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.surface/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!

HINTS:•Locations in same hemisphere = SUBTRACT!•Locations in different hemispheres = ADD!• Solar Declination is 0° = SUBTRACT!

Formulas:

1. Zenith Angle = 90 – Sun Angle

2. Solar Elevation Angle = 90 – Zenith Angle

1. Zenith Angle = 90 – Sun Angle

2. Solar Elevation Angle = 90 – Zenith Angle

• Location gives you Zenith Angle

• Date gives you Solar Declination

• Location gives you Zenith Angle

• Date gives you Solar Declination

Calculating Solar Declination

• Use formula: 23.5 * sine (n)

OR• Use an Analemma!

1. 66.5 – 23.5°(SD) = 43°(ZA)

2. 90° – 43°(ZA) = 47°(SA)

SD = 23½°N

47°

1. June 21: summer solstice (23½ °N)

2. NH tilted towards the sun

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

SUN ANGLE: 36½°

Heating efficiency of 58.78%

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° Sb. ZA: 23½° + 60° = 83½°c. SA: 90° – 83½° = 6½°

**units determined by 1/sin(SA)

83½° ZA

8.834 units

The larger the unit, the cooler the temperature.WHY?