Lab 3:
Earth Sun-Geometry
• 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
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
Earth-Sun Geometry
http://www.geography.hunter.cuny.edu/~tbw/wc.notes/2.heating.earth.su
rface/01_EarthSun.html
Equinoxes:
– Midway between solstices
• Autumnal equinox – September 22 or 23
• Vernal equinox – March 21 or 22
Rotation Animation
Sun angles vary with latitude:
– High sun angles in the tropics
– Medium sun angles at mid-latitude
– Low sun angles in the arctic
Sun Angle by Season
• 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)
Finding Zenith
1. 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!
Formulas:
• Location gives you Zenith Angle
• Date gives you Solar Declination
1. Zenith Angle = 90 – Sun Angle
2. Solar Elevation Angle = 90 – Zenith Angle
Calculating Solar Declination
• Use formula:
23.5 * sine (n)
OR
• Use an Analemma!
1. June 21: summer
solstice (23½ °N)
2. NH tilted
towards the sun
SD = 23½°N
47
°
1. 66.5 – 23.5°(SD) = 43°(ZA)
2. 90° – 43°(ZA) = 47°(SA)
SUN ANGLE: 36½°
0
1
2
3
4
5
6
7
8
9
0
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
8.834 units
1. Note your latitude!
2. Determine –
a. Sun at 90°
b. ZA (difference between your locations)
c. SA (90° – ZA)
a. Sun at 90°: 23½° S
b. ZA: 23½° + 60° = 83½°
c. SA: 90° – 83½° = 6½°
**units determined by 1/sin(SA)
The larger the unit, the cooler the temperature.
WHY?