1
00:00:00,000 --> 00:00:13,240
Hi, I'm Christy Carlson Romano.

2
00:00:13,240 --> 00:00:17,380
You know me as Wren Stevens from Disney Channel's hit TV series, Even Stevens.

3
00:00:17,380 --> 00:00:21,220
On this episode of NASA Connect, you'll learn about the concept of scaling and the math

4
00:00:21,220 --> 00:00:23,180
principles associated with it.

5
00:00:23,180 --> 00:00:27,900
You'll also learn about the transit of Venus, an astronomical event that is way cool.

6
00:00:27,900 --> 00:00:31,980
So stay tuned, because Jennifer Pulley, your host, is going to take you on another exciting

7
00:00:31,980 --> 00:00:34,900
episode of NASA Connect.

8
00:00:57,900 --> 00:01:08,780
Hi, I'm Jennifer Pulley, and welcome to NASA Connect, the show that connects you to math,

9
00:01:08,780 --> 00:01:11,620
science, technology, and NASA.

10
00:01:11,620 --> 00:01:16,620
Today, we are at NASA Kennedy Space Center on the east coast of Florida, and behind me

11
00:01:16,620 --> 00:01:20,100
is the Vehicle Assembly Building, or VAB.

12
00:01:20,100 --> 00:01:24,500
This is where NASA assembles all the components of the space shuttle system.

13
00:01:24,500 --> 00:01:29,740
Kennedy Space Center is also a site where NASA launches satellites that study the Earth

14
00:01:29,740 --> 00:01:31,260
and our solar system.

15
00:01:31,260 --> 00:01:37,100
In fact, the satellite Voyager 1, which was launched right here back in 1977, is very

16
00:01:37,100 --> 00:01:39,380
close to leaving our solar system.

17
00:01:39,380 --> 00:01:44,340
It's over 13 billion kilometers, or 8 billion miles, from Earth.

18
00:01:44,340 --> 00:01:45,740
Can you imagine that?

19
00:01:45,740 --> 00:01:47,780
Thirteen billion kilometers?

20
00:01:47,780 --> 00:01:51,020
Whew, it would be hard to count that high.

21
00:01:51,020 --> 00:01:58,420
But look at all the digits that 13 billion represents.

22
00:01:58,420 --> 00:02:04,820
I don't know about you, but it's hard for me to imagine just how far away 13 billion

23
00:02:04,820 --> 00:02:06,020
kilometers is.

24
00:02:06,020 --> 00:02:11,740
I mean, how large is the solar system?

25
00:02:11,740 --> 00:02:20,180
It would probably make more sense to us if we could see a scale model of the solar system.

26
00:02:20,180 --> 00:02:25,060
This would give a better understanding of how far away Voyager 1 or the other planets

27
00:02:25,060 --> 00:02:29,220
in the solar system are from Earth.

28
00:02:29,220 --> 00:02:34,980
The focus of today's program is to learn why we use scale models to determine the size

29
00:02:34,980 --> 00:02:39,020
and distance of objects in our solar system and beyond.

30
00:02:39,020 --> 00:02:44,740
In order to learn how to scale the solar system, we must first understand the concept of scaling.

31
00:02:44,740 --> 00:02:49,780
During the course of the program, you will be asked to answer several inquiry-based questions.

32
00:02:49,780 --> 00:02:53,700
After the questions appear on the screen, your teacher will pause the program to allow

33
00:02:53,700 --> 00:02:56,820
you time to answer and discuss the questions.

34
00:02:56,820 --> 00:03:00,460
This is your time to explore and become critical thinkers.

35
00:03:00,460 --> 00:03:05,540
Students working in groups take a few minutes to answer the following questions.

36
00:03:05,540 --> 00:03:09,220
What does it mean to scale?

37
00:03:09,220 --> 00:03:15,060
Why is it sometimes necessary to use scale models or drawings?

38
00:03:15,340 --> 00:03:20,380
List some math terms associated with scale models or drawings.

39
00:03:20,380 --> 00:03:24,340
It's now time to pause the program and answer the questions.

40
00:03:24,340 --> 00:03:31,860
A scale model or drawing is used to represent an object that is too large or too small to

41
00:03:31,860 --> 00:03:35,400
be drawn or built at actual size.

42
00:03:35,400 --> 00:03:41,180
The scale gives the ratio of the measurements in the model or drawing to the measurements

43
00:03:41,180 --> 00:03:43,220
of the actual object.

44
00:03:43,380 --> 00:03:49,140
Remember guys, a ratio is a fraction that is used to compare the size of two numbers

45
00:03:49,140 --> 00:03:50,140
to each other.

46
00:03:50,140 --> 00:03:51,700
Let's take a look at an example.

47
00:03:51,700 --> 00:03:55,860
One of the most common types of scale drawings is a map.

48
00:03:55,860 --> 00:04:01,380
Maps are very useful when planning a trip, whether it is across town or across the country.

49
00:04:01,380 --> 00:04:06,860
Norbert and Zot are planning to drive from NASA Kennedy Space Center to Washington, D.C.

50
00:04:06,860 --> 00:04:11,220
Norbert wants to estimate the distance he and Zot will travel.

51
00:04:11,220 --> 00:04:17,220
The scale on Norbert's map reads 1 centimeter equals 100 kilometers.

