1. Lab 3: Earth Sun-Geometry

2. Primary cause for Earth’s seasons!
Earth’s axis is tilted 23½° (from the perpendicular to the plane of the ecliptic)
Primary cause for Earth’s seasons!
Tilt is oriented in the same direction all year:
North Pole points towards Polaris

4. Earth-Sun Geometry Solstices: Summer (June 21 or 22)
Northern Hemisphere is tilted 23½° toward the sun
Sun’s rays are directly over head at 23½° N (Tropic of Cancer)
Winter (December 21 or 22)
Northern Hemisphere is tilted 23½° away from the sun
Sun’s rays are directly over head at 23½° S
(Tropic of Capricorn)
Solar Noon = Sun at highest point in the sky

5. Earth-Sun Geometry

6. Equinoxes: Midway between solstices
Autumnal equinox – September 22 or 23
Vernal equinox – March 21 or 22
Rotation Animation

11. Sun angles vary with latitude:
High sun angles in the tropics
Medium sun angles at mid-latitude
Low sun angles in the arctic

12. Sun Angle by Season

13. Solar declination: latitude at which the sun is directly above at solar noon (only between 23 ½ N-S)
Zenith angle (ZA): the angle between a point directly overhead & the sun at solar noon (related to the 90 degrees)
Solar elevation angle (SA): the angle of the sun above the horizon at solar noon (relates to 0 degrees)

14. Finding Zenith Know where the sun is directly overhead + or –
2. Latitude of location
HINTS:
Locations in same hemisphere = SUBTRACT!
Locations in different hemispheres = ADD!
Solar Declination is 0° = SUBTRACT!

15. Formulas:
Location gives you Zenith Angle
Date gives you Solar Declination
1. Zenith Angle = 90 – Sun Angle 2. Solar Elevation Angle = 90 – Zenith Angle

17. Calculating Solar Declination
Use formula:
23.5 * sine (n) OR
Use an Analemma!

18. June 21: summer solstice (23½ °N)
NH tilted towards the sun
SD = 23½°N
47°
66.5 – 23.5°(SD) = 43°(ZA)
90° – 43°(ZA) = 47°(SA)

19. SUN ANGLE: 36½° 1 2 3 4 5 6 7 8 9
0.00
1.75
3.49
5.23
6.98
8.72
10.45
12.19
13.92
15.64 10
17.36
19.08
20.79
22.50
24.19
25.88
27.56
29.24
30.90
32.56 20
34.20
35.84
37.46
39.07
40.67
42.26
43.84
45.40
46.95
48.48 30
50.00
51.5
52.99
54.46
55.92
57.36
58.78
60.18
61.57
62.93 40
64.28
65.61
66.91
68.20
69.47
70.71
71.93
73.14
74.31
75.47 50
76.60
77.71
78.80
79.86
80.90
81.92
82.90
83.87
84.80
85.72 60
86.60
87.46
88.29
89.10
89.88
90.63
91.36
92.05
92.72
93.36 70
93.97
94.55
95.11
95.63
96.13
96.59
97.03
97.44
97.81
98.16 80
98.48
98.77
99.03
99.25
99.45
99.62
99.76
99.86
99.94
99.98
Heating efficiency of 58.78%

20. **units determined by 1/sin(SA)
83½° ZA
8.834 units
Note your latitude!
Determine –
Sun at 90°
ZA (difference between your locations)
SA (90° – ZA)
Sun at 90°: 23½° S
ZA: 23½° + 60° = 83½°
SA: 90° – 83½° = 6½°
**units determined by 1/sin(SA)
The larger the unit, the cooler the temperature.
WHY?