1
00:00:00,000 --> 00:00:14,800
Hey, Bill Nye the Science Guy here.

2
00:00:14,800 --> 00:00:17,920
When you dream about going places, where does your mind take you?

3
00:00:17,920 --> 00:00:18,920
Somewhere on Earth?

4
00:00:18,920 --> 00:00:20,480
Or to the stars?

5
00:00:20,480 --> 00:00:24,520
If you spend time looking at the stars, you'll notice one that's a bit red.

6
00:00:24,520 --> 00:00:26,960
It's actually not a star at all, it's the planet Mars.

7
00:00:26,960 --> 00:00:29,480
It's the next place humans are going to explore.

8
00:00:29,480 --> 00:00:33,600
Of course, none of this exploration could be done without science and mathematics.

9
00:00:33,600 --> 00:00:38,320
On this episode of NASA Connect, NASA researchers will show you how the principles of geometry

10
00:00:38,320 --> 00:00:42,440
are used to survey and map our planet Earth and the planet Mars.

11
00:00:42,440 --> 00:00:47,320
So hang tight as Vance, Jennifer and the NASA Science Guys survey Earth and Mars on this

12
00:00:47,320 --> 00:00:49,400
episode of NASA Connect.

13
00:01:18,320 --> 00:01:24,840
Hey guys, welcome to NASA Connect, the show that connects you to the world of math, science,

14
00:01:24,840 --> 00:01:26,280
technology and NASA.

15
00:01:26,280 --> 00:01:27,360
I'm Jennifer Pulley.

16
00:01:27,360 --> 00:01:28,360
And I'm Van Hughes.

17
00:01:28,360 --> 00:01:32,120
Today, we're here at the Virginia Living Museum in Newport News, Virginia.

18
00:01:32,120 --> 00:01:36,160
And right now, we're standing on a sundial, which is basically a plate marked with hour

19
00:01:36,160 --> 00:01:37,680
lines and a gnomon.

20
00:01:37,680 --> 00:01:41,280
A gnomon is a raised projection that casts a shadow from the sun.

21
00:01:41,280 --> 00:01:44,360
Jennifer, why don't you come be the gnomon?

22
00:01:44,400 --> 00:01:47,960
According to your shadow, it's time to start the show.

23
00:01:47,960 --> 00:01:53,320
Well Van, this isn't a bad way to tell time, but you know, I think I'd rather use my watch.

24
00:01:53,320 --> 00:01:58,200
You know, throughout history, the sun and stars governed people's days, years and even

25
00:01:58,200 --> 00:01:59,560
their lives.

26
00:01:59,560 --> 00:02:04,320
Using sundials and observing shadows was one way ancient people told time.

27
00:02:04,320 --> 00:02:09,520
Get this, you can even measure height and distance with shadows cast from the sun.

28
00:02:09,520 --> 00:02:14,880
In fact, you can even measure the circumference of an entire planet, like Earth or Mars, with

29
00:02:14,880 --> 00:02:16,920
something as simple as a shadow.

30
00:02:16,920 --> 00:02:18,400
And geometry.

31
00:02:18,400 --> 00:02:23,760
On today's NASA Connect, we will examine how NASA researchers use the principles of geometry

32
00:02:23,760 --> 00:02:28,800
to survey the world around us and the worlds beyond us.

33
00:02:28,800 --> 00:02:34,800
We'll focus our telescope to see how geometry and satellites are used to measure, map and

34
00:02:34,800 --> 00:02:37,200
survey other planets like Mars.

35
00:02:37,480 --> 00:02:41,520
Which, by the way, can be seen quite well in this planetarium.

36
00:02:41,520 --> 00:02:47,360
Anyway, we'll visit some students from George Washington University who are studying and

37
00:02:47,360 --> 00:02:52,440
surveying the Martian landscape at NASA Langley Research Center in Hampton, Virginia.

38
00:02:52,440 --> 00:02:57,320
And we'll visit a researcher from NASA's Jet Propulsion Laboratory in Pasadena, California,

39
00:02:57,320 --> 00:03:02,160
who will show us how geometry is used by NASA's Mars Global Surveyor.

40
00:03:02,160 --> 00:03:06,520
Later on in the show, students from Central Middle School in Charlotte Courthouse, Virginia

41
00:03:06,520 --> 00:03:07,520
will join us.

42
00:03:07,520 --> 00:03:10,160
They've got an awesome experiment you'll want to try.

43
00:03:10,160 --> 00:03:15,040
Plus, NASA's Educational Technology Program Manager, Dr. Shelley Canright, will introduce

44
00:03:15,040 --> 00:03:19,240
us to some students from Davis Middle School in Hampton, Virginia.

45
00:03:19,240 --> 00:03:22,720
These students are using the internet to create their own Mars Surveyor.

46
00:03:22,720 --> 00:03:26,400
We'll learn more about this web-based activity later in the show.

47
00:03:26,400 --> 00:03:30,720
Hey, as we go through the show, our friend Norbert will visit you too.

48
00:03:30,720 --> 00:03:34,640
Every time he appears with a cue card, that's your cue to think about the answers to the

49
00:03:34,640 --> 00:03:36,160
questions he gives you.

50
00:03:37,080 --> 00:03:40,960
Plus, we'll go to NASA Ames Research Center in Moffett Field, California.

