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.surface/01_EarthSun.html

Equinoxes:– Midway between solstices

• Autumnal equinox – September 22 or 23• Vernal equinox – March 21 or 22

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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

• Solar elevation angle (SA): the angle of the sun above the horizon at solar noon

Finding Zenith - The 3 D’s

1. Date2. (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 location2. Find solar declination based on date (where the sun is

directly overhead3. Find Zenith (difference between location and solar

declination)4. Find Sun Angle = 90 – Zenith

SUN ANGLE + ZENITH WILL ALWAYS = 90HINTS:

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

Calculating Solar Declination

• Use formula: 23.5 * sine (n)OR

• Use an Analemma!http://www.analemma.com/Pages/framesPage.html

Daylight Hours

• Length of daylight (in addition to solar intensity) is another principal factor that determines solar radiation receipt on earth.

• Circle of illumination – any given time half of the earth is illuminated by the sun.

• Daylight length changes daily throughout the year for every location not on the equator

• So, solar radiation exposure time, like solar intensity, is not distributed uniformly on earth. Except on the equinoxes (everywhere receives 12 hrs of days and 12 hrs of night).

Yearly daylight hrs – equator; 30oN; 60oN

Solar angle; azimuth; daylight hours

Earth – Sun Geometry at 40oN: Solstices

•Sun has it’s longest arc…• Rises North of East• Sets North of West

Earth – Sun Geometry at 40oN: Solstices

•Sun has it’s shortest arc…• Rises South of East• Sets South of West

Earth – Sun Geometry at 40oN: Equinoxes

• Equinoxes:– Midway between solstices

• Autumnal equinox – September 22 or 23• Vernal equinox – March 21 or 22

•Sun arc is “normal”…• Rises in the East• Sets in the West

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

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?

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°

Radiation Intensity