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+12h
+10h
+12h
+10h
30m
+11
+6h
+3h +4h
30m 30m
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 30m +10h
+11h
30m
+10h
30m
Locations where time differs by a
fraction of an hour from standard
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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?
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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
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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
7.
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 (24 × 60 ×
60) 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 86,400.002 seconds, and it is increasing by about
0.0014 second each century. Over a year the 0.002 second add up to most of a
second: 365 × 0.002 ≈ 0.7 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.
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• 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.
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Unit 7 The Time of Day
KEY TERMS
a.m. (ante meridian), 53
apparent noon, 53
Arctic Circle, 54
daylight saving time, 57
international date line, 57
leap second, 58
meridian, 53
p.m. (post meridian), 53
sidereal day, 54
sidereal time, 54
solar day, 53
standard time, 56
tidal braking, 58
time zone, 56
universal time (UT), 57
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
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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
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