51
00:03:40,960 --> 00:03:46,240
There, we'll get all the latest information on the search for life on Mars and learn all

52
00:03:46,240 --> 00:03:49,200
about green slime.

53
00:03:49,200 --> 00:03:54,880
So hang tight, as NASA Connect takes you on a global surveyor mission to our planet Earth

54
00:03:54,880 --> 00:03:56,880
and to planet Mars.

55
00:03:56,880 --> 00:04:07,520
What is surveying?

56
00:04:07,520 --> 00:04:11,120
How do surveyors use geometry?

57
00:04:11,120 --> 00:04:15,200
Surveying is the measurement of angles and distances, elevation and direction.

58
00:04:15,200 --> 00:04:20,200
It's especially useful for locating property boundaries, construction layout and map making.

59
00:04:20,200 --> 00:04:24,960
Okay, Terry, can you tell me how surveyors use this equipment and geometry to survey

60
00:04:24,960 --> 00:04:25,960
land?

61
00:04:26,040 --> 00:04:27,560
First, let's look at this transit.

62
00:04:27,560 --> 00:04:33,040
It contains a telescope, a compass, and a protractor, and it's used to measure horizontal

63
00:04:33,040 --> 00:04:34,960
and vertical angles.

64
00:04:34,960 --> 00:04:38,720
You can measure angles in the field with this and measure those same angles back at your

65
00:04:38,720 --> 00:04:41,100
desk with a protractor.

66
00:04:41,100 --> 00:04:45,880
This instrument is used to lay out objects like football fields, baseball fields, soccer

67
00:04:45,880 --> 00:04:46,880
fields.

68
00:04:46,880 --> 00:04:51,000
Today, let's demonstrate how we use this by laying out this football field.

69
00:04:51,000 --> 00:04:52,000
Alright.

70
00:04:52,000 --> 00:04:55,640
First, we pick a starting point and set the transit over the point.

71
00:04:55,640 --> 00:04:58,360
We call this point corner number one.

72
00:04:58,360 --> 00:05:03,000
Then we measure 300 feet to the next corner and call it corner number four.

73
00:05:03,000 --> 00:05:05,480
We mark this corner with a corner marker.

74
00:05:05,480 --> 00:05:10,720
With zero on the scale, we look through the telescope and line up corner number four.

75
00:05:10,720 --> 00:05:15,400
We know that the angle between the sides of a rectangle is 90 degrees, so we turn the

76
00:05:15,400 --> 00:05:21,160
telescope towards corner number two until we can read 90 degrees on the transit circle

77
00:05:21,160 --> 00:05:22,160
or scale.

78
00:05:22,680 --> 00:05:28,040
Now we measure the width of the football field, 150 feet, and mark corner number two.

79
00:05:28,040 --> 00:05:32,240
Next, we move the transit over corner number two.

80
00:05:32,240 --> 00:05:37,400
With zero on the scale, we look through the telescope at corner number one marker.

81
00:05:37,400 --> 00:05:42,160
We turn the telescope towards corner number three until we can read 90 degrees on the

82
00:05:42,160 --> 00:05:43,160
scale.

83
00:05:43,160 --> 00:05:46,840
We measure 300 feet and mark corner number three.

84
00:05:46,840 --> 00:05:49,920
We now have all of the corners marked.

85
00:05:49,920 --> 00:05:54,840
Applying one of the basic rules of geometry, we know that the sum of the interior angles

86
00:05:54,840 --> 00:06:01,840
of a four-sided polygon is 360 degrees, so our last angle must measure 90 degrees for

87
00:06:01,840 --> 00:06:03,560
a correct layout.

88
00:06:03,560 --> 00:06:08,360
The rule for checking the angles of any object is that the sum of the interior angles of

89
00:06:08,360 --> 00:06:13,720
a closed polygon is equal to the number of sides minus two times 180 degrees.

90
00:06:13,720 --> 00:06:19,320
You know, Jennifer, the art and science of surveying had been used for over 3,400 years

91
00:06:19,320 --> 00:06:21,480
to map and measure our world.

92
00:06:21,480 --> 00:06:26,880
Today, scientists at NASA are preparing to measure and map the planets of our solar system.

93
00:06:26,880 --> 00:06:28,960
Hmm, who knows?

94
00:06:28,960 --> 00:06:31,920
Maybe one day one of you will help survey Mars.

95
00:06:31,920 --> 00:06:36,760
Did you know that George Washington was a surveyor before he became president?

96
00:06:36,760 --> 00:06:41,160
Did you know Lewis and Clark used transits on the Exploration Mission?

97
00:06:41,160 --> 00:06:48,320
To understand angles and circumference, let's look at something we can all relate to, pizza.

98
00:06:48,320 --> 00:06:49,320
Take a slice of pizza.

99
00:06:49,320 --> 00:06:53,920
Can you tell just by looking at it how many slices were in the original pizza and how

100
00:06:53,920 --> 00:06:55,760
big a round it was?

101
00:06:55,760 --> 00:06:56,760
Sure you can.

102
00:06:56,760 --> 00:06:58,440
All it takes is a little geometry.

103
00:06:58,440 --> 00:07:02,760
A pizza usually has eight identical slices, but not all of them.

104
00:07:02,760 --> 00:07:06,280
So let's measure the angle width of this slice.

105
00:07:06,280 --> 00:07:08,720
That's the part you put in your mouth first.

106
00:07:08,720 --> 00:07:13,840
Excuse me, sir, what does this protractor read?

