Lab B. Earth - Sun Relationships

LAB B - EARTH-SUN RELATIONSHIPS Introduction Solar radiation is received at the Earth’s surface in varying quantities, depending on latitude and the position of Earth in its orbit around the Sun. Solar radiation and its geographic distribution is the underlying cause of Earth’s varying weather patterns and their long-term effect - climate. A basic understanding of Earth-Sun relationships will help the student comprehend why summers are so hot and winters cooler in Phoenix, why there is no winter at the Equator and why it is so cold in winter at the North Pole. Materials needed: pencil, textbook and calculator Part I. Earth-Sun Relationships A. Review the terms below. Students should become familiar with each of these terms and their geographic locations. Plane of the Ecliptic Rotation (Polar) Axis Circle of Illumination Spring (Vernal) Equinox Tropic of Cancer Arctic Circle Summer Solstice Autumnal (Fall) Equinox Tropic of Capricorn Antarctic Circle Winter Solstice B. Using Figure B-1, answer the questions below. a. Which line is already drawn on the diagram? ________________________ b. How much is this line tilted from vertical? __________________________ c. Draw and label the following items on the diagram of Earth below. Make sure to include the numerical value of the latitude where appropriate. Circle of Illumination Plane of the Ecliptic Equator Tropic of Cancer Tropic of Capricorn Arctic Circle Antarctic Circle What date is this? Figure B-1: Earth – Sun Configuration B-1 _______________ C. Figure B-2 (below) is a representation of the Earth's orbit around the Sun. Place the number of the location which indicates the correct Earth-Sun relationship for the Northern Hemisphere at the: June Solstice ____________ Autumnal (Fall) Equinox ____________ December Solstice ____________ Spring (Vernal) Equinox ____________ D. Using Figure B-2 (below), determine at what latitude the Sun’s rays would strike perpendicular (90°angle) as the Earth orbits from Location 1 to 4 around the Sun (these are the solar declinations for the four positions): Location 1: ____________ Location 3: ____________ Location 2: ____________ Location 4: ____________ Figure B-2: Earth Orbiting the Sun E. How many times during the year would the Sun’s rays strike perpendicular (90° angle) at the following locations? a. Honolulu, Hawaii (latitude = 21°N) _______________________ b. Phoenix, Arizona (latitude = 33.5°N) ______________________ c. Sorocaba, Brazil (latitude = 23.5°S) _______________________ B-2 Part II. Daylight and Darkness The length of day and night for any location (latitude) is directly related to the Earth's position in its orbit around the Sun. Using Table B-1, answer the following questions: Table B-1: Length of Daylight at Time of June Solstice (Source: Smithsonian Meteorological Tables, 6th revised edition) Latitude Duration 24 hours 24 hours 24 hours 18 hours 16 hours 15 hours 14 hours 13 hours 12 hours 12 hours 11 hours 10 hours 10 hours 9 hours 8 hours 5 hours 0 hours 0 hours 0 hours 90° N 80° N 70° N 60° N 50° N 40° N 30° N 20° N 10° N 0° 10° S 20° S 30° S 40° S 50° S 60° S 70° S 80° S 90° S 53 minutes 23 minutes 1 minute 5 minutes 21 minutes 43 minutes 0 minutes 32 minutes 55 minutes 12 minutes 20 minutes 4 minutes 52 minutes A. How many hours of daylight would be experienced on June 21st at? Point Barrow, Alaska 70° N South Pole 90ºS ________________ Equator 0° _______________ ________________ Porto Alegre, Brazil 30°S New Orleans, Louisiana 30°N _______________ Winnipeg, ________________ Manitoba (Canada) 50°N B-3 _______________ B. How many hours of darkness would be experienced on Dec. 21st at? Point Barrow, Alaska 70°N South Pole 90°S ______________ Equator 0° _______________ ______________ _______________ Winnipeg, Manitoba 50°N ______________ Porto Alegre, Brazil 30°S New Orleans, Louisiana 30°N _______________ Part III. Calculating Solar Altitude (Elevation Angle) Calculating the angle of the Sun above the horizon at solar noon, termed the Solar Altitude, is relatively simple. The Solar Altitude can range from 0° (on the Earth’s horizon) to 90° (directly overhead) and changes daily for every location on Earth. To calculate Solar Altitude (a) or Elevation Angle, one only needs to