52
00:04:17,220 --> 00:04:22,940
How can he estimate the distance in kilometers from Kennedy Space Center to Washington, D.C.

53
00:04:22,940 --> 00:04:24,620
using the given scale?

54
00:04:24,620 --> 00:04:30,620
The scale can be written as the fraction 1 centimeter over 100 kilometers.

55
00:04:30,620 --> 00:04:37,540
The first number, 1 centimeter, represents the map distance and the second number, 100

56
00:04:37,540 --> 00:04:40,780
kilometers, represents the actual distance.

57
00:04:40,780 --> 00:04:46,780
First, using a metric ruler and the given map, measure the linear distance from Kennedy

58
00:04:46,780 --> 00:04:49,800
Space Center to Washington, D.C.

59
00:04:49,800 --> 00:04:56,140
On Norbert's map, this distance is approximately 13 and a half centimeters.

60
00:04:56,140 --> 00:05:00,620
Now we have all the information we need to set up our proportion.

61
00:05:00,620 --> 00:05:05,360
Remember guys, a proportion is a pair of equal ratios.

62
00:05:05,360 --> 00:05:11,180
The first ratio is the map scale and the second ratio is the distance from Kennedy

63
00:05:11,180 --> 00:05:14,600
Space Center to Washington, D.C.

64
00:05:14,600 --> 00:05:18,720
Let's set these two ratios equal to each other.

65
00:05:18,720 --> 00:05:22,700
N represents the distance that we are trying to calculate.

66
00:05:22,700 --> 00:05:30,560
This proportion can be read as 1 centimeter is to 100 kilometers as 13 and a half centimeters

67
00:05:30,560 --> 00:05:33,520
is to N kilometers.

68
00:05:33,520 --> 00:05:39,040
In a proportion, the cross products of the two ratios are equal.

69
00:05:39,040 --> 00:05:45,960
In other words, the product of the top value from the first ratio and the bottom value

70
00:05:45,960 --> 00:05:53,360
from the second ratio is equal to the product of the top value of the second ratio and the

71
00:05:53,360 --> 00:05:56,480
bottom value from the first ratio.

72
00:05:56,480 --> 00:06:04,160
We can write the cross product as 1 centimeter times N kilometers equals 100 kilometers times

73
00:06:04,160 --> 00:06:06,920
13 and a half centimeters.

74
00:06:06,920 --> 00:06:12,440
Using multiplication, Norbert calculated the actual distance between Kennedy Space Center

75
00:06:12,440 --> 00:06:17,520
and Washington, D.C. to be about 1,350 kilometers.

76
00:06:17,520 --> 00:06:22,020
Students, here is an important point for you to remember.

77
00:06:22,020 --> 00:06:26,080
Proportions often include different units of measurements.

78
00:06:26,080 --> 00:06:33,560
Units must be the same across the top and bottom or down the left and right sides.

79
00:06:33,560 --> 00:06:40,720
If the units only match diagonally, then the ratios do not form a proportion.

80
00:06:40,720 --> 00:06:43,960
So guys, are you still having trouble trying to understand scaling?

81
00:06:43,960 --> 00:06:49,440
Okay, well let's look at another example, this time using a scale model.

82
00:06:49,440 --> 00:06:53,720
Right behind me is a replica of the space shuttle and this right here, this is a scale

83
00:06:53,720 --> 00:06:55,360
model of the space shuttle.

84
00:06:55,360 --> 00:07:05,320
The actual space shuttle has a length of 37.2 meters, a height of 17.3 meters, and

85
00:07:05,320 --> 00:07:10,960
a width or wingspan of 23.8 meters.

86
00:07:10,960 --> 00:07:16,000
Now this shuttle model is a 1,100 scale of the actual space shuttle.

87
00:07:16,000 --> 00:07:20,240
Now that is 1 meter equals 100 meters.

88
00:07:20,240 --> 00:07:25,600
So using that scale, let's set up a proportion to calculate the length of this space shuttle

89
00:07:25,600 --> 00:07:27,040
model.

90
00:07:27,040 --> 00:07:32,520
The first ratio is the model scale and the second ratio is the length of the model to

91
00:07:32,520 --> 00:07:35,400
the actual shuttle length.

92
00:07:35,400 --> 00:07:38,680
N represents the length of the shuttle model.

93
00:07:38,680 --> 00:07:42,120
We set these two ratios equal to each other.

94
00:07:42,120 --> 00:07:48,520
Now remember, in our proportion, the cross products of the two ratios are equal.

95
00:07:48,520 --> 00:07:59,240
We write the cross product as 1 meter times 37.2 meters equals 100 meters times N meters.

96
00:07:59,240 --> 00:08:07,080
Dividing 37.2 by 100 gives us the length of the shuttle model, which is 0.372 meters or

97
00:08:07,080 --> 00:08:09,080
approximately 14 and a half inches.

98
00:08:09,080 --> 00:08:11,080
Well, that wasn't too bad, was it?

99
00:08:11,080 --> 00:08:14,360
Do you think you can handle the other two dimensions?

100
00:08:14,360 --> 00:08:24,000
So now it's your turn to calculate the height and the width or wingspan of the shuttle model

101
00:08:24,000 --> 00:08:25,480
using the given scale.

