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gray whales
single cell protozoa
quarks atoms
humans
Astronomical units are used to measure distances within the solar system. Light- years are used to measure distances to all other bodies far beyond our solar system. Distances measured from Earth to some bodies can be determined using triangulation and parallax.
As you learned in Chapter 10, astronomers believe that the age of the universe is 13.7 billion years. To help you put into perspective how much a billion is, imagine that you started counting to a billion right now. If you kept counting steadily at a number per second, day and night, it would take you 31 years, 259 days, 1 hour, 46 minutes, and 40 seconds before you were finally able to gasp out “1 billion!” Not only is the universe astronomically old, it is also astronomically big, and the distances between its celestial bodies are astronomically far. In this section, you will learn about scales and techniques that astronomers have developed to measure the tremendous distances between those components.
Just How Big Is Space?
It is not easy for most of us to imagine the truly immense scale of the universe. “Scale” refers to the size of an object compared with its surroundings or another object. Think of a flea trying to understand the size of a sports arena. Now imagine that the flea is surrounded by 100 sports arenas. If someone told the flea how vast the space was around it in all directions, the flea would find it extremely difficult to envision. For humans, trying to understand the size of the universe is just as difficult. If you did Conduct an Investigation 11–2C, Strolling Through the Solar System, modelling the relative sizes of the bodies in our solar system and the distance between them, you are probably beginning to get an idea of how challenging it is to describe scale in the universe. Figure 11.20 shows the relative sizes of components in the universe, from quarks to galaxies.
11.3 Measuring Distances in Space
Words to Know
light-year parallax triangulation
396 MHR • Unit 4 Space Exploration
D id You Know? Imagine a pile of 100 copies of this textbook. If the total number of words in that pile represented the volume of the universe, Earth would not even be the dot on an i.
Figure 11.20 The relative size of components in the universe
104 106 108 1010 1012 1014 1016 1018 1020 1022 1024 1026 1028 1030
largest asteroid
Greater Vancouver
solar system
distance from Earth to Proxima Centuri
galaxies observable universe
Earth Sun
Chapter 11 The components of the universe are separated by unimaginably vast distances. • MHR 397
11-3A^ Pointing in the Right Direction F i n d^ O u t^ A C T I V I T Y
The astrolabe is a device that was used by early astronomers to pinpoint the locations of objects in space. The instrument itself has had various forms and has been in use for more than 2000 years. In this activity, you will use an astrolabe to determine the angle and height of objects in different positions around your classroom.
Materials
- astrolabe
- directional compass
- pen
- paper
What to Do
1. Copy the table shown below into your notebook. (Your teacher will pick the target objects you should use.) 2. Use the compass to find out which part of your classroom faces due north. Then use the compass to determine the angle of the first object in relation to due north. Record this in the “Angle” column of your table. Remember that degrees increase in order clockwise from north. 3. Use the astrolabe to determine the height of the object. Make your measurement from a sitting position at your desk. Record this value in the “Height” column of your table.
Step 3
4. Repeat steps 2 and 3 for three more objects assigned by your teacher.
What Did You Find Out?
1. Describe the difficulties of locating objects using this technique. 2. What could be done to improve this way of measuring? 3. Compare your coordinates (angle and height measurements) with those of a classmate. Why are they different? 4. How does the time of day you take a measurement using an astrolabe affect the ability of someone else to find the same location? 5. Write a general rule about the accuracy of using an astrolabe to share the location of objects in the sky.
Object Angle Height
Example: Top hinge of door
Chapter 11 The components of the universe are separated by unimaginably vast distances. • MHR 399
Techniques for Indirectly Measuring Distance
As telescopes become larger and use more sophisticated technology, astronomers are increasingly able to see objects farther away. Telescopes cannot, however, directly determine the distance to objects in space. It is also not possible to physically measure such long distances. For these reasons, astronomers use a number of techniques to measure distances indirectly. Two such techniques have been used for thousands of years to determine distances on Earth: triangulation and parallax.
Triangulation
Imagine you are standing at the side of a lake and can see a small island in the distance. If you cannot reach the island, you have no way of directly measuring how far it is from where you are. The same problem confronts astronomers but on a far greater scale. How is it possible to determine the distance to stars and other objects in space if you are not able to reach them? There is a solution, fortunately, and it involves using simple geometry. By measuring two angles and the length of a baseline, the distance to any object that is visible can be determined (Figure 11.22). This technique is called triangulation. To use triangulation to determine the distance to the island from the shoreline, you would follow the steps below. These steps are illustrated in Figure 11.23 on the next page.
