1
00:00:00,000 --> 00:00:03,000
So, how was the activity?

2
00:00:03,000 --> 00:00:08,000
Hopefully it helped reinforce the math concepts you learned earlier in today's program.

3
00:00:08,000 --> 00:00:10,000
Now, let's review.

4
00:00:10,000 --> 00:00:14,000
In the beginning of the program, we talked about the importance of scaling,

5
00:00:14,000 --> 00:00:17,000
especially when it comes to maps and models.

6
00:00:17,000 --> 00:00:22,000
You learned that fractions, decimals, ratios, and proportions

7
00:00:22,000 --> 00:00:26,000
are all important math concepts when dealing with scales.

8
00:00:26,000 --> 00:00:29,000
Sten introduced you to the astronomical unit,

9
00:00:29,000 --> 00:00:32,000
the unit used to scale the solar system.

10
00:00:32,000 --> 00:00:35,000
Later in the program, I have an interesting challenge for you.

11
00:00:35,000 --> 00:00:39,000
But before we get to that, Sten has a few more questions for you.

12
00:00:39,000 --> 00:00:44,000
Let's head back to Sten now and learn more about scaling the solar system.

13
00:00:47,000 --> 00:00:49,000
Hey, it's great to have you back.

14
00:00:49,000 --> 00:00:54,000
In the last segment, we introduced the scale of the solar system and the astronomical unit.

15
00:00:54,000 --> 00:00:59,000
Believe it or not, astronomers once knew only what the distances were in astronomical units,

16
00:00:59,000 --> 00:01:01,000
not in actual miles.

17
00:01:01,000 --> 00:01:05,000
Recall the following chart that shows the distances of the planets to the sun.

18
00:01:05,000 --> 00:01:08,000
Between 1609 and 1619,

19
00:01:08,000 --> 00:01:13,000
the astronomer Johannes Kepler used precise measurements of the planets in the sky

20
00:01:13,000 --> 00:01:15,000
to determine their orbits.

21
00:01:15,000 --> 00:01:18,000
But his geometric model was based on the scale of the Earth's orbit,

22
00:01:18,000 --> 00:01:21,000
not on its actual diameter in kilometers or miles.

23
00:01:21,000 --> 00:01:24,000
He determined the ratio of the distance of each planet to the sun

24
00:01:24,000 --> 00:01:26,000
relative to Earth's distance to the sun.

25
00:01:26,000 --> 00:01:29,000
His baseline unit, the distance from Earth to the sun,

26
00:01:29,000 --> 00:01:34,000
was designated as exactly 1 AU, or 1 astronomical unit.

27
00:01:34,000 --> 00:01:39,000
The problem is that Kepler could not accurately determine the distance between the Earth and the sun.

28
00:01:39,000 --> 00:01:44,000
The best estimates at that time ranged from 50 million miles to over 200 million miles.

29
00:01:44,000 --> 00:01:49,000
But by the 1890s, astronomers began to know that number very precisely.

30
00:01:49,000 --> 00:01:54,000
How did scientists without modern space technology and rockets do this?

31
00:01:54,000 --> 00:01:58,000
You can't just send a spacecraft to the sun and back to determine the distance.

32
00:01:58,000 --> 00:02:01,000
Human life, including Norbert and Zott,

33
00:02:01,000 --> 00:02:04,000
couldn't survive the intense heat produced by the sun.

34
00:02:04,000 --> 00:02:07,000
So the question for this segment of the program is,

35
00:02:07,000 --> 00:02:12,000
how do we determine that the Earth is 93 million miles, or 149 million kilometers, from the sun?

36
00:02:12,000 --> 00:02:15,000
This would be a good time to pause the program

37
00:02:15,000 --> 00:02:18,000
and discuss the question with your teacher and your peers.

38
00:02:19,000 --> 00:02:21,000
So, did you come up with any good ideas?

39
00:02:21,000 --> 00:02:23,000
If you didn't, don't worry about it.

40
00:02:23,000 --> 00:02:27,000
After all, it took astronomers about 2,000 years to figure out how to do it.

41
00:02:29,000 --> 00:02:33,000
The answer is that astronomers used a geometric technique called parallax

42
00:02:33,000 --> 00:02:35,000
to determine the distance between the Earth and the sun.

43
00:02:35,000 --> 00:02:38,000
Parallax is the apparent change in position of an object

44
00:02:38,000 --> 00:02:41,000
when you look at it from two different stations or points of view.

45
00:02:41,000 --> 00:02:45,000
It sounds mysterious, but you use this technique all the time.

46
00:02:45,000 --> 00:02:48,000
For example, let me show you how parallax works

47
00:02:48,000 --> 00:02:51,000
by using my thumb and that rocket in the background.

48
00:02:51,000 --> 00:02:54,000
First, hold your thumb out at arm's length.

49
00:02:54,000 --> 00:02:58,000
Now look at your thumb with your left eye open and your right eye closed.

50
00:02:58,000 --> 00:03:01,000
What do you notice about the position of your thumb?

51
00:03:01,000 --> 00:03:05,000
There seems to be an apparent change in position of your thumb from two points of view,

52
00:03:05,000 --> 00:03:07,000
your left eye and your right eye.

53
00:03:07,000 --> 00:03:12,000
Your brain uses this information to figure out how far away things are from you.

54
00:03:12,000 --> 00:03:15,000
Actual parallax calculations can be quite complicated,

55
00:03:15,000 --> 00:03:18,000
but here's an example of how we can determine the distance to that rocket

56
00:03:18,000 --> 00:03:21,000
using many of the same geometric principles.

