# Latitude, Angle of Sun and Solar Energy

Subject:

Science

6, 7, 8, 9, 10, 11, 12

Title – Latitude, Angle of Sun and Solar Energy
By – Mark Wenning
Primary Subject – Science (Astronomy & Physics)

Description:

• Students massage spreadsheet data by using sorts to tease out the relationships between latitude, angle of the sun, surface area of light beam and temperature.
• Also introduces possible confounding variable of elevation and the need to control for elevation.
• Uses data in a spreadsheet and a flashlight beam lab or Sketchup file to see light surface area increase or decrease with angle change.
• The student lab worksheet and teacher guide are included (below).

California Earth Sciences Standards – Earth in the Solar System:

1. The structure and composition of the universe can be learned from studying stars and galaxies and their evolution.
e.   As a basis for understanding this concept, students know the appearance, general composition, relative position and size, and motion of objects in the solar system, including planets, planetary satellites, comets, and asteroids.
The ISTE National Educational Technology Standards:
1. Creativity and Innovation:
Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
a.   Students apply existing knowledge to generate new ideas, products, or processes.
1. Research and Information Fluency:
Students apply digital tools to gather, evaluate, and use information.
d.   Students process data and report results.
1. Technology Operations and Concepts:
Students demonstrate a sound understanding of technology concepts, systems, and operations.
a.   Students understand and use technology systems.
b.   Students select and use applications effectively and productively.
c.   Students troubleshoot systems and applications.

# Worksheet and Lab: Latitude, Angle of Sun and Solar Energy

Names:

Partner 1 ___________________          Partner 2 ___________________

Why is it hot in the summer (select the best answer)?

1. Because it’s summer.
2. Because the earth is closer to the sun.
3. Because the solar energy is stronger.
4. Because the solar energy is concentrated over a smaller surface area.
5. Because the winter snow melted.

Let’s try an experiment.

Lab protocol:

1. Each lab team will use a flashlight that has been taped to one end of a meter stick.
2. Hold the meter stick perpendicular to the floor with the flashlight pointing down.
3. Turn the flashlight on and focus the beam so that you get a nicely defined small circle of light projecting on the floor.
4. Measure and record the diameter of the circle.
5. Then tilt the meter stick so that it is at a 45° angle to the floor.
6. Measure and record the longest distance across the oval.
7. Estimate and record how much more surface area the 45° angle circle covers versus the 90° angle circle (2x, 3x, 3.5x?).
8. Now compare the brightness of the light where it hits the floor surface by shining the light at 45° and 90°.

Record which setting had a brighter area of light?

Gathering and analyzing data:

Let’s look at some data to try to see patterns that might relate to the question as to why it’s hotter in the summer. Open the file Latitude/Angle of the Sun Spreadsheet. There are six columns of data: City, State, Latitude, Angle of the Sun (at noon on Spring Equinox day), Surface Area covered by a square meter of light energy and Elevation.

Science is often driven by data. Huge amounts a data. Data that can look like this – messy and unwieldy. Let’s try to organize it to see if any patterns emerge that might help us answer the question why it’s hot in the summer.

There are a number of different data points associated with every city. We are interested in factors (there may be more than one) that might influence temperature. How can we organize the spreadsheet so that a pattern or patterns might emerge. Well, since we’re interested in temperature, let’s organize the data by temperature.

• Click on any cell (box) in the spreadsheet and hold the command key (apple key for Macs) and push “A” to select all.
• Go to the Data menu and pull down to Sort.
• Pull down the Sort by options menu and choose Avg. Annual Temp. and then select descending radio button and click OK.

It looks like there is somewhat of a relationship between temperature and latitude and angle of the sun. Let’s explore more.

• Click on any cell (box) in the spreadsheet and hold the command key (apple key for Macs) and push “A” to select all.
• Go to the Data menu and pull down to Sort.
• Pull down the Sort by options menu and choose Angle of the Sun and then select ascending radio button and click OK.

There does seem to be a direct inverse relationship between angle of the sun and latitude. At noon on Spring Equinox day at 71.3° latitude of Barrow, Alaska, the sun is at an 18.7° angle in relation to the surface of the earth.