107
00:07:13,840 --> 00:07:16,960
The protractor reads an angle width of 45 degrees.

108
00:07:16,960 --> 00:07:17,960
Right.

109
00:07:18,600 --> 00:07:21,680
Now, what is the measurement of all the other angles touching the center?

110
00:07:21,680 --> 00:07:25,680
They have to be equal or the same measurement, 45 degrees.

111
00:07:25,680 --> 00:07:26,680
Right.

112
00:07:26,680 --> 00:07:31,600
Now, most pizzas are circular and circles measure 360 degrees.

113
00:07:31,600 --> 00:07:39,200
If you divide 360 degrees by 45 degrees, the original pizza had eight slices.

114
00:07:39,200 --> 00:07:42,880
Now, let's figure the circumference of this pizza.

115
00:07:42,880 --> 00:07:44,720
Most pizzas are measured in inches.

116
00:07:44,720 --> 00:07:49,640
So, using the pizza with eight slices, if the length of the crust arc is five and a

117
00:07:49,640 --> 00:07:51,880
half inches, how round is your pizza?

118
00:07:51,880 --> 00:08:00,720
If there are eight slices and the crust arc measures 5.5 inches long, then eight times

119
00:08:00,720 --> 00:08:04,440
5.5 inches equals 44 inches.

120
00:08:04,440 --> 00:08:08,280
The pizza has a circumference of 44 inches.

121
00:08:08,280 --> 00:08:09,280
Great.

122
00:08:09,280 --> 00:08:10,280
Try this one.

123
00:08:10,840 --> 00:08:16,000
The angle width of your pizza slice measures 30 degrees and the crust arc is two and a

124
00:08:16,000 --> 00:08:17,400
half inches.

125
00:08:17,400 --> 00:08:22,200
How many slices would there be in the original pizza and what is the circumference?

126
00:08:22,200 --> 00:08:23,480
I've got it.

127
00:08:23,480 --> 00:08:28,160
360 degrees divided by 30 degrees equals 12 slices.

128
00:08:28,160 --> 00:08:33,920
12 slices times 2.5 inches equals a circumference of 30 inches.

129
00:08:33,920 --> 00:08:39,320
So, sir, would you rather eat a 12-slice pizza or an 8-slice pizza?

130
00:08:39,360 --> 00:08:41,360
Hmm, I'll choose the 8-slices.

131
00:08:41,360 --> 00:08:43,360
I couldn't possibly eat 12.

132
00:08:46,760 --> 00:08:51,760
Did you know that over 2,000 years ago, a Greek librarian used geometry to determine

133
00:08:51,760 --> 00:08:53,360
the circumference of the Earth?

134
00:08:58,360 --> 00:08:59,360
Hi, there.

135
00:08:59,360 --> 00:09:00,360
It's Tom.

136
00:09:00,360 --> 00:09:01,360
Can you explain the circumference of the Earth?

137
00:09:01,360 --> 00:09:07,240
What are the angle relationships between parallel lines and a transversal?

138
00:09:07,280 --> 00:09:12,320
The concept of the Earth being a large sphere was not unknown to the ancient Greeks.

139
00:09:12,320 --> 00:09:17,040
An everyday observation, such as the disappearance of ships below the horizon, indicated that

140
00:09:17,040 --> 00:09:19,760
the Earth might be spherical or round.

141
00:09:19,760 --> 00:09:21,480
But how large was it?

142
00:09:21,480 --> 00:09:26,400
The person who figured it out was a librarian named Aristophanes, who lived in Alexandria,

143
00:09:26,400 --> 00:09:29,520
Egypt about 300 BC.

144
00:09:29,520 --> 00:09:33,400
While looking through a scroll one day, he read that at noon on the longest day of the

145
00:09:33,400 --> 00:09:39,120
year, a vertical column cast no shadow in Syene, a city south of Alexandria.

146
00:09:39,120 --> 00:09:42,840
Aristophanes knew that this did not happen in Alexandria.

147
00:09:42,840 --> 00:09:47,720
He thought to himself, how was it possible to have shadows in Alexandria and not in Syene

148
00:09:47,720 --> 00:09:49,920
at the same time of day?

149
00:09:49,920 --> 00:09:56,320
Aristophanes figured out that the sun must be directly overhead in Syene but not in Alexandria.

150
00:09:56,320 --> 00:09:57,320
Aha!

151
00:09:57,320 --> 00:10:01,200
Here was proof that the Earth's surface is curved.

152
00:10:01,400 --> 00:10:05,160
Using a little geometry, Aristophanes set out to determine the circumference of the

153
00:10:05,160 --> 00:10:09,000
Earth and find out just how big it is.

154
00:10:09,000 --> 00:10:14,880
Just like our pizza example, if our friend Aristophanes could determine the central angle

155
00:10:14,880 --> 00:10:20,920
at the center of the Earth and the length of the edge or arc, then he could figure out

156
00:10:20,920 --> 00:10:22,600
the circumference of the Earth.

157
00:10:22,600 --> 00:10:27,840
Now, finding the length of the edge or arc was fairly simple math.

158
00:10:27,840 --> 00:10:33,200
Aristophanes asked a friend to walk from Alexandria to Syene to measure the distance

159
00:10:33,200 --> 00:10:35,040
between the two cities.

160
00:10:35,040 --> 00:10:41,160
His friend estimated the distance to be around 800 kilometers or about 500 miles.