102
00:08:25,480 --> 00:08:30,640
Remember, the height of the actual shuttle is 17.3 meters.

103
00:08:30,640 --> 00:08:40,520
The width or wingspan is 23.8 meters, and the scale is 1 meter equals 100 meters.

104
00:08:40,520 --> 00:08:46,640
It's now time to pause the program to calculate the height and width of the shuttle model.

105
00:08:46,640 --> 00:08:48,840
So guys, how did you do?

106
00:08:48,840 --> 00:08:51,360
Let's check your answers with mine.

107
00:08:51,360 --> 00:08:58,200
Earlier, we calculated the length of the shuttle model to be 0.372 meters.

108
00:08:58,200 --> 00:09:05,760
I calculated the height of the model to be 0.173 meters or approximately 7 inches and

109
00:09:05,760 --> 00:09:12,920
the width or wingspan to be 0.238 meters or approximately 9 and a half inches.

110
00:09:12,920 --> 00:09:14,640
Did you get the same answers?

111
00:09:14,640 --> 00:09:16,640
If you did, great job.

112
00:09:16,640 --> 00:09:19,000
And if you didn't, don't be discouraged.

113
00:09:19,000 --> 00:09:21,800
Just go back and check over your work carefully.

114
00:09:21,800 --> 00:09:26,200
Make sure you set up your proportions and multiplied correctly.

115
00:09:26,200 --> 00:09:31,120
You know, scientists and engineers learn a great deal from making mistakes.

116
00:09:31,120 --> 00:09:35,200
Now that you have a better understanding of scaling, let's turn our attention to the focus

117
00:09:35,200 --> 00:09:38,960
of today's program, which is scaling the solar system.

118
00:09:38,960 --> 00:09:44,400
Dr. Stan Odenwald, an astronomer and scientist at NASA Goddard Space Flight Center, has a scoop.

119
00:09:44,400 --> 00:09:49,040
Thanks, Jennifer.

120
00:09:49,040 --> 00:09:53,080
When we talk about the distances between points of interest, we instinctively use units that

121
00:09:53,080 --> 00:09:55,320
make sense to us and that are convenient.

122
00:09:55,320 --> 00:09:59,720
For example, what unit of measure would you use to describe the distance from Washington,

123
00:09:59,720 --> 00:10:02,280
D.C. to Los Angeles, California?

124
00:10:02,280 --> 00:10:06,560
Would you use miles, inches, kilometers, or meters?

125
00:10:06,560 --> 00:10:08,080
What about your height?

126
00:10:08,080 --> 00:10:10,860
Would you measure it in inches or feet?

127
00:10:10,860 --> 00:10:12,960
And how about the width of your classroom?

128
00:10:12,960 --> 00:10:16,280
Do you use kilometers, meters, or feet?

129
00:10:16,280 --> 00:10:20,560
You can choose any unit of measure you wish, as long as it's convenient for everyone to

130
00:10:20,560 --> 00:10:21,960
understand.

131
00:10:21,960 --> 00:10:25,960
When describing distances at the scale of the solar system, even units like miles and

132
00:10:25,960 --> 00:10:29,840
kilometers lead to numbers that are in the millions or the billions, and that makes it

133
00:10:29,840 --> 00:10:31,920
very hard to understand them.

134
00:10:31,920 --> 00:10:38,080
For example, the distance between the Earth and the Sun is about 149 million kilometers.

135
00:10:38,080 --> 00:10:42,800
Between the Sun and Pluto, the distance is about 5.9 billion kilometers.

136
00:10:42,800 --> 00:10:45,920
But suppose we wanted to compare these two numbers.

137
00:10:45,920 --> 00:10:52,420
It's not easy to see that Pluto is about 40 times as far from the Sun as Earth is.

138
00:10:52,420 --> 00:10:56,400
It would make sense to use a smaller scale in order to get a better idea of the distances

139
00:10:56,400 --> 00:10:57,800
between the planets.

140
00:10:57,800 --> 00:11:00,720
To come up with that scale, we have to define a baseline.

141
00:11:00,720 --> 00:11:05,200
The baseline that astronomers use is the distance between the Earth and the Sun.

142
00:11:05,200 --> 00:11:08,080
This distance is known as the astronomical unit.

143
00:11:08,080 --> 00:11:13,440
The astronomical unit, or AU, represents the distance between the Earth and the Sun, which

144
00:11:13,440 --> 00:11:15,920
is about 93 million miles.

145
00:11:15,920 --> 00:11:20,140
The astronomical unit is the baseline that astronomers use to determine the distances

146
00:11:20,140 --> 00:11:24,280
to the planets in our solar system and to the stars beyond.

147
00:11:24,280 --> 00:11:28,440
So let's have a look at the scale of the solar system, where one astronomical unit equals

148
00:11:28,440 --> 00:11:30,680
93 million miles.

149
00:11:30,680 --> 00:11:34,600
Based on the astronomical unit, it's easy to compare the distances between all the other

150
00:11:34,600 --> 00:11:36,520
objects in the solar system.

151
00:11:36,520 --> 00:11:41,000
The accompanying chart shows the distances to the planets from the Sun in terms of astronomical

152
00:11:41,000 --> 00:11:42,320
units.

153
00:11:42,320 --> 00:11:43,840
Let's look at Mars.