1. What is the mathematical relationship between angle of the sun and latitude (hint: scroll down to Quito, Ecuador at 0° on the equator? _________________________________________________________________

When you go outside on a sunny day it is usually hotter than on a cloudy day. As you may have guessed, the heat is due to the sunlight… but it is not heat energy that travels here from the sun. Do you know why? ____________________________________________

What does travel from the sun to Earth is light energy, in the form of photons that hit the planet surface. That light energy is then converted to thermal energy.

2. Beside clouds, what else might influence how much light energy hits a specific area of the planet (hint: think about the little lab we just did)?
______________________________________________________________________________

Look at your spreadsheet. There also seems to be another direct inverse relationship between angle of the sun and something else besides latitude.

3. As the angle of the sun increases, what decreases? ______________________________________
4. If the same amount of energy (1 square meter) is distributed over either 3 square meters of earth surface or ……. 1 square meter, which surface receives a more intense or concentrated amount of energy, say in just one of its square centimeters? _______________________________________

For the most part, the closer to the equator as city is the higher the angle of the sun AND the less surface area a square meter of sunlight is distributed over AND the higher average annual temperature. There are some exceptions. You may have noticed the average annual temperature of Quito, Ecuador is only 15Â° Celsius and yet, it’s on the Equator! There might be some other factor or factors at work.

5. Can you see any data in our spreadsheet about Quito, Ecuador that might be different than most other cities?
____________________________________________________________________
6. In California it rains over most of the state during the winter months, but on the very same day, high in the Sierra mountains, it will be snowing. Can anyone guess why it’s colder in the mountains?
_______________________________________________________________________________

If we suspect the higher altitude might be why Quito has a colder climate than expected, how might we check to see if altitude has an effect on average annual temperature?
___________________________________________________________________________________

Now let’s get back to the original question…… Why is it hot in the summer?

7. Does a city’s latitude change as summer solstice approaches?______
8. What does change? _______

Why is it hot in the summer (select the best answer)?

1. Because it’s summer.
2. Because the earth is closer to the sun.
3. Because the solar energy is stronger.
4. Because the solar energy is concentrated over a smaller surface area.
5. Because the winter snow melted.

Due to the tilt of the Earth, which always points the same way, as the earth revolves around the sun, the angle of the sun changes no matter where one is located. As summer solstice approaches, the sun beam at 90Â° angle (at noon) is positioned a little more north each day, until the solstice when it is at latitude 23.5° N. From then on, until to winter solstice, the 90Â° angle moves further southward with each day.

9. If the angle of the sun is at 50° in Columbus, Ohio on March equinox (when it is 90Â° at the equator), what will the angle be in Columbus on summer solstice when 90° is at 23.5° N? ______
10. How did you figure that out? ________________________________________________________
11. What will the approximate surface area be for 1 square meter of light (hint: you have a large dataset to pick the answer from)?_____
12. If the surface area for 1 square meter of light is smaller, will the energy be more concentrated?_____
13. If the surface area is smaller and the energy more concentrated, how will that affect temperature? _______
14. What will the sun’s angle be in Columbus on winter solstice (it’s 90° at 23.5° S)? ______
15. What will the approximate surface area be for 1 square meter of light?_____
16. If the surface area for 1 square meter of light is larger, will the energy be more concentrated?______
17. If the surface area is larger and the energy less concentrated, how will that affect temperature? ______

Applying what we have learned:

Science is about learning about the world. One of the ways scientists study the world is to collect data. The data can then be organized and sometimes it falls into patterns. Scientists often use patterns to make predictions.
1. Rochester, NY is at 43.12Â° latitude and Fort Worth, TX is at 32.83 (they’re both at about the same elevation). Predict which of these two cities might have the higher average temperature?
________________________________________________________________________________
2. If we suspect that latitude/angle of the sun/surface area (they are all directly related) might effect average annual temperature, why is it better to look just at cities of the similar elevation?
________________________________________________________________________________
3. Denver, CO is at the same latitude as Atlantic City, NJ. However, Denver is at 5,280 ft. elevation and Atlantic City is at 66 ft. Predict which of these two cities might have the higher average temperature?
_____________________________________________________________________

Teacher Worksheet and Lab: Latitude, Angle of Sun and Solar Energy

Names:

Partner 1 ___________________          Partner 2 ___________________

Why is it hot in the summer (select the best answer)?