161
00:10:41,160 --> 00:10:45,600
Finding the central angle, however, would take some geometry.

162
00:10:45,600 --> 00:10:52,040
First, Aristophanes assumed correctly, I might add, that the sun's rays are parallel since

163
00:10:52,040 --> 00:10:53,600
the sun is so far away.

164
00:10:53,600 --> 00:10:54,600
Check this out.

165
00:10:54,720 --> 00:10:59,480
In this diagram, we can see that there is no shadow at Syene, while there is a shadow

166
00:10:59,480 --> 00:11:01,320
in Alexandria.

167
00:11:01,320 --> 00:11:06,400
The line that is formed by the gnomon, or vertical column at Alexandria and the center

168
00:11:06,400 --> 00:11:13,160
of the Earth, cuts or intersects the two parallel lines formed from the sun's rays.

169
00:11:13,160 --> 00:11:17,560
A line that intersects two parallel lines is called a transversal.

170
00:11:17,560 --> 00:11:23,040
The two angles formed from the transversal line and the parallel lines are called alternate

171
00:11:23,040 --> 00:11:25,200
interior angles.

172
00:11:25,200 --> 00:11:28,160
And according to geometric rule, they are equal.

173
00:11:28,160 --> 00:11:29,680
Let's prove it.

174
00:11:29,680 --> 00:11:34,520
Take a piece of paper of any width and draw a diagonal line on it.

175
00:11:34,520 --> 00:11:37,240
Label the angles A and B just like this.

176
00:11:37,240 --> 00:11:42,240
Now, cut the paper along the diagonal so you have two triangles.

177
00:11:42,240 --> 00:11:45,960
Compare angles A and B by placing one angle on top of the other.

178
00:11:45,960 --> 00:11:47,880
Hey, what do you notice?

179
00:11:47,880 --> 00:11:51,640
The angles are equal no matter what size paper you started with.

180
00:11:51,640 --> 00:11:52,640
Right.

181
00:11:52,640 --> 00:11:58,600
When two parallel lines are intersected by a transversal, the alternate interior angles

182
00:11:58,600 --> 00:11:59,600
are equal.

183
00:11:59,600 --> 00:12:00,600
Huh.

184
00:12:00,600 --> 00:12:03,320
Aristophanes was quite a geometer.

185
00:12:03,320 --> 00:12:08,760
From his measurements, Aristophanes calculated the sun's rays made an angle of 7.5 degrees

186
00:12:08,760 --> 00:12:09,920
at Alexandria.

187
00:12:09,920 --> 00:12:15,800
Now, since this angle was formed by two parallel lines and a transversal, the central angle

188
00:12:15,800 --> 00:12:19,600
of the Earth must also be 7.5 degrees.

189
00:12:19,600 --> 00:12:24,680
By knowing these two things, the central angle and the distance from Alexandria to

190
00:12:24,680 --> 00:12:29,200
Syene, Aristophanes calculated the circumference of the Earth.

191
00:12:29,200 --> 00:12:38,000
360 degrees divided by 7.5 degrees equals 48 slices of the Earth.

192
00:12:38,000 --> 00:12:39,000
Are you still with me?

193
00:12:39,000 --> 00:12:40,000
Okay.

194
00:12:40,000 --> 00:12:41,000
Hang tight.

195
00:12:41,000 --> 00:12:42,000
We're almost there.

196
00:12:42,000 --> 00:12:47,080
Now, if you remember that the estimated distance between Alexandria and Syene is 800 kilometers

197
00:12:47,080 --> 00:12:53,920
and you multiply that distance by the number of slices in the Earth, 48, what is the circumference

198
00:12:53,920 --> 00:12:55,720
of the Earth?

199
00:12:55,720 --> 00:13:04,680
Well, if you estimated that distance to be 38,000 kilometers, you're absolutely right.

200
00:13:04,680 --> 00:13:09,720
Aristophanes' estimate was really close to the Earth's circumference, which is 40,074

201
00:13:09,720 --> 00:13:10,720
kilometers.

202
00:13:10,720 --> 00:13:17,480
His percentage error was about 5% and was probably due to an error in the distance between

203
00:13:17,480 --> 00:13:18,480
the two cities.

204
00:13:18,480 --> 00:13:19,480
5%?

205
00:13:19,480 --> 00:13:20,480
Huh.

206
00:13:20,480 --> 00:13:25,920
That's pretty good, considering Aristophanes used only his feet, his eyes, his imagination,

207
00:13:25,920 --> 00:13:28,920
and of course, his knowledge of geometry.

208
00:13:28,920 --> 00:13:32,600
There are other ways that we survey the Earth, which Aristophanes never dreamed of.

209
00:13:32,600 --> 00:13:35,400
NASA scientists use airplanes and satellites.

210
00:13:35,400 --> 00:13:40,280
But what if we wanted to survey other planets like Mars?

211
00:13:40,840 --> 00:13:42,840
NASA scientists are doing that right now.

212
00:13:42,840 --> 00:13:46,840
But first, let's head to Central Middle School in Charlotte Courthouse, Virginia.

213
00:13:46,840 --> 00:13:49,840
There, students are following in the footsteps of Aristophanes.

214
00:13:50,840 --> 00:13:51,840
Hi!

215
00:13:51,840 --> 00:13:57,840
We're from Central Middle School in Charlotte Courthouse, Virginia.

