Calculating the Sun’s Energy SummaryThe sun is a main sequence star (G-2, yellow dwarf) that is the closest stellar object to our planet. It has long been the inspiration for humans throughout civilization, as the main life-sustaining source of light and heat; without the sun's energy, life as we know it would not exist. In this lesson, students will be able to explain the fusion reactions that are vital to the sun's existence, measure the energy output of the sun, and compare the sun's energy to conventional fossil-fuel resources here on earth.KeywordsSolar wind, helium, hydrogen, fusion, core, sunspot, plasma, solar eclipse, radiationLearning ObjectivesAfter this lesson, students should be able to: Describe how the sun was formed, it's current stage of stellar evolution. Identify solar features, including sun spots, solar flares, eclipse . Quantify the energy output of the sun, and compare/contrast solar energy to other forms used here on earth.Introduction / Motivation The Sun is a G2 main sequence star, and is the central feature around which our solar system is arranged. This fiery ball of hydrogen and helium is at least 4.5 billion years old, and contains over 99% of all the matter in our solar system; a million Earths could fit within the Sun! With a diameter of over 1.39 x 106 km and a mass of 1.99 x 1030 kg (330,00 Earths!), the Sun is a dynamic star with its own atmosphere that is layered with denser gasses at its core. The photosphere is the portion of the start that produces visible light, allowing us to see the radiant energy even though it lies beneath two additional atmospheric layers. Beyond the photosphere is the chromosphere, which is only visible when the photosphere is blocked, such as during a solar eclipse. The choromosphere can also be imaged using filters. The outermost region of the Sun is its' corona, which extends many millions of kilometers beyond the Sun's photosphere. The visible light seen in the corona is only a fraction of what is emitted from the photosphere, though the corona often shows up brilliantly during a solar eclipse (see figure 22.2). It appears as star-burst shaped spicules that flare-out from the Sun in all directions. Some of this energy can escape the Sun's atmosphere, flowing into space as in streamers of protons and electrons, known as solar wind. The Sun's corona peeks out during the 1998 total solar eclipse in Antigua, West Indies. This is a phenomenon known as "the diamond ring" effect, which takes place just seconds before totality. Photo credit: Kelly Knight Units of Measurement Distances are measured in light-years (ly), or the AU (astronomical unit: the distance from the Earth to the Sun). Energy units include BTU's, kilowatt-hours. For a video of the Sun's layers and images of solar flares, click here: https://www.nasa.gov/mission_pages/sunearth/videos/index.html Solar Energy: Visible light is part of the electromagnetic (EM) radiation (EMR) that is emitted by ...

1. Calculating the Sun’s Energy
SummaryThe sun is a main sequence star (G-2, yellow dwarf)
that is the closest stellar object to our planet. It has long been
the inspiration for humans throughout civilization, as the main
life-sustaining source of light and heat; without the sun's
energy, life as we know it would not exist. In this lesson,
students will be able to explain the fusion reactions that are
vital to the sun's existence, measure the energy output of the
sun, and compare the sun's energy to conventional fossil-fuel
resources here on earth.KeywordsSolar wind, helium, hydrogen,
fusion, core, sunspot, plasma, solar eclipse, radiationLearning
ObjectivesAfter this lesson, students should be able to:
Describe how the sun was formed, it's current stage of stellar
evolution.
Identify solar features, including sun spots, solar flares, eclipse
.
Quantify the energy output of the sun, and compare/contrast
solar energy to other forms used here on earth.Introduction /
Motivation
The Sun is a G2 main sequence star, and is the central feature
around which our solar system is arranged. This fiery ball of
hydrogen and helium is at least 4.5 billion years old, and
contains over 99% of all the matter in our solar system; a
million Earths could fit within the Sun! With a diameter of
over 1.39 x 106 km and a mass of 1.99 x 1030 kg (330,00
Earths!), the Sun is a dynamic star with its own atmosphere that
is layered with denser gasses at its core. The photosphere is the
portion of the start that produces visible light, allowing us to
see the radiant energy even though it lies beneath two additional
atmospheric layers. Beyond the photosphere is the
chromosphere, which is only visible when the photosphere is
blocked, such as during a solar eclipse. The choromosphere can
also be imaged using filters. The outermost region of the Sun is
its' corona, which extends many millions of kilometers beyond