154
00:11:43,840 --> 00:11:47,800
We can quickly see that Mars is one and a half times further away from the Sun than

155
00:11:47,800 --> 00:11:49,060
Earth is.

156
00:11:49,060 --> 00:11:52,520
So how far is Mars from the Sun in miles?

157
00:11:52,520 --> 00:11:56,600
Remember the process Jennifer demonstrated earlier in the program to solve problems involving

158
00:11:56,600 --> 00:11:57,800
scaling?

159
00:11:57,800 --> 00:12:01,200
We can solve the Mars distance problem using a proportion.

160
00:12:01,200 --> 00:12:06,840
The first ratio is the scale, and the second ratio is the distance of Mars to the Sun.

161
00:12:06,840 --> 00:12:10,880
And miles represents the distance from Mars to the Sun.

162
00:12:10,880 --> 00:12:14,960
After setting these ratios equal to each other, let's find the cross products.

163
00:12:14,960 --> 00:12:21,840
The equation becomes 1 times n equals 93 million times 1.52.

164
00:12:21,840 --> 00:12:26,680
Multiplying, we get the distance from Mars to the Sun to be approximately 141 million

165
00:12:26,680 --> 00:12:28,560
miles.

166
00:12:28,560 --> 00:12:32,920
Using the astronomical unit instead of the mile or the kilometer makes it easier to compare

167
00:12:32,920 --> 00:12:35,520
the distances between the planets and the Sun.

168
00:12:35,520 --> 00:12:39,420
For example, it's easier to remember that Mars is one and a half times further away

169
00:12:39,420 --> 00:12:43,760
from the Sun than the Earth than it is to remember that it's 48 million miles farther

170
00:12:43,760 --> 00:12:47,720
away from the Sun than the Earth.

171
00:12:47,720 --> 00:12:51,920
If you recall from earlier in the program, the Voyager spacecraft is 8 billion miles

172
00:12:51,920 --> 00:12:54,800
or 13 billion kilometers from the Earth.

173
00:12:54,800 --> 00:12:59,880
It's at the far edge of our solar system, ready to head out into interstellar space.

174
00:12:59,880 --> 00:13:03,880
Based on what you've learned about scaling and the astronomical unit, can you estimate

175
00:13:03,880 --> 00:13:08,080
the distance of Voyager 1 from the Earth in astronomical units?

176
00:13:08,080 --> 00:13:12,040
Working with a partner, take a few minutes and see if you can solve this problem.

177
00:13:12,040 --> 00:13:15,600
Voyager 1 is over 8 billion miles away from Earth.

178
00:13:15,600 --> 00:13:20,840
Guess how far, in astronomical units, Voyager 1 is from the Earth.

179
00:13:20,840 --> 00:13:25,920
Remember the scale is 1 astronomical unit equals 93 million miles.

180
00:13:25,920 --> 00:13:30,280
Teachers, you may now pause the program so students can answer the problem.

181
00:13:30,280 --> 00:13:32,880
Okay, so what did you come up with?

182
00:13:32,880 --> 00:13:37,880
If you said that Voyager was 86 astronomical units away from the Earth, you're correct.

183
00:13:37,880 --> 00:13:40,280
Do you have a sense for how far that is?

184
00:13:40,280 --> 00:13:44,880
The planet Pluto is 40 astronomical units away from the Earth, so that means Voyager

185
00:13:44,880 --> 00:13:48,440
is twice as far away from the Earth as the planet Pluto.

186
00:13:48,440 --> 00:13:52,600
Suppose that Voyager 1 were stationary and you were able to ride in a car traveling at

187
00:13:52,600 --> 00:13:55,400
55 miles per hour to get to it.

188
00:13:55,400 --> 00:14:00,400
The trip would take you over 16,000 years just to reach the satellite.

189
00:14:00,400 --> 00:14:03,040
That would be quite a lengthy and expensive vacation.

190
00:14:03,040 --> 00:14:06,960
Jennifer, I think the students are ready for that hands-on activity now.

191
00:14:06,960 --> 00:14:08,680
Could you send them back to me when you're finished?

192
00:14:08,680 --> 00:14:12,280
I have a real tough question for them to answer.

193
00:14:13,280 --> 00:14:14,280
Thanks, Sten.

194
00:14:14,280 --> 00:14:17,280
We'll get back to you a little later in the program.

195
00:14:17,280 --> 00:14:22,400
But first, students from Brewster Middle School at Camp Lejeune, North Carolina, will preview

196
00:14:22,400 --> 00:14:25,280
this program's hands-on activity.

197
00:14:25,280 --> 00:14:31,960
Hi, NASA Connect has asked us to show you this program's hands-on activity.

198
00:14:31,960 --> 00:14:37,480
In this activity, you will use graphing, measurement, and ratios to construct a scaled model of

199
00:14:37,480 --> 00:14:42,120
the solar system and relate each planet to the sun.

200
00:14:42,120 --> 00:14:46,920
And you will explore the scales needed to represent the size of the planets and the

201
00:14:46,920 --> 00:14:49,440
distances to the sun.

202
00:14:49,440 --> 00:14:53,480
You can download a copy of the educator guide containing directions and a materials list

203
00:14:53,480 --> 00:14:55,400
from the NASA Connect website.