1. Measure a straight baseline along the shore. Remember, the longer the baseline, the more accurate the calculations. Example: 120 m 2. At one end of the line, use a protractor to measure angle A between the baseline and a particular point on the island, such as the bottom of a tree. Example: 75° 3. Move to the opposite end of the baseline and again measure angle B between the baseline and the same point on the same tree. Example: 65° 4. Using the two angles and the length of the baseline, construct a scale drawing. 5. On your scale drawing, mark a perpendicular line between the baseline and the tree. Measure the length of this line, and then calculate the actual distance according to the scale of the drawing. The distance to the tree will match the scale distance. Example: The scale distance was 8.2 cm. At 1 cm equal to 20 m, the true distance is 164 m (8.2 20).
angles to be measured
baseline
point on the distant object
distance to be measured in a scale diagram
lines drawn from the baseline ends to the point on the distant object
A B
Figure 11.22 Triangulation to calculate a distance
400 MHR • Unit 4 Space Exploration
120 m
A B
75˚ 65˚
tree on island
baseline (6.0 cm) Scale of drawing: 1 cm = 20 m
measurement of unknown distance (8.2 cm)
A B
a. Create a baseline. Mark off a long, straight line, 120 m long, just up from the shore. The end of the baseline where you start measuring can be marked with a stake.
b. Measure the angles from the ends of the baseline. Stand at one end of the baseline, facing the island, and imagine a straight line extended to a point on the island (for example, to a tall tree). Then, measure angle A between that line and the baseline, and record it. At the other end of the baseline, repeat the procedure for angle B. Suppose the two angles you record are 75º for angle A and 65º for angle B.
c. Make a scale drawing of the imaginary triangle. First, choose an appropriate scale (in this case, 1 cm = 20 m), and draw the baseline. Then, using a protractor and a ruler, draw a line from each end of the baseline at the angles you recorded. The point at which the two lines cross is the position of the object (in this example, the tree). The shortest distance from that point to the baseline (the dotted line) represents the distance between the shore and the tree on the island. In this case, the line measures 8.2 cm, or 164 m in real life.
Figure 11.23 This example shows how you could use triangulation to calculate the distance from the shoreline of the lake to the island.
Sun
Venus
Earth
d
a
402 MHR • Unit 4 Space Exploration
The effect of parallax is used to find the distance to stars that are reasonably close to Earth. You might think that finding the distance to the nearest star to us, the Sun, would be easy. In reality, however, the Sun is too close to allow us to determine an accurate distance using parallax.
To solve this problem, astronomers had to combine a new technology with an ancient technique: radar and trigonometry. Radar signals travel at the speed of light. Astronomers can measure the amount of time it takes for a signal to bounce off an object and return to the transmitter. The distance can then be calculated. However, astronomers could not just aim for the Sun, because its surface provides nothing solid from which to reflect a signal. For that reason, they bounced the signal off the nearby planet Venus and used trigonometry to calculate the distance. In this activity, you will simulate the calculation of the distance to the Sun.
Materials
- pen
- paper
- calculator
- ruler
- protractor
What to Do
1. On the diagram shown here, use the ruler to measure the distance from Earth to Venus in centimetres. Record this number in your notebook and label it “a”. 2. Use the protractor to measure the angle . Record this value. 3. The distance to the Sun, d, can be calculated using the formula: d =. Use the calculator to determine the distance to the Sun on the diagram. 4. Multiply your calculated value using the scale 1 cm = 14 000 000 km. This value will give you the relative distance from Earth to the Sun.
What Did You Find Out?
1. This technique has provided an extremely accurate value for the actual distance from Earth to the Sun. Describe any problems you experienced using the technique in this activity. 2. Suggest how you could make your calculation using this technique more accurate.
11-3B^ How Close Is the Sun? F i n d^ O u t^ A C T I V I T Y
a cos
Chapter 11 The components of the universe are separated by unimaginably vast distances. • MHR 403
Safety
- NEVER look directly at the Sun under any circumstances.
Materials
For each group:
- metre stick
- 2 squares of cardboard (20 cm 20 cm), one with a 1 cm diameter hole
- white paper (6 cm 6 cm)
- aluminum foil (4 cm 4 cm)
- clear adhesive tape
- pin, or mechanical pencil
- ruler
- pencil
- calculator
The Sun is about 150 million km away from Earth. In this activity, using a simple tool and some straightforward arithmetic, we can produce a very accurate calculation of the diameter of the Sun.
Question
How can you determine the diameter of the Sun?