1. Because it’s summer.
2. Because the earth is closer to the sun.
3. Because the solar energy is stronger.
4. Because the solar energy is concentrated over a smaller surface area.
5. Because the winter snow melted.

Let’s try an experiment.

NOTE: Teachers should try the lab ahead of time to make sure you can darken the room AND (very important) the flashlights you will use can be focused to exhibit defined edges to the circles of light.

Lab protocol:

1. Each lab team will use a flashlight that has been taped to one end of a meter stick.
2. Hold the meter stick perpendicular to the floor with the flashlight pointing down.
3. Turn the flashlight on and focus the beam so that you get a nicely defined small circle of light projecting on the floor.
4. Measure and record the diameter of the circle.
5. Then tilt the meter stick so that it is at a 45° angle to the floor.
6. Measure and record the longest distance across the oval.
7. Estimate and record how much more surface area the 45° angle circle covers versus the 90° angle circle (2x, 3x, 3.5x?).
8. Now compare the brightness of the light where it hits the floor surface by shining the light at 45° and 90°.

Record which setting had a brighter area of light?

NOTE: Teachers should become familiar with the spreadsheet ahead of time to make sure you can do the sorts. The spreadsheet should initially be set to a sort by city names A – Z.

Gathering and analyzing data:

Let’s look at some data to try to see patterns that might relate to the question as to why it’s hotter in the summer. Open the file Latitude/Angle of the Sun Spreadsheet. There are six columns of data: City, State, Latitude, Angle of the Sun (at noon on Spring Equinox day), Surface Area covered by a square meter of light energy and Elevation.

Science is often driven by data. Huge amounts a data. Data that can look like this – messy and unwieldy. Let’s try to organize it to see if any patterns emerge that might help us answer the question why it’s hot in the summer.

There are a number of different data points associated with every city. We are interested in factors (there may be more than one) that might influence temperature. How can we organize the spreadsheet so that a pattern or patterns might emerge. Well, since we’re interested in temperature, let’s organize the data by temperature.

• Click on any cell (box) in the spreadsheet and hold the command key (apple key for Macs) and push “A” to select all.
• Go to the Data menu and pull down to Sort.
• Pull down the Sort by options menu and choose Avg. Annual Temp. and then select descending radio button and click OK.

It looks like there is somewhat of a relationship between temperature and latitude and angle of the sun. Let’s explore more.

• Click on any cell (box) in the spreadsheet and hold the command key (apple key for Macs) and push “A” to select all.
• Go to the Data menu and pull down to Sort.
• Pull down the Sort by options menu and choose Angle of the Sun and then select ascending radio button and click OK.

There does seem to be a direct inverse relationship between angle of the sun and latitude. At noon on Spring Equinox day at 71.3° latitude of Barrow, Alaska, the sun is at an 18.7° angle in relation to the surface of the earth.

1. What is the mathematical relationship between angle of the sun and latitude (hint: scroll down to Quito, Ecuador at 0° on the equator?

At noon on the equinox days the angle of the sun added to its specific latitude always totals 90. NOTE: This is only true at noon on equinoxes.

When you go outside on a sunny day it is usually hotter than on a cloudy day. As you may have guessed, the heat is due to the sunlight… but it is not heat energy that travels here from the sun. Do you know why?

Heat cannot travel through a vacuum (not many will know this).

What does travel from the sun to Earth is light energy, in the form of photons that hit the planet surface. That light energy is then converted to thermal energy.

2. Beside clouds, what else might influence how much light energy hits a specific area of the planet (hint: think about the little lab we just did)?