know: 1. the latitude for a particular location (the observer’s location), and 2. the Solar Declination, the location on the Earth where the Sun’s rays strike at a 90° angle at solar noon. A Table of Solar Declinations can be found in Table B-2 on the following page. The Solar Altitude for any location at any time of the year can be calculated using the following formula: a = 90° - (latitude +/- solar declination) Step 1: Determine the latitude for the location (if not given). Step 2: Determine the Solar Declination (SD), the Sun's latitude for that day. (Table B-2). Step 3: Plug latitude and solar declination into the equation above. Use the following rule to determine if you will add or subtract the numbers within the parentheses. If solar declination and latitude are in the same hemisphere = SUBTRACT (larger – smaller) If solar declination and latitude are in different hemispheres = ADD • If the Solar Altitude (a) comes out negative, then the sun is below the horizon (it’s dark outside). Give your answer as “BH” or “Below Horizon”. Example: Calculate the Solar Altitude for 10°S on December 21. Latitude = 10°S Solar Declination = 23.5°S => Sun and latitude are in the same hemisphere, so subtract using the larger number first. a = 90° – (23.5° – 10°) => a = 90° – (13.5°) => 76.5°. B-4 Using the formula on the previous page and Table B-2 (below), calculate the Solar Altitude for the locations in Questions A-H (the latitude of each location is provided). Be sure to show all work on a separate sheet of paper. Table B-2: Table of Solar Declinations (Locations where the Sun’s rays strike the Earth’s surface at a 90° angle at solar noon) Date January 5 15 25 February 5 15 25 March 5 15 20 Equinox Solar Declination 23° S 22° S 20° S 16° S 13° S 9° S 7° S 3° S Equator 0° Date April 5 15 25 May 5 15 25 June 5 15 21 Solstice Solar Declination 5½° N 9° N 12½° N 15 ½° N 18° N 20½° N 22° N 23° N Tropic of Cancer 23½° N Date July 5 15 25 August 5 15 25 September 5 15 22 Equinox Solar Declination 22½° N 21½° N 19½° N 17° N 13½° N 10½° N 7°N 3° N Equator 0° Date October 5 15 25 November 5 15 25 December 5 15 21 Solstice Solar Declination 4½° S 7½° S 11½° S 15½° S 18½° S 21° S 22½° S 23° S Tropic of Capricorn 23½°S A. 1) 2) 3) Phoenix, Arizona June Solstice December Solstice Spring Equinox 33 ½°N _______ _______ _______ E. 1) 2) 3) Circle, Alaska June Solstice December Solstice Autumnal Equinox 66 ½°N _______ _______ _______ B. 1) 2) 3) Mexico City, Mexico June Solstice December Solstice Autumnal Equinox 19° N F. 1) 2) 3) Sydney, Australia June Solstice December Solstice Vernal Equinox 33½°S _______ _______ _______ C. 1) 2) 3) Kampala, Uganda June Solstice April 5 October 15 0° _______ _______ _______ G. Cape Horn, Chile 1) May 15 2) December 21 3) Autumnal Equinox D. 1) 2) 3) Coats Land, Antarctica 74°S June 21 _______ December Solstice _______ September 22 _______ _______ _______ _______ 56°S _______ _______ _______ H. Cordoba, Argentina 32°S 1) November 15 _______ 2) July 20* _______ 3) March 20 _______ * Use Table B-2 and estimate B-5 Part IV. Radiation Intensity Using the information from page B-5, answer the following questions. A. Which one of the following cities would have the most intense solar radiation for the June Solstice? ______________________. Why did you choose this answer? _______ ____________________________________________________________________ Phoenix, Arizona Mexico City, Mexico Circle, Alaska Kampala, Uganda B. Which one of the following cities would have the most intense solar radiation for the December Solstice? ________________________. Why did you choose this answer? ____________________________________________________________________ Sydney, Australia Coats Land, Antarctica Cape Horn, Chile Phoenix, Arizona C. Describe the relationship between sun angle and radiation intensity? ________________ _______________________________________________________________________ D. How many hours of daylight does Circle, Alaska receive on the June Solstice? ________ E. How many hours of daylight does Phoenix, Arizona receive on the June Solstice? ______ F. Why isn’t Circle, Alaska hotter than Phoenix in June? ___________________________ _______________________________________________________________________ B-6