1. Calculating Sun Angles Today you will calculate the angle of the sun at NOON (12:00) for different locations on Earth.

2. Calculating Sun Angles You will be working with complementary angles. Remember, complementary angles always add up to 90 o.

3. Calculating Sun Angles High sun angles (45 o to 90 o ) mean more intense sunlight.

4. Calculating Sun Angles High sun angles (45 o to 90 o ) mean more intense sunlight. 80 o

5. Calculating Sun Angles High sun angles (45 o to 90 o ) mean more intense sunlight. Low sun angles (0 o to 45 o ) mean less intense sunlight. 80 o

6. Calculating Sun Angles High sun angles (45 o to 90 o ) mean more intense sunlight. Low sun angles (0 o to 45 o ) mean less intense sunlight. 30 o 80 o

7. Latitude of 90 o Sun Angle Changes Over the year, the latitude where the sun’s rays form a 90 o angle, at noon, with the surface, moves slowly between the Tropic of Cancer and the Tropic of Capricorn.

8. Equinox On March 22 and on September 22, the sun’s rays form a 90 o angle at noon at the equator. Path of incoming sun’s rays 0 o latitude

9. Equinox On March 22 and on September 22, the sun’s rays form a 90 o angle at noon at the equator. Vertical Pole standing at the equator will not cast a shadow at noon! Path of incoming sun’s rays 0 o latitude

10. Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree.

11. Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 1 o latitude

12. Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 1 o latitude 89 o

13. Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 1 o latitude 89 o 2 o latitude

14. Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 2 o latitude 88 o 1 o latitude 89 o

15. Solstices

16. June 22

17. Solstices June 22 –The sun forms a 90 o angle at noon at 23.5 o N

18. Solstices June 22 –The sun forms a 90 o angle at noon at 23.5 o N –This latitude is called the Tropic of Cancer.

19. Solstices June 22 –The sun forms a 90 o angle at noon at 23.5 o N –This latitude is called the Tropic of Cancer. –This is the summer solstice for the Northern Hemisphere.

20. Solstices June 22 –The sun forms a 90 o angle at noon at 23.5 o N –This latitude is called the Tropic of Cancer. –This is the summer solstice for the Northern Hemisphere. –This is the winter solstice for the Southern Hemisphere.

21. Solstices December 22

22. Solstices December 22 –The sun forms a 90 o angle at noon at 23.5 o S

23. Solstices December 22 –The sun forms a 90 o angle at noon at 23.5 o S –This latitude is called the Tropic of Capricorn

24. Solstices December 22 –The sun forms a 90 o angle at noon at 23.5 o S –This latitude is called the Tropic of Capricorn –This is winter solstice for the Northern Hemisphere.

25. Solstices December 22 –The sun forms a 90 o angle at noon at 23.5 o S –This latitude is called the Tropic of Capricorn –This is winter solstice for the Northern Hemisphere. –This is the summer solstice for the Southern Hemisphere.

26. Solstices On the summer solstice the sun’s rays form a 90 o angle at noon at 23.5 o N Vertical Pole standing at 23.5 o will not cast a shadow at noon! Path of incoming sun’s rays 23.5 o N

27. Solstices On the summer solstice, for every degree of latitude you move away from 23.5 o, the sun angle at noon decreases by 1 degree. 24.5 o N (23.5 +1)

28. Solstices On the summer solstice, for every degree of latitude you move away from 23.5 o, the sun angle at noon decreases by 1 degree. 89 o 24.5 o N (23.5 +1)

29. Solstices On the summer solstice, for every degree of latitude you move away from 23.5 o, the sun angle at noon decreases by 1 degree. 89 o 24.5 o N (23.5 +1) 25.5 o N (23.5 +2)

30. Solstices On the summer solstice, for every degree of latitude you move away from 23.5 o, the sun angle at noon decreases by 1 degree. 88 o 25.5 o N (23.5 +2) 89 o 24.5 o N (23.5 +1)

31. Noon Sun Angle Equation

32. You are about to find the angle of the sun at noon at different latitudes.

33. Noon Sun Angle Equation You are about to find the angle of the sun at noon at different latitudes. –To do this, you will use the following formula:

34. Noon Sun Angle Equation You are about to find the angle of the sun at noon at different latitudes. –To do this, you will use the following formula: Noon Sun Angle = 90 - Zenith Angle

35. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle

36. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle You need to subtract from 90 because the angles you are working with are complementary.