57
00:03:21,000 --> 00:03:25,000
Suppose we wanted to approximate the distance between where I'm standing right here

58
00:03:25,000 --> 00:03:27,000
and that rocket over there.

59
00:03:27,000 --> 00:03:31,000
And suppose also that there was a body of water in between that we couldn't get across.

60
00:03:31,000 --> 00:03:35,000
Would you believe that we could do that by just using a pencil, a piece of paper,

61
00:03:35,000 --> 00:03:38,000
a ruler, a piece of rope and a protractor?

62
00:03:38,000 --> 00:03:42,000
The first thing we do is to lay our rope in a straight line.

63
00:03:42,000 --> 00:03:46,000
The rope will serve as our baseline and is 10 meters in length.

64
00:03:46,000 --> 00:03:50,000
Standing on the left end of the rope, which we will call position A,

65
00:03:50,000 --> 00:03:54,000
hold the protractor so that it is parallel to the baseline.

66
00:03:54,000 --> 00:03:56,000
Place the pencil on the inside of the protractor

67
00:03:56,000 --> 00:04:00,000
and move it along the curve until it lines up with the object.

68
00:04:00,000 --> 00:04:05,000
Being careful not to move your pencil, have a partner read and record the angle measurement.

69
00:04:05,000 --> 00:04:09,000
We then need to repeat the same procedure on the other side of the rope.

70
00:04:09,000 --> 00:04:11,000
We will call this position B.

71
00:04:11,000 --> 00:04:15,000
We now have two angle measurements and our baseline measurement, which is 10 meters,

72
00:04:15,000 --> 00:04:17,000
the length of our rope.

73
00:04:17,000 --> 00:04:21,000
On a sheet of paper along the bottom, we draw a line 10 centimeters long

74
00:04:21,000 --> 00:04:23,000
to represent our baseline.

75
00:04:23,000 --> 00:04:29,000
For this exercise, let the scale be 1 meter equals 1 centimeter.

76
00:04:29,000 --> 00:04:35,000
Mark one end of the drawn line as point A and the other end as point B.

77
00:04:35,000 --> 00:04:40,000
Using our protractor at point A, we measure an angle that is the same number of degrees

78
00:04:40,000 --> 00:04:44,000
as the angle we measured outside for point A.

79
00:04:44,000 --> 00:04:47,000
Let's mark and draw the angle.

80
00:04:47,000 --> 00:04:50,000
At point B, we do the same thing.

81
00:04:50,000 --> 00:04:53,000
Now measure an angle that is the same number of degrees

82
00:04:53,000 --> 00:04:56,000
as the angle we measured outside for point B.

83
00:04:56,000 --> 00:05:00,000
As you can see, the two lines intersect.

84
00:05:00,000 --> 00:05:04,000
We mark the point of intersection as point C.

85
00:05:04,000 --> 00:05:09,000
Now we draw a line perpendicular from point C to the baseline.

86
00:05:09,000 --> 00:05:13,000
Using our metric ruler, we can measure the distance of this perpendicular line.

87
00:05:13,000 --> 00:05:17,000
Finally, using the scale 1 meter equals 1 centimeter,

88
00:05:17,000 --> 00:05:22,000
we can approximate the distance the actual object was from the baseline.

89
00:05:22,000 --> 00:05:26,000
In our case, the object is approximately 20 meters away.

90
00:05:26,000 --> 00:05:30,000
In this example, we used a geometric technique called triangulation,

91
00:05:30,000 --> 00:05:34,000
which assumes that we know the baseline length and the two base angles.

92
00:05:34,000 --> 00:05:39,000
When astronomers use parallax, they measure the baseline length and the vertex angle.

93
00:05:39,000 --> 00:05:42,000
It is hard to use the parallax method in the classroom

94
00:05:42,000 --> 00:05:45,000
because you can't measure the vertex angle exactly.

95
00:05:45,000 --> 00:05:49,000
With proper measuring technology, this is not a problem for astronomers.

96
00:05:49,000 --> 00:05:51,000
To find the actual Sun-Earth distance,

97
00:05:51,000 --> 00:05:57,000
parallax observations of the transit of Venus were made between 1761 and 1882.

98
00:05:57,000 --> 00:06:00,000
The transit of Venus occurs whenever the planet Venus

99
00:06:00,000 --> 00:06:03,000
passes in front of the Sun as viewed from the Earth.

100
00:06:03,000 --> 00:06:06,000
By observing the apparent shift in position of Venus

101
00:06:06,000 --> 00:06:10,000
against the background of the solar disk as seen from two different places on Earth,

102
00:06:10,000 --> 00:06:13,000
astronomers were able to use this parallax shift

103
00:06:13,000 --> 00:06:16,000
to determine the distance from the Earth to the Sun.

104
00:06:16,000 --> 00:06:18,000
The first Venus transit occurred in 1882,

105
00:06:18,000 --> 00:06:24,000
and we are fortunate to have another transit of Venus happening on Tuesday, June 8, 2004.

106
00:06:24,000 --> 00:06:29,000
This is an historic event because no one alive today was around when the last one occurred.

107
00:06:29,000 --> 00:06:31,000
To learn more about the transit of Venus,

108
00:06:31,000 --> 00:06:37,000
let's visit Dr. Janet Luhmann at the University of California's Space Science Lab in Berkeley, California.