204
00:14:55,400 --> 00:15:00,720
Working in groups, students will complete the activity by using the scale model chart

205
00:15:00,720 --> 00:15:03,400
and the planet templates.

206
00:15:03,400 --> 00:15:05,880
Each group will be assigned a planet.

207
00:15:05,880 --> 00:15:09,560
Cut out your assigned planet using the planet template.

208
00:15:09,600 --> 00:15:17,720
The scale for this activity is 1 toilet paper sheet equals 30,102,900 kilometers.

209
00:15:17,720 --> 00:15:22,440
Using the scale, students complete column 4 on the scale model chart.

210
00:15:22,440 --> 00:15:25,560
Remember the math concepts you learned earlier in the program?

211
00:15:25,560 --> 00:15:28,680
This is your chance to put your math skills to the test.

212
00:15:28,680 --> 00:15:32,680
Next, you will complete column 5 on the scale model chart.

213
00:15:32,680 --> 00:15:39,480
The scale needed to complete this column is 1 AU or astronomical unit equals 5 toilet

214
00:15:39,480 --> 00:15:41,160
paper sheets.

215
00:15:41,160 --> 00:15:45,320
Groups should check each other's work to make sure all values are correct.

216
00:15:45,320 --> 00:15:49,680
After completing the scale model chart, each group should roll out the number of toilet

217
00:15:49,680 --> 00:15:52,840
paper sheets needed for its assigned planet.

218
00:15:52,840 --> 00:15:55,200
Now it's time to head to the staging area.

219
00:15:55,200 --> 00:15:59,160
This could be in a gym, hallway, or even outside.

220
00:15:59,160 --> 00:16:02,000
Place the sun in a central position.

221
00:16:02,000 --> 00:16:06,480
Students attach your pre-measured toilet paper strip to the sun and let it extend outward

222
00:16:06,480 --> 00:16:08,720
in various directions.

223
00:16:08,720 --> 00:16:12,600
Don't forget to tape your assigned planet on the end of the strip.

224
00:16:12,600 --> 00:16:17,240
You will need about 23 meters or 75 feet in one direction.

225
00:16:17,240 --> 00:16:21,680
Based on your solar system model, you will be asked to answer several critical thinking

226
00:16:21,680 --> 00:16:23,360
questions.

227
00:16:23,360 --> 00:16:26,840
Graphing is a great way to visually represent data.

228
00:16:26,840 --> 00:16:32,080
Each group will construct and analyze two graphs using an appropriate type of graph

229
00:16:32,080 --> 00:16:34,040
and scale of your choice.

230
00:16:34,040 --> 00:16:36,640
Be careful with the type of graph you choose.

231
00:16:36,640 --> 00:16:39,520
Don't forget to check out the web activity for this program.

232
00:16:39,520 --> 00:16:46,160
You can download it from the NASA Connect website.

233
00:16:46,160 --> 00:16:47,920
Great job Brewster Middle School.

234
00:16:47,920 --> 00:16:52,520
Okay, now that you guys have a preview of this program's hands-on activity, now it's

235
00:16:52,520 --> 00:16:58,320
time to pause the program and see if you can construct a scale model of the solar system.

236
00:16:58,320 --> 00:17:01,000
So how was the activity?

237
00:17:01,000 --> 00:17:06,440
Hopefully it helped reinforce the math concepts you learned earlier in today's program.

238
00:17:06,440 --> 00:17:08,160
Now let's review.

239
00:17:08,160 --> 00:17:12,760
In the beginning of the program, we talked about the importance of scaling, especially

240
00:17:12,760 --> 00:17:15,160
when it comes to maps and models.

241
00:17:15,160 --> 00:17:22,340
You learned that fractions, decimals, ratios, and proportions are all important math concepts

242
00:17:22,340 --> 00:17:24,420
when dealing with scales.

243
00:17:24,420 --> 00:17:30,500
STEN introduced you to the astronomical unit, the unit used to scale the solar system.

244
00:17:30,500 --> 00:17:33,900
Later in the program, I have an interesting challenge for you.

245
00:17:33,900 --> 00:17:37,660
But before we get to that, STEN has a few more questions for you.

246
00:17:37,660 --> 00:17:43,260
Let's head back to STEN now and learn more about scaling the solar system.

247
00:17:43,260 --> 00:17:47,380
Hey, it's great to have you back.

248
00:17:47,380 --> 00:17:52,140
In the last segment, we introduced the scale of the solar system and the astronomical unit.

249
00:17:52,140 --> 00:17:56,380
Believe it or not, astronomers once knew only what the distances were in astronomical

250
00:17:56,380 --> 00:17:58,980
units, not in actual miles.

251
00:17:58,980 --> 00:18:03,820
Recall the following chart that shows the distances of the planets to the sun.

252
00:18:03,820 --> 00:18:10,040
Between 1609 and 1619, the astronomer Johannes Kepler used precise measurements of the planets

253
00:18:10,040 --> 00:18:12,780
in the sky to determine their orbits.

254
00:18:12,780 --> 00:18:17,380
But his geometric model was based on the scale of the Earth's orbit, not on its actual diameter

255
00:18:17,380 --> 00:18:19,620
in kilometers or miles.

256
00:18:19,620 --> 00:18:23,220
He determined the ratio of the distance of each planet to the sun relative to Earth's

257
00:18:23,220 --> 00:18:24,860
distance to the sun.

