1
GEOG 101 Physical Geography
Lab 2: Earth-Sun System: Global Energy Balance (Credit: Based on UCSB Geography Department laboratory with major modifications by D. Fairbanks and N. Sato)
Name ANSWER KEY Lab Section Date Materials and sources:
• a calculator • a ruler • colored pencil • a measuring tape • an overhead projector • a globe • your textbook (chapter 2) • an Internet connection
Introduction: Earth depends on energy from the sun. This lab will explore how the amount of solar energy we receive varies with latitude, distance from the sun, and time of year. You’ll learn why the length of time between sunrise and sunset (the day length) changes through the year, and why it’s different at other latitudes. You’ll also learn how seasons work, and why some latitudes experience extreme differences between summer and winter, while at other latitudes, there’s almost no difference between the seasons at all.
Key Terms: Insolation Aphelion Autumnal equinox Daylight Length Inverse square law Diurnal cycle Orbit Light intensity Rotation Perihelion Revolution Solar declination Solar constant Circle of Illumination Subsolar point Solar zenith angle Solar irradiance Summer solstice Vernal equinox Winter solstice
Section 1: Earth-Sun Distance and Insolation Sun-distance relationships play a major role in Earth’s global energy budget. The amount of energy the Earth, as a whole, receives from the sun depends on the temperature of the surface of the sun and the orbital distance between the Earth and the sun. We measure energy output from a source in Watts (joule/second = Watt). The average energy received at the top of the atmosphere distributed over a unit area at the average Earth-Sun distance is called the solar constant, which has a value of approximately 1370 Watts per square meter (1370 W m-2). Energy intercepted by a unit area on the Earth’s surface is called insolation (incoming solar radiation). There are several ways to change the average amount of energy received by the Earth (Solar Constant). These include changing the power emitted by the source (the sun), or changing the distance between the sun and the Earth. Both of these changes have occurred gradually over the Earth’s history. In this section, we will explore the relationship between insolation and the distance from the sun, using an overhead projector and a wall or whiteboard.
2
In Class Experiment—The Problem Step 1: Formulate a hypothesis concerning the relationship between insolation and distance from the sun. Write your hypothesis in the space below. I believe insolation decreases exponentially as you get farther from the sun. Step 2: Collect data Position an overhead projector such that it is shining onto a whiteboard 1 meter away. This distance should be measured between the whiteboard and the front of the projector by laying out a measuring tape 3 meters distance from the whiteboard wall. Now measure the width of the area that is illuminated by the projector, and square that value to find the total illuminated area (you can assume the illuminated area is a square). Record this in the table on the next page. Repeat this with the front of the projector at several different distances to complete the table. Make a new measurement every 50 centimeters (0.50 meters).
At some point in the experiment – any distance will work – have a friend hold a 12-inch-diameter globe in the middle of the illuminated area, with the back surface of the globe touching the whiteboard. 1a) You’ll notice that half of the globe’s surface area is illuminated at any time. This holds true for the Earth as well. Stand right next to the projector (but not blocking any of its light), viewing from the perspective of the “sun.” From your perspective, the illuminated portion of the globe appears as a flat disk, called the circle of illumination. Calculate the area of this circle of illumination, using the formula for the area of a flat circle (A = π * r2). The radius of your globe is 0.1524 meters, and your answer will be in square meters (a measurement of area). This area will be the same throughout the experiment. A = π x 0.15242 = π x 0.1524 x 0.1524 = 0.072965877 m2 1b) A small amount of the projector’s light is scattered and absorbed by the air between the globe and the projector bulb, but this effect is negligible. In the solar system, this effect is almost zero, because the amount of matter in space between the sun and the top of Earth’s atmosphere (thermopause) is insignificant (i.e. vacuum of space). As you’re completing the table on the next page, notice how the brightness of the illuminated area changes. Why does the brightness decrease with distance, if the amount of light energy absorbed by the air is negligible? Hint: the wattage of the projector’s bulb is constant through this experiment (and the sun’s output is nearly constant). What changes with distance that would affect the brightness of the illuminated area?
The amount of light hitting any given area becomes more diffuse (“spread out”) as you increase the distance.