37. Noon Sun Angle Equation Sun Angle = 90 - Zenith Angle

38. Noon Sun Angle Equation Sun Angle = 90 - Zenith Angle The zenith angle is the distance between the subsolar point and the latitude you are “at”.

39. Noon Sun Angle Equation Sun Angle = 90 - Zenith Angle The zenith angle is the distance between the subsolar point and the latitude you are “at”. The subsolar point is the latitude where the sun’s rays form a 90 o angle at noon.

40. Noon Sun Angle Equation Sun Angle = 90 - Zenith Angle The zenith angle is the distance between the subsolar point and the latitude you are “at”. The subsolar point is the latitude where the sun’s rays form a 90 o angle at noon. In other words: Noon Sun Angle = 90 - (latitude your are at ± latitude where sun is 90 o at noon)

41. Noon Sun Angle Equation To calculate the zenith angle between the subsolar point and the latitude you are “at” requires a bit of thought….

42. Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract.

43. Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. –Example: Subsolar Point = 0 o

44. Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. –Example: Subsolar Point = 0 o You are at 45 o N.

45. Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. –Example: Subsolar Point = 0 o You are at 45 o N. Zenith Angle = (45 - 0) =

46. Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. –Example: Subsolar Point = 0 o You are at 45 o N. Zenith Angle = (45 - 0) = 45

47. Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add.

48. Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. –Example: Subsolar Point = 23.5 o S

49. Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. –Example: Subsolar Point = 23.5 o S You are at 45 o N.

50. Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. –Example: Subsolar Point = 23.5 o S You are at 45 o N. Zenith Angle = (45 + 23.5) =

51. Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. –Example: Subsolar Point = 23.5 o S You are at 45 o N. Zenith Angle = (45 + 23.5) = 68.5

52. Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. If the subsolar point and your latitude are in different hemispheres, add.

53. Noon Sun Angle Equation Let’s do some problems together!

54. Noon Sun Angle Equation  It is the June 22 nd solstice (summer).

55. Noon Sun Angle Equation  It is the June 22 nd solstice (summer).  The subsolar point is 23.5 o N

56. Noon Sun Angle Equation  It is the June 22 nd solstice (summer).  The subsolar point is 23.5 o N  You are visiting a friend in Brussels, Belgium

57. Noon Sun Angle Equation  It is the June 22 nd solstice (summer).  The subsolar point is 23.5 o N  You are visiting a friend in Brussels, Belgium

58. Noon Sun Angle Equation  It is the June 22 nd solstice (summer).  The subsolar point is 23.5 o N  You are visiting a friend in Brussels, Belgium

59. Noon Sun Angle Equation  It is the June 22 nd solstice (summer).  The subsolar point is 23.5 o N  You are visiting a friend in Brussels, Belgium  Your latitude is 50 o N

60. Noon Sun Angle Equation  It is the June 22 nd solstice (summer).  The subsolar point is 23.5 o N  You are visiting a friend in Brussels, Belgium  Your latitude is 50 o N  What is the angle of the sun at noon?

61. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle

62. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract!

63. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5 =

64. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5 = 26.5

65. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5 = 26.5 Noon Sun Angle = 90 - 26.5 =

66. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5 = 26.5 Noon Sun Angle = 90 - 26.5 = 63.5 o

67. Noon Sun Angle Equation  A noon sun angle of 63.5 o is considered a high angle.  This answer makes sense because it is summer time where you are.