Procedure
1. Use the metre stick, cardboard, paper, aluminum foil, and tape to assemble the apparatus shown here. 2. Using the pin, carefully poke a small hole in the aluminum foil. 3. Move outdoors. Steadying the apparatus against your stomach, aim the aluminum foil end toward the Sun. Try to capture the image of the Sun’s disk in focus on the white paper. 4. Have your partner use a pencil to mark the diameter of the Sun’s image on the white paper. 5. Repeat step 4 two or three more times. 6. Measure the diameters you have marked off and calculate an average diameter.
Analyze
1. To calculate the Sun’s diameter, use the average diameter you have measured in the following formula. d = diameter (cm) D = Sun’s diameter (km) 2. Your teacher will provide you with the accepted value. Use that to calculate your percent error.
% error = 100%
Conclude and Apply
1. (a) What was your calculated percent error? (b) Do you think your percent error is reasonable? Explain. 2. What do you think were sources of error in this activity? 3. Suggest ways the activity could be improved to lower your percent error.
11-3C^ How Wide Is the Sun?
SkillCheck
- Observing
- Measuring
- Evaluating information
- Working co-operatively
Conduct an INVESTIGATION
Inquiry Focus
white paper to sketch on
hole in cardboard covered with foil
metre stick tape to Sun
Step 1
D
image pinhole Sun
100 cm 150 000 000 km
d
d 100 cm
actual diameter – calculated diameter actual value
D
150 000 000 km
Checking Concepts
1. What is an astronomical unit? 2. Define a light-year. 3. Explain how you would use triangulation to determine the distance to an object on Earth’s surface. 4. Why do you need to have a baseline to make a triangulation measurement? 5. Describe what parallax means. 6. Why are kilometres usually not used to indicate distances in space?
Understanding Key Ideas
7. Why are the distances between bodies in the solar system not measured in light-years? 8. Why is it best to use a long baseline when determining distances using triangulation? 9. Explain why parallax is not a good technique for determining distances of stars that are extremely far away (that is, greater than 500 light-years). 10. A student is trying to determine the distance from where she is standing to a tall tree in a field nearby. She collected and recorded the following data: Angle A 45° Angle B 62° Baseline 10 m Scale: 1 cm 5 m In your notebook, draw a scale model using these figures and calculate the distance to the tree. 11. Parallax and triangulation are considered to be indirect measurement techniques. Why are such techniques used to measure distances in space?
Our closest neighbouring star after the Sun is Proxima Centauri. It is a small red dwarf star less than as bright as the Sun. It would take 10 stars the size of Proxima Centauri to equal the mass of the Sun. The distance to the star is 4.2 light-years, relatively close compared with distances to other objects. Imagine humans sent explorers in a spacecraft to observe a solar system discovered around Proxima Centauri. Describe the difficulties that we on Earth would have in communicating with the spacecraft as it travelled farther from Earth and eventually arrived at the star.
1 100
P ause and R eflect
Chapter 11 The components of the universe are separated by unimaginably vast distances. • MHR 405
406 MHR • Unit 4 Space Exploration
Chapter
Prepare Your Own Summary
In this chapter, you learned about several components of space. Create your own summary of the key ideas from this chapter. You may include graphic organizers or illustrations with your notes. (See Science Skill 12 for help with using graphic organizers.) Use the following headings to organize your notes:
1. Life Cycles of Stars 2. Analyzing the Composition of Stars 3. The Solar System 4. Measuring Distances in Space
Checking Concepts
1. What is the process that creates energy in stars? 2. At which stage in a star’s life will it turn into a supernova? 3. How old is the solar system? 4. Draw a labelled cross-section of the Sun’s outer atmosphere. Label the chromosphere, photosphere, sunspots, and prominences. 5. How does the temperature of sunspots compare with temperatures in the rest of the photosphere? 6. How can storms on the Sun affect people on Earth? 7. What name do astronomers give to the average distance between the Sun and Earth? 8. Why do we refer to the inner planets as “terrestrial”? 9. Describe characteristics all the Jovian planets share. 10. Copy and complete the diagram of the solar system shown below, labelling the key parts. 11. Why does a comet’s tail always point away from the Sun? 12. Why are light-years used to measure distances in space?
m a s s i v e s t a r s
i n t e r m e d i a t e m a s s (^) stars lowm asss tars
hotter bluer
temperature colour
luminosity our Sun white dwarfs
supergiants (^) red giants
dimmer
red dwarfs
cooler redder
dim & hot
bright & hot
dim & cool
bright & cool brighter
m
a i n
s e
q u
e n c
e
Hertzsprung- Russell diagram, Question 15 on the next page
Solar system, Question 10
