Calculating Sun Angles

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

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

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

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

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

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

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

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

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

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

27. 24.5o N (23.5 +1) 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.

28. 89o 24.5o N (23.5 +1) 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.

29. 89o 24.5o N (23.5 +1) 25.5o N (23.5 +2) 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.

30. 89o 88o 24.5o N (23.5 +1) 25.5o N (23.5 +2) 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.

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”. • Thesubsolar pointis 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”. • Thesubsolar pointis 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 = (45 + 23.5) =