68. Noon Sun Angle Equation Good Job!!! Let’s try another one!

69. Noon Sun Angle Equation  It is the March 22 nd.

70. Noon Sun Angle Equation  It is the March 22 nd.  It is the Spring Equinox.

71. Noon Sun Angle Equation  It is the March 22 nd.  It is the Spring Equinox.  The subsolar point is 0 o

72. Noon Sun Angle Equation  It is the March 22 nd.  It is the Spring Equinox.  The subsolar point is 0 o  You are going to go skiing in New Zealand.

73. Noon Sun Angle Equation  It is the March 22 nd.  It is the Spring Equinox.  The subsolar point is 0 o  You are going to go skiing in New Zealand.

74. Noon Sun Angle Equation  It is the March 22 nd.  It is the Spring Equinox.  The subsolar point is 0 o  You are going to go skiing in New Zealand.  Your latitude is 43 o S

75. Noon Sun Angle Equation  It is the March 22 nd.  It is the Spring Equinox.  The subsolar point is 0 o  You are going to go skiing in New Zealand.  Your latitude is 43 o S  What is the angle of the sun at noon?

76. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle

77. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract!

78. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0 =

79. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0 = 43

80. Noon Sun Angle Equation Noon Sun Angle = 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0 = 43 Noon Sun Angle = 90 - 43 =

81. Noon Sun Angle Equation Noon Sun Angle = 90 - Arc Distance Arc Distance: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0 = 43 Noon Sun Angle = 90 - 43 = 47 o

82. Noon Sun Angle Equation  A noon sun angle of is 47 o a moderate angle.  This answer makes sense because it is spring time where you are.  The snow may be melting, but you can probably still get in a few runs!

83. Noon Sun Angle Equation Excellent work! Let’s try one last problem together.

84. Noon Sun Angle Equation  It is the December 22 nd.

85. Noon Sun Angle Equation  It is the December 22 nd.  It is the Winter Solstice.

86. Noon Sun Angle Equation  It is the December 22 nd.  It is the Winter Solstice.  The subsolar point is 23.5 o S

87. Noon Sun Angle Equation  It is the December 22 nd.  It is the Winter Solstice.  The subsolar point is 23.5 o S  You just won a trip to Oulu, Finland

88. Noon Sun Angle Equation  It is the December 22 nd.  It is the Winter Solstice.  The subsolar point is 23.5 o S  You just won a trip to Oulu, Finland

89. Noon Sun Angle Equation  It is the December 22 nd.  It is the Winter Solstice.  The subsolar point is 23.5 o S  You just won a trip to Oulu, Finland

90. Noon Sun Angle Equation  It is the December 22 nd.  It is the Winter Solstice.  The subsolar point is 23.5 o S  You just won a trip to Oulu, Finland  Your latitude is 64 o N

91. Noon Sun Angle Equation  It is the December 22 nd.  It is the Winter Solstice.  The subsolar point is 23.5 o S  You just won a trip to Oulu, Finland  Your latitude is 64 o N  What is the angle of the sun at noon?

92. Noon Sun Angle Equation Noon Sun Angle = 90 - Arc Distance

93. Noon Sun Angle Equation Noon Sun Angle = 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add!

94. Noon Sun Angle Equation Noon Sun Angle = 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 + 23.5 =

95. Noon Sun Angle Equation Noon Sun Angle = 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 + 23.5 = 87.5

96. Noon Sun Angle Equation Noon Sun Angle = 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 + 23.5 = 87.5 Noon Sun Angle = 90 - 87.5 =

97. Noon Sun Angle Equation Noon Sun Angle = 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 + 23.5 = 87.5 Noon Sun Angle = 90 - 87.5 = 2.5 o

98. Noon Sun Angle Equation  A noon sun angle of is 2.5 o a VERY low angle.  This answer makes sense because it is wintertime where you are.  You will need to take a lot of warm clothes for this trip!

99. Noon Sun Angle Equation Congratulations! You get to try some of these problems on your own. All the hints you’ve been shown are on your worksheet! Good Luck