216
00:13:57,840 --> 00:14:02,840
NASA Connect asked us to show you how to do the student activity for this show.

217
00:14:02,840 --> 00:14:09,320
In this lesson, you will work in small groups to take accurate measurements of shadows using

218
00:14:09,360 --> 00:14:12,360
geometry to determine the size of an angle.

219
00:14:12,360 --> 00:14:15,360
Here are the materials you'll need for each group.

220
00:14:15,360 --> 00:14:19,360
A straight stick approximately 91 centimeters long.

221
00:14:19,360 --> 00:14:22,360
A meter stick or tape measure.

222
00:14:22,360 --> 00:14:27,360
A piece of string approximately 91 centimeters and a rocker weight.

223
00:14:27,360 --> 00:14:30,360
A scientific calculator.

224
00:14:30,360 --> 00:14:32,360
Index card.

225
00:14:32,360 --> 00:14:34,360
Compass.

226
00:14:34,360 --> 00:14:37,360
Copies of the student data chart for each student.

227
00:14:37,360 --> 00:14:38,360
Let's begin.

228
00:14:38,400 --> 00:14:42,400
Divide the class in research groups of three to five members.

229
00:14:43,400 --> 00:14:49,400
Set your measurement station by first placing the gnomon perpendicular to the ground.

230
00:14:49,400 --> 00:14:54,400
For your measurement to be accurate, it is critical that the gnomon is vertical.

231
00:14:54,400 --> 00:15:03,400
To check the vertical position, tie the rock or weight to the string and dangle it above the ground in front of the gnomon.

232
00:15:03,400 --> 00:15:06,400
Next, measure the height of the gnomon.

233
00:15:06,440 --> 00:15:11,440
Place an index card under the station to mark where the shadow ends.

234
00:15:11,440 --> 00:15:16,440
Take measurements every two minutes beginning at least ten minutes before local noon,

235
00:15:16,440 --> 00:15:20,440
which is the time that the sun is highest in the sky.

236
00:15:20,440 --> 00:15:26,440
This will most likely not be noon as indicated on your time measuring device.

237
00:15:26,440 --> 00:15:32,440
Students should note that when the sun is highest in the sky, the shadow length is the shortest.

238
00:15:32,480 --> 00:15:39,480
Since the edge of the shadow is fuzzy and the shadow is moving from east to west in the northern hemisphere,

239
00:15:39,480 --> 00:15:42,480
be careful in deciding where to place your mark.

240
00:15:42,480 --> 00:15:45,480
Record your data on data chart one.

241
00:15:45,480 --> 00:15:54,480
Now, back in your classroom, locate the latitude and longitude of your school location and record it on data chart number one.

242
00:15:54,480 --> 00:15:57,480
Identify your best shadow length.

243
00:15:57,480 --> 00:16:01,480
This is the best shadow length at local noon time.

244
00:16:01,520 --> 00:16:09,520
Next, calculate the tangent by dividing the length of the shadow by the height of the gnomon.

245
00:16:09,520 --> 00:16:15,520
Locate this number, or the nearest rounded number, on the tangent table.

246
00:16:15,520 --> 00:16:25,520
The measure of the tangent can also be found by dividing the length of a shadow by the height of an object on the scientific calculator.

247
00:16:25,520 --> 00:16:29,520
Record tangent on student data chart.

248
00:16:29,560 --> 00:16:33,560
Make a scale drawing of your gnomon and shadow.

249
00:16:33,560 --> 00:16:38,560
Complete the triangle and measure the tangent with a protractor to verify your calculations.

250
00:16:38,560 --> 00:16:40,560
What's next, Jennifer?

251
00:16:40,560 --> 00:16:47,560
Let's analyze the data by reviewing the results of this activity and by responding to the following questions.

252
00:16:47,560 --> 00:16:52,560
Did the weather conditions affect the results of this activity?

253
00:16:52,560 --> 00:16:55,560
If so, how?

254
00:16:55,600 --> 00:17:03,600
As the shadow lengthens over time, how will the angle be affected?

255
00:17:03,600 --> 00:17:12,600
If each group uses a gnomon with a different length, how will that affect the results of this activity?

256
00:17:12,600 --> 00:17:23,600
For more activities like this, check out our website at edu.larc.nasa.gov forward slash connect.

257
00:17:23,640 --> 00:17:31,640
NASA Connect would like to give a special thanks to the mentors from the AIAA chapter at Howard University in Washington, D.C.

258
00:17:31,640 --> 00:17:34,640
We appreciate all your help with the student activity.

259
00:17:34,640 --> 00:17:36,640
Okay, let's review.

260
00:17:36,640 --> 00:17:42,640
We've seen how the sun's position, satellites, and geometry help us survey the Earth.

261
00:17:42,640 --> 00:17:45,640
But what if we wanted to survey Mars?

262
00:17:45,640 --> 00:17:51,640
Well, we don't live on Mars, so how do scientists and NASA survey the red planet?

263
00:17:51,680 --> 00:17:52,680
I thought you'd never ask.

264
00:17:52,680 --> 00:17:57,680
Let's visit NASA's Jet Propulsion Laboratory in Pasadena, California and find out.

265
00:18:01,680 --> 00:18:04,680
What is the Mars Global Surveyor and where is it?

266
00:18:04,680 --> 00:18:10,680
How does the Mars Global Surveyor use geometry to survey the Martian landscape?