Angle of the sun

Look at your spreadsheet. There also seems to be another direct inverse relationship between angle of the sun and something else besides latitude.

3. As the angle of the sun increases, what decreases?

Surface area hit by a specific beam of light

4. If the same amount of energy (1 square meter) is distributed over either 3 square meters of earth surface or ……. 1 square meter, which surface receives a more intense or concentrated amount of energy, say in just one of its square centimeters?

1 square meter

For the most part, the closer to the equator as city is the higher the angle of the sun AND the less surface area a square meter of sunlight is distributed over AND the higher average annual temperature. There are some exceptions. You may have noticed the average annual temperature of Quito, Ecuador is only 15° Celsius and yet, it’s on the Equator! There might be some other factor or factors at work.

5. Can you see any data in our spreadsheet about Quito, Ecuador that might be different than most other cities?

It’s at 9350 feet.

6. In California it rains over most of the state during the winter months, but on the very same day, high in the Sierra mountains, it will be snowing. Can anyone guess why it’s colder in the mountains?

Air is less dense and traps less reflected heat.

If we suspect the higher altitude might be why Quito has a colder climate than expected, how might we check to see if altitude has an effect on average annual temperature?

Check other high altitude cities and compare with cities at lower altitude BUT at the same latitude NOTE: Cities on coast are often cooler as well.

Now let’s get back to the original question…… Why is it hot in the summer?

7. Does a city’s latitude change as summer solstice approaches? No.
8. What does change? Angle of the sun.

Why is it hot in the summer (select the best answer)?

1. Because it’s summer.
2. Because the earth is closer to the sun.
3. Because the solar energy is stronger.
4. Because the solar energy is concentrated over a smaller surface area.
5. Because the winter snow melted.

Due to the tilt of the Earth, which always points the same way, as the earth revolves around the sun, the angle of the sun changes no matter where one is located. As summer solstice approaches, the sun beam at 90Â° angle (at noon) is positioned a little more north each day, until the solstice when it is at latitude 23.5° N. From then on, until to winter solstice, the 90Â° angle moves further southward with each day.

9. If the angle of the sun is at 50° in Columbus, Ohio on March equinox (when it is 90° at the equator), what will the angle be in Columbus on summer solstice when 90° is at 23.5° N? 73.5°
10. How did you figure that out?

Since the perpendicular angle moved 23.5 north, add 23.5 to 90 and then subtract the latitude.

11. What will the approximate surface area be for 1 square meter of light (hint: you have a large dataset to pick the answer from)? 1.042948913 or approx.
12. If the surface area for 1 square meter of light is smaller, will the energy be more concentrated? Yes.
13. If the surface area is smaller and the energy more concentrated, how will that affect temperature? Hotter.
14. What will the sun’s angle be in Columbus on winter solstice (it’s 90° at 23.5° S)? 26.5°
15. What will the approximate surface area be for 1 square meter of light? 2.241158452 or approx.
16. If the surface area for 1 square meter of light is larger, will the energy be more concentrated? Less.
17. If the surface area is larger and the energy less concentrated, how will that affect temperature? Cooler.

Applying what we have learned:

Science is about learning about the world. One of the ways scientists study the world is to collect data. The data can then be organized and sometimes it falls into patterns. Scientists often use patterns to make predictions.

They can check the spreadsheet after making predictions.

1. Rochester, NY is at 43.12° latitude and Fort Worth, TX is at 32.83 (they’re both at about the same elevation). Predict which of these two cities might have the higher average temperature? Fort Worth, TX
2. If we suspect that latitude/angle of the sun/surface area (they are all directly related) might effect average annual temperature, why is it better to look just at cities of the similar elevation?

To eliminate the possible effect of elevation (control)

3. Denver, CO is at the same latitude as Atlantic City, NJ. However, Denver is at 5,280 ft. elevation and Atlantic City is at 66 ft. Predict which of these two cities might have the higher average temperature?

Atlantic City, NJ

More Data Discovery Lessons:

Download this lesson and more Mark Wenning Data Discovery science lessons designed to engage students with real-world data relevant to content taught in middle and high school science courses at: