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Earth’s Tilt

October 11, 2013

A listener asks how the earth’s tilt is measured.

Transcript

BOB HIRSHON (host):

Sizing up earth’s tilt. I’m Bob Hirshon and this is Science Update.

Axial tilt is responsible for the changes in seasons. (Dennis Nilsson/Wikipedia)

The earth tilts about 23.4 degrees—in the summer months, the north pole is tilted toward the sun, giving us more daylight and warmth, and in the winter, it’s tilted away. Tyler from Missouri emailed us to ask how scientists know that angle. NASA Physicist Betsy Pugel says that if you’re willing to wait until noon at the winter solstice—December 21st—you can measure it yourself by standing a ruler outside on the ground.

BETSY PUGEL (NASA):

Just take the length of the ruler, divide it by the length of the shadow, and then go into a calculator and calculate the inverse tangent and it will give you what that angle is. And so that angle is related to the tilt of the earth where you are.

HIRSHON:

She adds that thousands of years ago, people worked out the tilt in much the same way, but without the calculator. I’m Bob Hirshon for AAAS, the Science Society.

————————————————————————————————————————————————————-

CALCULATE EARTH’S TILT ON DECEMBER 21st USING BETSY PUGEL’S HANDY EARTH TILT CALCULATOR!

Click here for a printable version of the instructions

Calculate your latititude!

Print your own graph paper!

Why take other people’s word for it that Earth has a tilt? Measure it for yourself on December 21st!

Tools:

  • A stick-like object (For example: a stick; a ruler; a meter stick; a broom handle) to stick into the ground
  • Tape measure or ruler/meter stick for measuring
  • Pen/Pencil/Crayon and paper (to record your data)
  • Graph paper (attached to this document)
  • Calculator or the internet and search engine (as your alternate calculator)
  • Warm clothes to brave the weather a few times throughout the day to make measurements

Note:  This will not work if it is a cloudy day. 

Note #2: This method works in places that are north of the “Tropic of Cancer,” which includes the Continental U.S. and Canada, Europe, most of Asia and the northernmost part of Africa.

Two approaches:

(1)   The Quick and Easy Version, which will take about 10 minutes max

(2)   Winter Solstice Tilt Measurement, The Extended Remix, takes a few hours, but makes you feel like a boss (science-style)

Directions:

(1)   Check the table below for your time zone (assuming US conventions here).

  1. If you are doing The Quick and Dirty Version, make sure that you’ve been able to set everything up about 10 minutes before the official solstice time.
  2. If you are doing The Extended Remix, prepare everything to start 1 hour before the solstice time and allow for an hour after the solstice takes place

(2)   Find out your latitude (you can use a search engine to do this for you) or use our table to roughly identify where your latitude is.

(3)   Find some level ground and place the stick in the ground (or snow) so that the stick is vertical and so that you are able to measure the shadow that it casts.  It’s important that you are able to see the shadow for all of your measurements.

(4)   Measure the length of the stick above the ground.  Write the length on the piece of paper.

(5)   Note the time and write that on your piece of paper.

(6)   Measure the length of the shadow of the stick.

(7)   If you are doing The Quick and Dirty Version, jump to the end of the instructions, where it says How do I calculate tilt?

(8)   If you are doing The Extended Remix, you’ll need to note the time and the length of the shadow every 10 minutes from one hour before the start of solstice to one hour after the time passes.   You will end up with 6 data points in the first hour: the solstice point and 6 data points after the solstice takes place.

Extended Remix Version:

(1)   If you do (8) as instructed, you will be able to plot the length of the shadow versus time using the graph paper

(2)   The graph should look something like this:

The shadow will be the shortest at the solstice point in time.

How Do I Calculate Tilt?:

You’ll need:

For the Quick and Dirty Version:

(1)   Using any calculator, calculate the following:  (Stick Length)/(Shadow Length).  Make sure that your answer is in degrees.  We’ll call this the Sun’s Angle.

(2)   Subtract this number from your latitude: (Your Latitude) – (Sun’s Angle) = Earth’s Tilt

(3)   Tada!

For the Extended Remix

(1)   Select the shadow length at the solstice.  It should be when the shadow of the stick is the shortest

(2)   Using any calculator, calculate the following:  (Stick Length)/(Shadow Length).  Make sure that your answer is in degrees.  We’ll call this the Sun’s Angle.

(3)   Subtract this number from your latitude: (Your Latitude) – (Sun’s Angle) = Earth’s Tilt

(4)   Tada!

2013 Winter Solstice (December 21st) Time in U.S. time zones :

Eastern Time Zone:     12:11 PM

Central Time Zone:     11:11 AM

Mountain Time Zone: 10:11 AM

Pacific Time Zone:  9:11 AM

Latitude Table (from factmonster.com)

 

Lat. n.

Long. w.

 

City

°

°

Time

Albany, N.Y.

42

40

73

45

12:00 noon

Albuquerque, N.M.

35

05

106

39

10:00 a.m.

Amarillo, Tex.

35

11

101

50

11:00 a.m.

Anchorage, Alaska

61

13

149

54

8:00 a.m.

Atlanta, Ga.

33

45

84

23

12:00 noon

Austin, Tex.

30

16

97

44

11:00 a.m.

Baker, Ore.

44

47

117

50

9:00 a.m.

Baltimore, Md.

39

18

76

38

12:00 noon

Bangor, Maine

44

48

68

47

12:00 noon

Birmingham, Ala.

33

30

86

50

11:00 a.m.

Bismarck, N.D.

46

48

100

47

11:00 a.m.

Boise, Idaho

43

36

116

13

10:00 a.m.

Boston, Mass.

42

21

71

5

12:00 noon

Buffalo, N.Y.

42

55

78

50

12:00 noon

Calgary, Alba., Can.

51

1

114

1

10:00 a.m.

Carlsbad, N.M.

32

26

104

15

10:00 a.m.

Charleston, S.C.

32

47

79

56

12:00 noon

Charleston, W. Va.

38

21

81

38

12:00 noon

Charlotte, N.C.

35

14

80

50

12:00 noon

Cheyenne, Wyo.

41

9

104

52

10:00 a.m.

Chicago, Ill.

41

50

87

37

11:00 a.m.

Cincinnati, Ohio

39

8

84

30

12:00 noon

Cleveland, Ohio

41

28

81

37

12:00 noon

Columbia, S.C.

34

0

81

2

12:00 noon

Columbus, Ohio

40

0

83

1

12:00 noon

Dallas, Tex.

32

46

96

46

11:00 a.m.

Denver, Colo.

39

45

105

0

10:00 a.m.

Des Moines, Iowa

41

35

93

37

11:00 a.m.

Detroit, Mich.

42

20

83

3

12:00 noon

Dubuque, Iowa

42

31

90

40

11:00 a.m.

Duluth, Minn.

46

49

92

5

11:00 a.m.

Eastport, Maine

44

54

67

0

12:00 noon

Edmonton, Alb., Can.

53

34

113

28

10:00 a.m.

El Centro, Calif.

32

38

115

33

9:00 a.m.

El Paso, Tex.

31

46

106

29

10:00 a.m.

Eugene, Ore.

44

3

123

5

9:00 a.m.

Fargo, N.D.

46

52

96

48

11:00 a.m.

Flagstaff, Ariz.

35

13

111

41

10:00 a.m.

Fort Worth, Tex.

32

43

97

19

11:00 a.m.

Fresno, Calif.

36

44

119

48

9:00 a.m.

Grand Junction, Colo.

39

5

108

33

10:00 a.m.

Grand Rapids, Mich.

42

58

85

40

12:00 noon

Havre, Mont.

48

33

109

43

10:00 a.m.

Helena, Mont.

46

35

112

2

10:00 a.m.

Honolulu, Hawaii

21

18

157

50

7:00 a.m.

Hot Springs, Ark.

34

31

93

3

11:00 a.m.

Houston, Tex.

29

45

95

21

11:00 a.m.

Idaho Falls, Idaho

43

30

112

1

10:00 a.m.

Indianapolis, Ind.

39

46

86

10

12:00 noon

Jackson, Miss.

32

20

90

12

11:00 a.m.

Jacksonville, Fla.

30

22

81

40

12:00 noon

Juneau, Alaska

58

18

134

24

8:00 a.m.

Kansas City, Mo.

39

6

94

35

11:00 a.m.

Key West, Fla.

24

33

81

48

12:00 noon

Kingston, Ont., Can.

44

15

76

30

12:00 noon

Klamath Falls, Ore.

42

10

121

44

9:00 a.m.

Knoxville, Tenn.

35

57

83

56

12:00 noon

Las Vegas, Nev.

36

10

115

12

9:00 a.m.

Lewiston, Idaho

46

24

117

2

9:00 a.m.

Lincoln, Neb.

40

50

96

40

11:00 a.m.

London, Ont., Can.

43

2

81

34

12:00 noon

Long Beach, Calif.

33

46

118

11

9:00 a.m.

Los Angeles, Calif.

34

3

118

15

9:00 a.m.

Louisville, Ky.

38

15

85

46

12:00 noon

Manchester, N.H.

43

0

71

30

12:00 noon

Memphis, Tenn.

35

9

90

3

11:00 a.m.

Miami, Fla.

25

46

80

12

12:00 noon

Milwaukee, Wis.

43

2

87

55

11:00 a.m.

Minneapolis, Minn.

44

59

93

14

11:00 a.m.

Mobile, Ala.

30

42

88

3

11:00 a.m.

Montgomery, Ala.

32

21

86

18

11:00 a.m.

Montpelier, Vt.

44

15

72

32

12:00 noon

Montreal, Que., Can.

45

30

73

35

12:00 noon

Moose Jaw, Sask., Can.

50

37

105

31

11:00 a.m.

Nashville, Tenn.

36

10

86

47

11:00 a.m.

Nelson, B.C., Can.

49

30

117

17

9:00 a.m.

Newark, N.J.

40

44

74

10

12:00 noon

New Haven, Conn.

41

19

72

55

12:00 noon

New Orleans, La.

29

57

90

4

11:00 a.m.

New York, N.Y.

40

47

73

58

12:00 noon

Nome, Alaska

64

25

165

30

8:00 a.m.

Oakland, Calif.

37

48

122

16

9:00 a.m.

Oklahoma City, Okla.

35

26

97

28

11:00 a.m.

Omaha, Neb.

41

15

95

56

11:00 a.m.

Ottawa, Ont., Can.

45

24

75

43

12:00 noon

Philadelphia, Pa.

39

57

75

10

12:00 noon

Phoenix, Ariz.

33

29

112

4

10:00 a.m.

Pierre, S.D.

44

22

100

21

11:00 a.m.

Pittsburgh, Pa.

40

27

79

57

12:00 noon

Portland, Maine

43

40

70

15

12:00 noon

Portland, Ore.

45

31

122

41

9:00 a.m.

Providence, R.I.

41

50

71

24

12:00 noon

Quebec, Que., Can.

46

49

71

11

12:00 noon

Raleigh, N.C.

35

46

78

39

12:00 noon

Reno, Nev.

39

30

119

49

9:00 a.m.

Richfield, Utah

38

46

112

5

10:00 a.m.

Richmond, Va.

37

33

77

29

12:00 noon

Roanoke, Va.

37

17

79

57

12:00 noon

Sacramento, Calif.

38

35

121

30

9:00 a.m.

St. John, N.B., Can.

45

18

66

10

1:00 p.m.

St. Louis, Mo.

38

35

90

12

11:00 a.m.

Salt Lake City, Utah

40

46

111

54

10:00 a.m.

San Antonio, Tex.

29

23

98

33

11:00 a.m.

San Diego, Calif.

32

42

117

10

9:00 a.m.

San Francisco, Calif.

37

47

122

26

9:00 a.m.

San Jose, Calif.

37

20

121

53

9:00 a.m.

San Juan, P.R.

18

30

66

10

1:00 p.m.

Santa Fe, N.M.

35

41

105

57

10:00 a.m.

Savannah, Ga.

32

5

81

5

12:00 noon

Seattle, Wash.

47

37

122

20

9:00 a.m.

Shreveport, La.

32

28

93

42

11:00 a.m.

Sioux Falls, S.D.

43

33

96

44

11:00 a.m.

Sitka, Alaska

57

10

135

15

8:00 a.m.

Spokane, Wash.

47

40

117

26

9:00 a.m.

Springfield, Ill.

39

48

89

38

11:00 a.m.

Springfield, Mass.

42

6

72

34

12:00 noon

Springfield, Mo.

37

13

93

17

11:00 a.m.

Syracuse, N.Y.

43

2

76

8

12:00 noon

Tampa, Fla.

27

57

82

27

12:00 noon

Toledo, Ohio

41

39

83

33

12:00 noon

Toronto, Ont., Can.

43

40

79

24

12:00 noon

Tulsa, Okla.

36

09

95

59

11:00 a.m.

Vancouver, B.C., Can.

49

13

123

06

9:00 a.m.

Victoria, B.C., Can.

48

25

123

21

9:00 a.m.

Virginia Beach, Va.

36

51

75

58

12:00 noon

Washington, D.C.

38

53

77

02

12:00 noon

Wichita, Kan.

37

43

97

17

11:00 a.m.

Wilmington, N.C.

34

14

77

57

12:00 noon

Winnipeg, Man., Can.

49

54

97

7

11:00 a.m