3
Complete these while working with the
projector Calculate these after you’re finished with the projector
Distance from board to projector (in meters)
Width of the lighted area of the whiteboard
(in meters)
Area of the whiteboard
receiving light = (width of lighted
region)2
Percentage of the overhead’s light energy received by the
globe = (your answer to question 1a /
area of whiteboard receiving light) * 100
1.00 meter
Measurements done as a class Percentages to the right are from a diff’t
lab section
12%
1.50 meters 6%
2.00 meters 4%
2.50 meters 2.5%
3.00 meters 1.5%
1c) From the table above, graph how the energy received by the globe changes with distance: Make sure that both axes have labels and units.
1d) Look carefully at the table and the graph that you completed above. Describe the relationship between distance and the percentage of the overhead’s light energy received by the globe. Is this a linear relationship? Why or why not? Explain what happens when you double the distance between the wall and the projector. This is an inverse exponential relationship, or specifically, an inverse square. It is not linear because it is not a straight line. If you double the distance between the wall and the projector, the amount of energy received decreases by a factor of four. Step 3: Based on the data you collected did you accept or reject your hypothesis? I was right! My hypothesis was accepted.
Free Multi-Width Graph Paper from http://incompetech.com/graphpaper/multiwidth/
Distance from board to projector (meters)
4
1e) Step 4: Can you make predictions from your experiment? Your answer for question 1d relates to the solar system. (The projector’s bulb represents the sun, and the distances you measured represent the distance to the sun from a planet.) Re-read the introduction section on the first page of this lab, and apply what you’ve learned thus far in the lab to explain why the solar constant would decrease if the distance between Earth and the sun doubled. Would the solar constant be approximately 686 W m-2, or would it be significantly less than that? Why? You won’t need any calculations to figure this out – just look at your table above from the projector experiment, and your answers to questions 1c and 1d. Yes we can make predictions. The solar constant would not be 686 W/m2, it would be less (it would be 343 W/m2, which is ¼ of 1330) Congratulations! You have just conducted an experiment proving that the Inverse Distance Square Law works! 1f) The Earth has a slightly lopsided orbit around the sun. The Earth is closest to the sun (about 147.3 million km away) on approximately January 3rd during Perihelion and farthest from the sun (about 152.1 million km away) on approximately July 4th, during Aphelion. This is easy to remember because Aphelion occurs when the Earth is farther Away from sun. Based upon your projector experiment above, is insolation higher at: (Circle one) perihelion or aphelion? Explain why that’s surprising, given that perihelion occurs around January 3, when the northern hemisphere is experiencing winter. Even though the earth is slightly closer to the sun on Jan 3, it is still winter in the northern hemisphere—It is still cold because the sun’s rays aren’t hitting the northern hemisphere directly, rather they are hitting at an angle (remember the magnifying glass on a leaf example). Perihelion and Aphelion only measure distance from the planet to the sun. They do NOT determine the seasons. The seasons are determined by the tilt of the Earth in relation to the sun. 1g) The following website shows the dates and times of perihelion, aphelion, the equinoxes, and solstices, for past and future years:
http://aa.usno.navy.mil/data/docs/EarthSeasons.php Why do the dates and times of these events vary from one year to the next? (Why doesn’t the vernal equinox always occur on March 20, UTC?). Hint: the Earth makes one orbit around the sun in 365.24 days. Also think…why do we have a leap year every once in four years? The number of days in each month and in each year are human creations—since the year is actually 365.24 days and not 365 exactly, we need to make corrections, like leap year. Therefore, the actual dates of the equinoxes and soltices will vary slightly from year to year.
5
Section 2: Latitude, Seasons, and Insolation 2a) Use your textbook to complete the following table:
Parallel (latitude value) Name
66.5° N Arctic Circle
23.5° N Tropic of Cancer
0° Equator
23.5° S Tropic of Capricorn
66.5° S Antarctic Circle 2b) The following website shows the Earth-Sun relationship.
http://esminfo.prenhall.com/science/geoanimations/animations/01_EarthSun_E2.html Click the “Show Earth Profile” button to display Earth and sun’s rays (that illuminate different parts of the Earth). Use this website to complete the following table:
Latitude that receives sun’s
rays from directly
overhead
Earth’s axial tilt
Which pole, if any,
receives no insolation
Which hemisphere receives more
insolation? (or are they approximately equal?)