267
00:18:10,680 --> 00:18:15,680
The Mars Global Surveyor is a spacecraft that is in orbit around Mars.

268
00:18:15,720 --> 00:18:22,720
Its purpose is to take pictures of Mars, to measure the temperature of the surface and the atmosphere of Mars,

269
00:18:22,720 --> 00:18:29,720
and to bounce laser signals off the surface of Mars to precisely determine the shape of Mars.

270
00:18:29,720 --> 00:18:34,720
You might think of Mars as simply being a sphere by looking at pictures of it.

271
00:18:34,720 --> 00:18:38,720
But to scientists, it has lots of bumps and ridges.

272
00:18:38,760 --> 00:18:48,760
For example, the poles of Mars are so cold that the atmosphere actually condenses out to form dry ice at the poles.

273
00:18:48,760 --> 00:18:54,760
And as much as 25% of the atmosphere condenses out into the dry ice at the poles.

274
00:18:54,760 --> 00:18:58,760
So there's quite a large change in the atmosphere.

275
00:18:58,760 --> 00:19:03,760
Also, Mars is known for having a large bulge on the side of it.

276
00:19:03,800 --> 00:19:08,800
It's the largest volcano in the solar system, known as Olympus Mons.

277
00:19:08,800 --> 00:19:16,800
And so one of the functions of the Mars Global Surveyor was to measure the shape of Mars to carefully determine how big is this bulge.

278
00:19:16,800 --> 00:19:22,800
Because it has a huge effect on the orbits of spacecraft. It's such a large bulge on the side.

279
00:19:22,800 --> 00:19:29,800
The way that we use geometry to convert the laser pulses into the shape of Mars,

280
00:19:29,840 --> 00:19:36,840
what we have to do is carefully time how long it takes for the pulses to reach Mars and bounce back to the spacecraft.

281
00:19:36,840 --> 00:19:46,840
And then we combine that with the shape of the orbit, which we determine by looking at how the radio signal changes as the spacecraft goes around Mars.

282
00:19:49,840 --> 00:19:54,840
What is aerobraking? How does geometry influence aerobraking?

283
00:19:54,880 --> 00:20:02,880
Aerobraking is when we use drag from the atmosphere to gradually shrink the orbit down.

284
00:20:02,880 --> 00:20:12,880
So what we have to do is use the drag from the atmosphere to gradually slow the orbit down so that it would shrink from this highly elliptical 45-hour orbit

285
00:20:12,880 --> 00:20:17,880
down to a very circular two-hour orbit around Mars.

286
00:20:17,880 --> 00:20:19,880
This is geometry in action.

287
00:20:19,920 --> 00:20:27,920
How would you like to try your hand at designing your own Mars Global Surveyor?

288
00:20:27,920 --> 00:20:34,920
Before introducing you to our featured EdTech activity in middle school, I wanted to give you a quick tour of Norbert's lab.

289
00:20:34,920 --> 00:20:40,920
You already know Norbert. He's that funny character that provides us with the cute cards and other learning activities and aids

290
00:20:40,920 --> 00:20:46,920
to help us understand the math, science and technology concepts presented in each of the NASA Connect programs.

291
00:20:46,960 --> 00:20:53,960
His lab is your interactive link to activities and resources on the web, so you'll get the most out of NASA Connect.

292
00:20:53,960 --> 00:21:00,960
Just click on the rooms to enter areas like Career Corner, where you'll meet some of our guests and members of our television team.

293
00:21:00,960 --> 00:21:06,960
There's a study room with terms and definitions related to the show, and a page with links to other cool sites.

294
00:21:06,960 --> 00:21:13,960
And this is where you'll get to the online activity, especially created in partnership with NASA's Learning Technologies team.

295
00:21:14,000 --> 00:21:22,000
To introduce us to the web activity for this show, let's pop in on a teacher and her students at Davis Middle School in Hampton, Virginia.

296
00:21:22,000 --> 00:21:27,000
Thanks, Jelly. My name is Vivian Carr, and I'm a math and science teacher here at Davis Middle School.

297
00:21:27,000 --> 00:21:35,000
My students love coming to the computer lab. They use it for reinforcement and enrichment of many skills in most of the content areas.

298
00:21:35,000 --> 00:21:41,000
Now I'd like to introduce you to Ruby Bruno. Ruby, tell us, how do you use technology?

299
00:21:41,040 --> 00:21:46,040
Technology is a tool that we use in several ways, for communication with others through email,

300
00:21:46,040 --> 00:21:53,040
for conducting research using the internet, for writing papers and preparing electronic presentations of our work,

301
00:21:53,040 --> 00:22:00,040
and for participating in problem-solving online projects such as NASA Connect to reinforce what we are learning in class.

302
00:22:00,040 --> 00:22:08,040
In the online component for this show, we're learning what goes into the design of a spacecraft used for planetary observation.

303
00:22:08,080 --> 00:22:14,080
To do this, we learn about different instruments used for observing planetary surfaces from space.

304
00:22:14,080 --> 00:22:16,080
One of these is a camera.

305
00:22:16,080 --> 00:22:24,080
We get to pick out what we think are the right batteries to use as well as the size of the solar panels required to run the spacecraft.

306
00:22:24,080 --> 00:22:32,080
We'll also have to consider the cost and weight of the vehicle as we try to put together the best possible planetary observer

307
00:22:32,080 --> 00:22:36,080
we can with all the variables given to us in the activity.

308
00:22:36,120 --> 00:22:40,120
Well, Jennifer, the students here at Davis Middle School leave you and our viewers with the challenge

309
00:22:40,120 --> 00:22:47,120
to assemble and test their very own Mars Surveyor in a cost-effective way that produces the best results.

310
00:22:47,120 --> 00:22:53,120
Viewers can find that challenge in Norbitz Lab on the NASA Connect website. See you on the web.

311
00:22:53,120 --> 00:22:59,120
Let's head to NASA Langley Research Center in Hampton, Virginia and meet up with some George Washington University graduate students.

312
00:22:59,120 --> 00:23:04,120
They are using pictures from the Mars Global Surveyor and geometry to survey Mars.

313
00:23:04,160 --> 00:23:09,160
Music

314
00:23:09,160 --> 00:23:11,160
How are shadows measured on Mars?

315
00:23:11,160 --> 00:23:17,160
How is geometry used to determine the height of land formation on Mars?

316
00:23:17,160 --> 00:23:21,160
Hey guys, I want you to meet Corey Hernandez and Brooke Anderson.

317
00:23:21,160 --> 00:23:24,160
They're graduate students at George Washington University.

318
00:23:24,160 --> 00:23:26,160
Guys, what are you studying over there?

319
00:23:26,160 --> 00:23:32,160
Well, with simple geometry and shadows, we're able to determine the elevation on Mars' surface

320
00:23:32,200 --> 00:23:37,200
such as a mountain, Olympus Mons, that's three times the size of Mount Everest

321
00:23:37,200 --> 00:23:41,200
or a valley, Valles Marineris, which is the size of the United States.

322
00:23:41,200 --> 00:23:43,200
Wow, those are some pretty large land formations.

323
00:23:43,200 --> 00:23:49,200
So, let me get this right, what you're telling me is that geometry is used to determine the elevation of land formations on Mars?

324
00:23:49,200 --> 00:23:53,200
Yes, and we set up an example here for you to demonstrate this.

325
00:23:53,200 --> 00:23:59,200
If this is a mountain on the surface of Mars, this is a protractor to measure the angle of the sun.

326
00:23:59,240 --> 00:24:02,240
This is a metric ruler to measure the length of a shadow.

327
00:24:02,240 --> 00:24:07,240
If this flashlight represents the sun, we know that, like here on Earth,

328
00:24:07,240 --> 00:24:11,240
the sun is directly overhead at 90 degrees at high noon, and as the day goes on,

329
00:24:11,240 --> 00:24:13,240
it goes down to zero degrees at sunset.

330
00:24:13,240 --> 00:24:17,240
So, Corey, what you're telling me is this model here creates a right triangle?

331
00:24:17,240 --> 00:24:21,240
The bottom leg can be represented by the length of the shadow,

332
00:24:21,240 --> 00:24:24,240
which we can get from taking a picture with the Mars Global Surveyor.

333
00:24:24,240 --> 00:24:28,240
Now, the sun makes an angle between the hypotenuse and the bottom leg.

334
00:24:28,280 --> 00:24:31,280
So, let's pretend it's mid-afternoon on Mars.

335
00:24:31,280 --> 00:24:35,280
The sun would be at about an angle of 45 degrees.

336
00:24:35,280 --> 00:24:37,280
Which, Brooke, how long is our shadow?

337
00:24:37,280 --> 00:24:39,280
It gives us about 17 centimeters.

338
00:24:39,280 --> 00:24:41,280
Wow, so you got your angle there.

339
00:24:41,280 --> 00:24:47,280
Yes. So, using our formula, remembering the tangent of 45 degrees is equal to 1,

340
00:24:47,280 --> 00:24:51,280
which we can find from our scientific calculators or our tangent tables,

341
00:24:51,280 --> 00:24:54,280
we can find the height of our mountain to be 17 centimeters.

342
00:24:54,320 --> 00:24:56,320
So, to double-check our answer,

343
00:24:56,320 --> 00:25:01,320
we can see that the height of our mountain is 17 centimeters.

344
00:25:01,320 --> 00:25:04,320
That's about what you calculated. That's pretty cool, Corey.

345
00:25:04,320 --> 00:25:08,320
Well, I looked at Mars through the telescope, and it is definitely red.

346
00:25:08,320 --> 00:25:11,320
But could green slime have once existed on the red planet?

347
00:25:11,320 --> 00:25:14,320
That's one of the many reasons NASA Ames Research Center

348
00:25:14,320 --> 00:25:17,320
in Moffett Field, California, is studying Mars.

349
00:25:17,320 --> 00:25:23,320
So, now let's join researcher Chris McKay with the latest on green slime.

350
00:25:23,360 --> 00:25:27,360
I'm interested in Mars, and in particular, life on Mars.

351
00:25:27,360 --> 00:25:30,360
We know that early in Mars' history, it had water, lots of water.

352
00:25:30,360 --> 00:25:33,360
We can see the rivers and lakes that were formed by that water.

353
00:25:33,360 --> 00:25:36,360
The question is, when it had water, did it have life?

354
00:25:36,360 --> 00:25:40,360
To understand how life might have survived on a cold planet like Mars

355
00:25:40,360 --> 00:25:43,360
and where to look for it, we go to places on Earth

356
00:25:43,360 --> 00:25:46,360
where life is surviving in very cold, dry conditions,

357
00:25:46,360 --> 00:25:47,360
Mars-like conditions.

358
00:25:47,360 --> 00:25:51,360
This is a rock from the Antarctic, the dry valleys of Antarctica,

359
00:25:51,400 --> 00:25:53,400
the most Mars-like place on Earth.

360
00:25:53,400 --> 00:25:56,400
In this rock, there's life, but it's hidden inside the rock.

361
00:25:56,400 --> 00:25:59,400
Just below the surface, there's a layer of green.

362
00:25:59,400 --> 00:26:02,400
These are algae and lichens, and they're growing inside the rock

363
00:26:02,400 --> 00:26:05,400
because the rock provides them a source of moisture,

364
00:26:05,400 --> 00:26:08,400
while at the same time allowing enough light to come through.

365
00:26:08,400 --> 00:26:11,400
By studying life forms in these environments,

366
00:26:11,400 --> 00:26:15,400
we learn about the strategies that life can use in a cold, dry place.

367
00:26:15,400 --> 00:26:18,400
We might apply those strategies to the search for life on Mars.

368
00:26:18,440 --> 00:26:21,440
And maybe we'll find evidence that there was life there

369
00:26:21,440 --> 00:26:25,440
when Mars was not too much colder than the dry valleys of Antarctica.

370
00:26:25,440 --> 00:26:28,440
Well, looks like the sun has shifted,

371
00:26:28,440 --> 00:26:30,440
and that's about all we have time for today.

372
00:26:30,440 --> 00:26:33,440
But before we go, Jennifer and I would love to hear from you

373
00:26:33,440 --> 00:26:34,440
with your comments and ideas,

374
00:26:34,440 --> 00:26:36,440
so why don't you drop us a line at

375
00:26:36,440 --> 00:26:43,440
NASA Connect, NASA LARC MS400, Hampton, Virginia 23681.

376
00:26:43,480 --> 00:26:50,480
And if you're on the web, email us at connect at edu.larc.nasa.gov.

377
00:26:50,480 --> 00:26:52,480
We'd like to thank everyone who helped us today.

378
00:26:52,480 --> 00:26:55,480
The Virginia Living Museum, George Washington University,

379
00:26:55,480 --> 00:26:58,480
our NASA researchers from NASA Langley Research Center,

380
00:26:58,480 --> 00:27:02,480
NASA Ames Research Center, and NASA's Jet Propulsion Laboratory,

381
00:27:02,480 --> 00:27:05,480
Dr. Shelley Canright, and especially the students

382
00:27:05,480 --> 00:27:07,480
and teachers from our middle school.

383
00:27:07,480 --> 00:27:08,480
Thanks, guys.

384
00:27:08,480 --> 00:27:12,480
If you would like a videotaped copy of this NASA Connect show

385
00:27:12,520 --> 00:27:14,520
and the Educator's Guide lesson plans,

386
00:27:14,520 --> 00:27:20,520
contact CORE, the NASA Central Operation of Resources for Educators.

387
00:27:20,520 --> 00:27:25,520
All this information and more is located on the NASA Connect website.

388
00:27:25,520 --> 00:27:27,520
For the NASA Connect series, I'm Jennifer Pulley.

389
00:27:27,520 --> 00:27:28,520
And I'm Van Hughes.

390
00:27:28,520 --> 00:27:31,520
See you next time.

391
00:27:31,520 --> 00:27:33,520
Take a slice of pizza.

392
00:27:33,520 --> 00:27:36,520
Oh, you got it.

393
00:27:36,520 --> 00:27:40,520
What is serving?

394
00:27:40,560 --> 00:27:43,560
One of the functions of the Mars Global Surveyor

395
00:27:43,560 --> 00:27:46,560
was to watch it fall off.

396
00:27:46,560 --> 00:27:51,560
How is geometry used to measure?

397
00:27:51,560 --> 00:27:54,560
Today, we'll use this.

398
00:27:54,560 --> 00:27:58,560
What are the angles?

399
00:27:58,560 --> 00:28:04,560
The sun would be at about an angle of 45 degrees.

400
00:28:04,560 --> 00:28:08,560
How are shatters?

401
00:28:08,600 --> 00:28:12,600
Guys, tell me what you're studying over there.

402
00:28:12,600 --> 00:28:13,600
Welcome to NASA Connect.

403
00:28:13,600 --> 00:28:14,600
Sorry, my fault.

404
00:28:14,600 --> 00:28:15,600
Welcome to NASA Connect.

405
00:28:15,600 --> 00:28:16,600
Sorry.

406
00:28:16,600 --> 00:28:17,600
And I'm Van Hughes.

407
00:28:17,600 --> 00:28:20,600
Today, we're here at the...

408
00:28:20,600 --> 00:28:22,600
I think I see...

409
00:28:22,600 --> 00:28:23,600
Whoa.

410
00:28:23,600 --> 00:28:24,600
Whoa.

411
00:28:24,600 --> 00:28:25,600
Whoa.

412
00:28:25,600 --> 00:28:26,600
Whoa.

413
00:28:26,600 --> 00:28:27,600
Whoa.

414
00:28:27,600 --> 00:28:28,600
Whoa.

415
00:28:28,600 --> 00:28:29,600
Whoa.

416
00:28:29,600 --> 00:28:30,600
Whoa.

417
00:28:30,600 --> 00:28:30,600