258
00:18:24,860 --> 00:18:30,500
His baseline unit, the distance from Earth to the sun, was designated as exactly 1 AU,

259
00:18:30,500 --> 00:18:32,780
or 1 astronomical unit.

260
00:18:32,780 --> 00:18:36,620
The problem is that Kepler could not accurately determine the distance between the Earth and

261
00:18:36,620 --> 00:18:37,620
the sun.

262
00:18:37,620 --> 00:18:42,620
The best estimates at that time ranged from 50 million miles to over 200 million miles.

263
00:18:42,620 --> 00:18:48,260
But by the 1890s, astronomers began to know that number very precisely.

264
00:18:48,260 --> 00:18:52,740
How did scientists without modern space technology and rockets do this?

265
00:18:52,740 --> 00:18:57,380
You can't just send a spacecraft to the sun and back to determine the distance.

266
00:18:57,380 --> 00:19:02,580
Human life, including Norbert and Zott, couldn't survive the intense heat produced by the sun.

267
00:19:02,580 --> 00:19:06,780
So the question for this segment of the program is, how do we determine that the Earth is

268
00:19:06,780 --> 00:19:11,360
93 million miles, or 149 million kilometers, from the sun?

269
00:19:11,360 --> 00:19:15,100
This would be a good time to pause the program and discuss the question with your teacher

270
00:19:15,100 --> 00:19:17,100
and your peers.

271
00:19:17,100 --> 00:19:19,300
So did you come up with any good ideas?

272
00:19:19,300 --> 00:19:20,820
If you didn't, don't worry about it.

273
00:19:20,820 --> 00:19:27,140
After all, it took astronomers about 2,000 years to figure out how to do it.

274
00:19:27,140 --> 00:19:31,460
The answer is that astronomers used a geometric technique called parallax to determine the

275
00:19:31,460 --> 00:19:33,820
distance between the Earth and the sun.

276
00:19:33,820 --> 00:19:37,180
Parallax is the apparent change in position of an object when you look at it from two

277
00:19:37,180 --> 00:19:39,700
different stations or points of view.

278
00:19:39,700 --> 00:19:43,060
It sounds mysterious, but you use this technique all the time.

279
00:19:43,060 --> 00:19:48,020
For example, let me show you how parallax works by using my thumb and that rocket in

280
00:19:48,020 --> 00:19:49,020
the background.

281
00:19:49,020 --> 00:19:52,380
First, hold your thumb out at arm's length.

282
00:19:52,380 --> 00:19:56,300
Now look at your thumb with your left eye open and your right eye closed.

283
00:19:56,300 --> 00:19:58,820
What do you notice about the position of your thumb?

284
00:19:58,820 --> 00:20:03,340
There seems to be an apparent change in position of your thumb from two points of view, your

285
00:20:03,340 --> 00:20:05,520
left eye and your right eye.

286
00:20:05,520 --> 00:20:10,140
Your brain uses this information to figure out how far away things are from you.

287
00:20:10,140 --> 00:20:14,300
General parallax calculations can be quite complicated, but here's an example of how

288
00:20:14,300 --> 00:20:19,180
we can determine the distance to that rocket using many of the same geometric principles.

289
00:20:19,180 --> 00:20:23,060
Suppose we wanted to approximate the distance between where I'm standing right here and

290
00:20:23,060 --> 00:20:24,700
that rocket over there.

291
00:20:24,700 --> 00:20:29,340
And suppose also that there was a body of water in between that we couldn't get across.

292
00:20:29,340 --> 00:20:34,140
Would you believe that we could do that by just using a pencil, a piece of paper, a ruler,

293
00:20:34,140 --> 00:20:36,500
a piece of rope and a protractor?

294
00:20:36,500 --> 00:20:40,020
The first thing we do is to lay our rope in a straight line.

295
00:20:40,020 --> 00:20:44,580
The rope will serve as our baseline and is 10 meters in length.

296
00:20:44,580 --> 00:20:49,060
Standing on the left end of the rope, which we will call position A, hold the protractor

297
00:20:49,060 --> 00:20:51,900
so that it is parallel to the baseline.

298
00:20:51,900 --> 00:20:56,340
Place the pencil on the inside of the protractor and move it along the curve until it lines

299
00:20:56,340 --> 00:20:57,700
up with the object.

300
00:20:57,700 --> 00:21:02,900
Being careful not to move your pencil, have a partner read and record the angle measurement.

301
00:21:02,900 --> 00:21:06,740
We then need to repeat the same procedure on the other side of the rope.

302
00:21:06,740 --> 00:21:08,940
We will call this position B.

303
00:21:09,020 --> 00:21:13,420
We now have two angle measurements and our baseline measurement, which is 10 meters,

304
00:21:13,420 --> 00:21:14,620
the length of our rope.

305
00:21:14,620 --> 00:21:19,780
On a sheet of paper along the bottom, we draw a line 10 centimeters long to represent our

306
00:21:19,780 --> 00:21:21,420
baseline.

307
00:21:21,420 --> 00:21:27,780
For this exercise, let the scale be 1 meter equals 1 centimeter.

308
00:21:27,780 --> 00:21:33,260
Mark one end of the drawn line as point A and the other end as point B.

309
00:21:33,260 --> 00:21:38,580
Using our protractor at point A, we measure an angle that is the same number of degrees

310
00:21:38,580 --> 00:21:42,580
as the angle we measured outside for point A.

311
00:21:42,580 --> 00:21:45,020
Let's mark and draw the angle.

312
00:21:45,020 --> 00:21:48,340
At point B, we do the same thing.

313
00:21:48,340 --> 00:21:52,740
Now measure an angle that is the same number of degrees as the angle we measured outside

314
00:21:52,740 --> 00:21:54,660
for point B.

315
00:21:54,660 --> 00:21:57,980
As you can see, the two lines intersect.

316
00:21:57,980 --> 00:22:02,420
We mark the point of intersection as point C.

317
00:22:02,420 --> 00:22:06,980
Now we draw a line perpendicular from point C to the baseline.

318
00:22:06,980 --> 00:22:11,380
Using our metric ruler, we can measure the distance of this perpendicular line.

319
00:22:11,380 --> 00:22:16,700
Finally, using the scale 1 meter equals 1 centimeter, we can approximate the distance

320
00:22:16,700 --> 00:22:19,860
the actual object was from the baseline.

321
00:22:19,860 --> 00:22:24,000
For our case, the object is approximately 20 meters away.

322
00:22:24,000 --> 00:22:28,460
In this example, we used a geometric technique called triangulation, which assumes that we

323
00:22:28,460 --> 00:22:31,860
know the baseline length and the two base angles.

324
00:22:31,860 --> 00:22:36,900
When astronomers use parallax, they measure the baseline length and the vertex angle.

325
00:22:36,940 --> 00:22:40,860
It is hard to use the parallax method in the classroom because you can't measure the vertex

326
00:22:40,860 --> 00:22:42,420
angle exactly.

327
00:22:42,420 --> 00:22:46,540
With proper measuring technology, this is not a problem for astronomers.

328
00:22:46,540 --> 00:22:51,500
To refine the actual Sun-Earth distance, parallax observations of the transit of Venus were

329
00:22:51,500 --> 00:22:55,460
made between 1761 and 1882.

330
00:22:55,460 --> 00:22:59,720
The transit of Venus occurs whenever the planet Venus passes in front of the Sun as viewed

331
00:22:59,720 --> 00:23:01,420
from the Earth.

332
00:23:01,420 --> 00:23:05,400
By observing the apparent shift in position of Venus against the background of the solar

333
00:23:05,400 --> 00:23:10,440
disk as seen from two different places on Earth, astronomers were able to use this parallax

334
00:23:10,440 --> 00:23:13,580
shift to determine the distance from the Earth to the Sun.

335
00:23:13,580 --> 00:23:17,960
The last Venus transit occurred in 1882, and we are fortunate to have another transit of

336
00:23:17,960 --> 00:23:21,720
Venus happening on Tuesday, June 8, 2004.

337
00:23:21,720 --> 00:23:26,800
This is an historic event because no one alive today was around when the last one occurred.

338
00:23:26,800 --> 00:23:31,120
To learn more about the transit of Venus, let's visit Dr. Janet Luhmann at the University

339
00:23:31,120 --> 00:23:34,360
of California's Space Science Lab in Berkeley, California.

340
00:23:36,400 --> 00:23:38,760
Thanks, Jen.

341
00:23:38,760 --> 00:23:44,280
A Venus transit occurs when Venus crosses the disk of the Sun as seen by an observer.

342
00:23:44,280 --> 00:23:48,400
It's like a solar eclipse in that Venus is located on the line between the Sun and the

343
00:23:48,400 --> 00:23:51,920
Earth, and therefore blocks some of the Sun's light.

344
00:23:51,920 --> 00:23:56,360
However, in a Venus transit, the amount of sunlight blocked is very small compared to

345
00:23:56,360 --> 00:24:01,120
a solar eclipse, and so the observer who is unaware will never notice it.

346
00:24:01,120 --> 00:24:05,160
Venus's circular shadow is much, much smaller than our Moon's shadow.

347
00:24:05,160 --> 00:24:09,400
Even though Venus is nearly the size of the Earth, it is much farther away than the Moon.

348
00:24:09,400 --> 00:24:14,640
In clear weather, Venus transits are visible with the naked eye or with a small telescope,

349
00:24:14,640 --> 00:24:18,240
which is why they became popular in the 1600s.

350
00:24:18,240 --> 00:24:22,880
Before the advent of radar, Venus transits were used mainly for the measurement of the

351
00:24:22,880 --> 00:24:27,140
astronomical unit, or the Sun-Earth distance, as you've heard earlier.

352
00:24:27,140 --> 00:24:31,980
The biggest activity surrounding the June 2004 Venus transit will be the International

353
00:24:31,980 --> 00:24:35,020
Network of Amateur Astronomers.

354
00:24:35,020 --> 00:24:39,240
These astronomers will measure the astronomical unit with the Venus transit using the same

355
00:24:39,240 --> 00:24:41,700
techniques as used by the early observers.

356
00:24:41,700 --> 00:24:47,060
An innovative aspect this time, however not available in 1882, is the widespread use of

357
00:24:47,060 --> 00:24:52,300
the Internet to organize international participation and the ease of access to the tools needed

358
00:24:52,300 --> 00:24:54,580
to make the parallax calculations.

359
00:24:54,580 --> 00:24:59,620
There also will be a few astronomical researchers who will try to exploit state-of-the-art observing

360
00:24:59,620 --> 00:25:04,220
tools to see what can be learned about the use of transits to investigate planets around

361
00:25:04,220 --> 00:25:05,780
other stars.

362
00:25:05,780 --> 00:25:08,980
Transits are currently being used to search for such planets.

363
00:25:08,980 --> 00:25:12,980
Perhaps this Venus transit will lead to some new technique or measurement that will allow

364
00:25:12,980 --> 00:25:19,100
future researchers to further study the terrestrial planets during long-range planet-finding missions.

365
00:25:19,100 --> 00:25:23,740
The Venus transit will also serve to remind us of Earth's place in the cosmos.

366
00:25:23,740 --> 00:25:27,980
The tiny dot crossing the solar disk is a terrestrial planet with an atmosphere, and

367
00:25:27,980 --> 00:25:29,700
yet it is far from an Earth.

368
00:25:29,700 --> 00:25:34,460
Venus was once called a twin Earth, in part because of its similar size and distance from

369
00:25:34,460 --> 00:25:35,620
the Sun.

370
00:25:35,620 --> 00:25:39,820
It is now known to be a place that is extremely hostile to life for reasons that are still

371
00:25:39,820 --> 00:25:40,900
under study.

372
00:25:40,900 --> 00:25:45,580
One can speculate how our own pale blue dot would look to some distant alien astronomer

373
00:25:45,580 --> 00:25:50,460
as it passed across the Sun in transit, and whether it has ever been so observed.

374
00:25:50,460 --> 00:25:53,660
Maybe one day humans will be able to observe the Earth transit.

375
00:25:53,660 --> 00:25:58,420
To learn more about the planet Venus and the Venus transit, check out the Sun-Earth Connection

376
00:25:58,420 --> 00:26:00,700
Education Forum website.

377
00:26:00,700 --> 00:26:05,180
Take it away, Jennifer.

378
00:26:05,180 --> 00:26:08,620
They say you learn something new every day, and I sure did.

379
00:26:08,620 --> 00:26:13,940
I'd never heard of transits before, and how astronomers and scientists use them to determine

380
00:26:13,940 --> 00:26:15,580
the astronomical unit.

381
00:26:15,580 --> 00:26:16,580
Thanks, Janet.

382
00:26:16,740 --> 00:26:20,740
Okay, guys, remember earlier in the program when I said I had an interesting challenge

383
00:26:20,740 --> 00:26:21,740
for you?

384
00:26:21,740 --> 00:26:25,140
Well, it's now time for Scaling the Solar System.

385
00:26:25,140 --> 00:26:31,420
Now, the astronomical unit, or AU, currently in use is derived from the average mean distance

386
00:26:31,420 --> 00:26:35,540
between the Earth and the Sun, which is approximately 93 million miles.

387
00:26:35,540 --> 00:26:42,160
Working in groups, your task is to make a proposal that uses the average mean distance

388
00:26:42,160 --> 00:26:47,780
between the Sun and another planet in our solar system as the basis for determining

389
00:26:47,780 --> 00:26:49,200
the astronomical unit.

390
00:26:49,200 --> 00:26:54,560
In other words, is there a better baseline distance to use rather than the Sun-Earth

391
00:26:54,560 --> 00:26:55,560
baseline?

392
00:26:55,560 --> 00:27:01,040
What about using a Sun-Jupiter baseline or a Sun-Pluto baseline?

393
00:27:01,040 --> 00:27:06,560
Once you choose another planet, you will have to recalculate the scale of the solar system

394
00:27:06,560 --> 00:27:12,520
using your new chosen baseline and then explain why your new baseline is a better choice than

395
00:27:12,520 --> 00:27:13,520
the Sun-Earth baseline.

396
00:27:13,520 --> 00:27:17,920
What are the advantages and disadvantages to your new scale?

397
00:27:17,920 --> 00:27:23,880
Detailed instructions and tips on how to make your proposal can be located at the NASA Connect

398
00:27:23,880 --> 00:27:24,880
website.

399
00:27:24,880 --> 00:27:28,360
From the website, we encourage you to submit your proposal.

400
00:27:28,360 --> 00:27:31,880
Your proposal will be seen by millions of students across the country.

401
00:27:31,880 --> 00:27:33,720
We look forward to your submittals.

402
00:27:34,000 --> 00:27:37,120
Well guys, that wraps up another episode of NASA Connect.

403
00:27:37,120 --> 00:27:42,840
I hope you have a better understanding of how and why astronomers and scientists use

404
00:27:42,840 --> 00:27:45,040
scale models of the solar system.

405
00:27:45,040 --> 00:27:48,320
We'd like to thank everyone who helped make this program possible.

406
00:27:48,320 --> 00:27:54,000
So until next time, stay connected to math, science, technology, and NASA.

407
00:27:54,000 --> 00:27:55,640
Bye from sunny Florida.

408
00:28:03,720 --> 00:28:31,720
Captioning funded by the NAC Foundation of America.

409
00:28:33,720 --> 00:28:35,720
NASA Jet Propulsion Laboratory, California Institute of Technology