March 20 (question 2a) 0° (Equator) 23.5° Neither Equal
June 21 (question 2b)
Tropic of Cancer 23.5° N 23.5° South North
September 22 (question 2a) Equator 23.5° Neither Equal
December 21 (question 2c)
Tropic of Capricorn
23.5° S 23.5° North South
2c) What is the season (for NH) when the area to the north of the Arctic Circle is in darkness 24 hours a day? Winter 2d) When Chico (~40° N) is experiencing summer, a location on the 40° S is experiencing _Winter__. 2e) What is the season (for NH) when the area to the south of the Antarctic Circle is in darkness 24 hours a day? Summer 2f) What event occurs on the days when ALL locations of Earth experience 12 hours of daytime and 12 hours of nighttime? Equinoxes (Spring, Fall)
6
2g) Comparing those locations (one on the 40° N and the other on the 40° S), which site is experiencing shorter day length on June 21? 40° S 2h) Again, comparing those locations (one on the 40° N and the other on the 40° S), which site is receiving more direct sunlight (solar radiation) on June 21? 40° N 2i) The Earth’s axial tilt, which is approximately 23.5°, appears repeatedly throughout this lab, especially in defining the Tropic of CaNcer (23.5° N), the Tropic of Capricorn (23.5° S), and the Arctic and Antarctic Circles, which are each 23.5° away from their respective poles (90° – 23.5° = 66.5°). On the figure below, (which is not to scale), notice that the Earth’s rotational axis is tilted and that the tilt does not change as the Earth revolves around the sun. That is, this “axial tilt” is always 23.5° off from perpendicular to the Earth’s orbital plane. We call this “axial parallelism.” Label each curved arrow with the season the northern hemisphere is experiencing in that portion of Earth’s orbit around the sun (winter, spring, summer, and autumn). Also, sketch an approximate position of the Earth’s current location on the diagram with the Earth’s axis and label the poles.
Spring Winter
Summer Fall
!Feb 4
7
2k) The following diagram portrays the sun and inner planets, to scale, as they would appear from a position 270 billion kilometers above the sun’s north pole. When seen from this orientation, the Earth orbits counterclockwise around the sun, and it also rotates counterclockwise around its axis. Two lines are drawn from the sun, containing all the possible paths that the sun’s rays could take to reach Venus. Draw similar lines for Earth: one from each edge of the sun, containing all the paths that solar rays could take to reach the Earth’s position shown here. You’ll notice these are almost parallel, which explains why the sun’s rays reaching Earth can be approximated as parallel.
Draw lines from the sun to the Earth, in the same manner as the lines drawn to Venus
8
Section 3: Day length, Latitude, Seasons, and Insolation The times of sunrise and sunset vary over the course of a year, and also vary by latitude. The following website uses very accurate algorithms to calculate sunrise and sunset times for any location on Earth – just input the latitude, longitude, and date:
http://www.esrl.noaa.gov/gmd/grad/solcalc/sunrise.html Similar algorithms were used to create the graph below. 3a) The graph below portrays the relationship between latitude and length of daylight on the two extremes (the solstices). All other days of the year will fall between the two curves in this graph (above the winter solstice line, and below the summer solstice line), for every point on Earth. Find the equator (0° latitude) in the graph below. How many hours of sunlight does the equator receive on any day of the year?_____12___ hours
3b ) Use a ruler to draw in and label the Arctic and Antarctic circles in the graph below. Which place will receive more hours of sunlight on June 21: a location on the Tropic of CaNcer, or a location just north of the Arctic Circle? Arctic Circle, because it is further north 3c) Which place will experience a greater change in daylight length from summer to winter: Chico (about 40° N latitude), or Minneapolis (45° N latitude)? Minneapolis, because it is further north 3d) Which place will experience a greater change in daylight length from summer to winter: Chico (approximately 40° N latitude), or Buenos Aires, Argentina (approximately 34° S latitude)? (Or will they be about the same?) Chico, because it is further from the equator
0
2
4
6
8
10
12
14
16
18
20
22
24
-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90 Latitude (negative for southern hemisphere)
H ou
rs o
f d ay
lig ht
(s un
se t-s
un ris
e)
June 21 December 21
Antarctic Circle Arctic Circle