Lab 3:
Earth Sun-Geometry
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
• 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
• Solar elevation angle (SA): the angle of the sun
above the horizon at solar noon
Finding Zenith - The 3 D’s
1. Date
2. (where the sun is) Directly Overhead =
3. Declination
Find the difference between the location and
the declination
HINTS:
•Locations in same hemisphere = SUBTRACT!
•Locations in different hemispheres = ADD!
• Solar Declination is 0° = SUBTRACT!
Steps to Find Zenith Angle and Sun Angle
1. Find location
2. Find solar declination based on date (where the
sun is directly overhead
3. Find Zenith (difference between location and
solar declination)
4. Find Sun Angle = 90 – Zenith
SUN ANGLE + ZENITH WILL ALWAYS = 90
HINTS:
•Locations in same hemisphere = SUBTRACT!
•Locations in different hemispheres = ADD!
• Solar Declination is 0° = SUBTRACT!
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
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)
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?
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