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 90o.

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

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

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

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

7. Latitude of 90o Sun Angle Changes
Over the year, the latitude where
the sun’s rays form a 90o 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 90o angle at noon at the equator.
Path of incoming sun’s rays
0o latitude

9. Equinox
On March 22 and on September 22, the sun’s rays form a 90o 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
0o 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.
1o 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.
1o latitude
89o

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.
1o latitude
89o
2o 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.
1o latitude
89o
2o latitude
88o

15. Solstices

16. Solstices
June 22

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

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

19. Solstices June 22 The sun forms a 90o angle at noon at 23.5o 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 90o angle at noon at 23.5o 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 90o angle at noon at 23.5o S

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

24. Solstices December 22 The sun forms a 90o angle at noon at 23.5o 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 90o angle at noon at 23.5o 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 90o angle at noon at 23.5o N
Vertical Pole standing at 23.5o will not cast a shadow at noon!
Path of incoming sun’s rays
23.5o N

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

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

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

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

31. Noon Sun Angle Equation

32. Noon Sun Angle Equation
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 90o 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 90o angle at noon.
In other words: Noon Sun Angle =
90 - (latitude your are at ± latitude where sun is 90o 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 = 0o

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

45. Noon Sun Angle Equation
If the subsolar point and your latitude are in the same hemisphere, subtract.
Example: Subsolar Point = 0o
You are at 45oN.
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 = 0o
You are at 45oN.
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 = 23.5o S

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

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

51. Noon Sun Angle Equation
If the subsolar point and your latitude are in different hemispheres, add.
Example: Subsolar Point = 23.5o S
You are at 45oN.
Zenith Angle = ( ) = 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 22nd solstice (summer).

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

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

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

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

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

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

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

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

67. Noon Sun Angle Equation
A noon sun angle of 63.5o 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 22nd.

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

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

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

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

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

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

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

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

82. Noon Sun Angle Equation
A noon sun angle of is 47o 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 22nd.

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

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

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

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

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

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

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

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

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

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

98. Noon Sun Angle Equation
A noon sun angle of is 2.5o 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