2. the Sun's photosphere. The visible light seen in the corona is
only a fraction of what is emitted from the photosphere, though
the corona often shows up brilliantly during a solar eclipse (see
figure 22.2). It appears as star-burst shaped spicules that flare-
out from the Sun in all directions. Some of this energy can
escape the Sun's atmosphere, flowing into space as in streamer s
of protons and electrons, known as solar wind.
The Sun's corona peeks out during the 1998 total solar eclipse
in Antigua, West Indies. This is a phenomenon known as "the
diamond ring" effect, which takes place just seconds before
totality. Photo credit: Kelly Knight
Units of Measurement
Distances are measured in light-years (ly), or the AU
(astronomical unit: the distance from the Earth to the Sun).
Energy units include BTU's, kilowatt-hours.
For a video of the Sun's layers and images of solar fl ares, click
here:
https://www.nasa.gov/mission_pages/sunearth/videos/index.htm
l
Solar Energy:
Visible light is part of the electromagnetic (EM) radiation
(EMR) that is emitted by objects. The wavelengths of radiation
emitted include dangerous cosmic rays, X-rays, radio waves,
infra-red and ultra-violet radiation. Visible light is a small part
of the full spectrum of EMR. For our sun, the EM radiation is
created by processes such as hydrogen fusion—a thermonuclear
reaction. In nebulae, gasses are heated enough to incandesce
(glow) much the same as a fluorescent light bulb does. The
sources of heat for glowing nebula may be EM radiation from
nearby stars or from hear generated by compression of these

3. same gasses. Specialized Terms
Word
Definition
Astronomical Unit (AU)
The average distance between the Earth and the Sun: 1.5 x 108
km = 93 million miles.
Chromosphere
The layer in the solar atmosphere between the photosphere and
corona.
Corona
The sun's outermost atmosphere.
Hydrogen fusion
The nuclear-reaction that fuses hydrogen atoms, producing heat
and Helium.
Luminosity
The electromagnetic radiation that is emitted from a star or
other stellar object. Sometimes expressed as a flux, or amount
per unit area.
Photosphere
The portion of the sun's atmosphere where visible light as at is
maxiumum.
Plasma
A hot, ionized gas.
Solar wind
The expulsion of electrons and protons from the sun; occurs in a
radial direction.
Sunspot
Isolated 'cool spots' in the sun's photosphere, caused by
protrusionsof the the sun's magnetic field.Watt's Better? Solar
Energy or Fossil Fuels?: This exercise will walk students
through basic energy calculations that investigate the different
energy values from solar radiation and the burning of fossil
fuels.
Conversion Chart for Energy Units
One kilowattt-hour = 3,413 Btu One barrel of oil = 1,640.8
kilowatt-hours

4. 1,367 W per square meter = solar constant Solar radiation
(entire sun) = 3.83 x 1023 kW
The sun's surface is an amazing 5700 K! Through super-heated
hydrogen and helium, large amount of energy are irradiated.
The solar radiation for the entire sun is 3.83 x 1023 kW
(Stanford Solar Center, 2016). For comparison, imagine the
radiant energy from a standard household light bulb (100 W).
As the sun's radiation travels away from the sun and towards the
earth, the rays become more diffuse. To account for this "loss"
in solar energy, scientists report incident radiation in terms of
the amount of incoming energy that would strike a plane on the
Earth's surface at 90 degrees (perpendicular) to the incoming
angle of the sun's rays (see illustration below). This is the
number is called the 'solar constant', and is reported in energy
per area; the solar constant is 1,367 W per square meter.
Incident solar energy hitting the earth's surface (ITACA, 2016)
The Earth, however, is a sphere, which must be accounted for in
our calculations. The formula for calculating the radiation
incident on a spherical surface area is, (where the radius of the
Earth, R, is 6,378 km):
solar constant x πR2 =1367 W/m2 x πR2
This value is then divided by half, to account for the
illuminated side of the earth (the opposing, or "dark side",
receives minimal incoming energy). This value, 684 W/m2 is
the average amount of energy incident on the side of the earth
that is facing the sun.

5. This incoming energy, however, is not completely received by
Earth. The Earth's atmosphere absorbs and diffuses incoming
radiation, and only about 30% makes it to the Earth’s surface.
This means the available energy for capture is:
0.7 * 684 W/m2 = 479 W/m2
If we (generously) assume that the amount of daylight during a
typical day is 12 hours, we can calculate the amount of energy
harnessed per day:
479 W/m2 * 12 hours = 5748 Wh/m2day
The energy E in kilowatt-hour (kWh) is equal to the power P in
watts (W), times the time period t in hours (hr) divided by 1000:
E(kWh) = P(W)× t(hr) / 1000
So kilowatt-hour = watt × hour / 1000
or 5748 Wh/m2day or 5.75 kWh/m2day
What does this mean? A 1 m x 1 m solar panel would be able to
receive 5.75 kWh of energy per day. For comparison, the
average US consumer uses 911 kWh per month, or 30 kWh per
day.
1. How many solar panels would it take to power a residential
property, assuming (generously) that a solar panel all ows for
100% conversion? Show your work.
Now let's look at fossil fuels...review the energy bill for your
home (or use one of the sample energy bills provided), and

6. write-down how many kWh of energy you used for the current
month.
2. How many kWh did you use in your home?
3. How many BTU's were required to create the kilowatt hours
your consumed? How many barrels of oil does this amount to?
Show your work
4. What is the going rate for a barrel of oil?
5. What is the difference between the price of barrels of oil you
consumed, and the price you paid for your electricity bill?
What might account for this price difference?
6. Compare and contrast using solar power vs. fossil fuels?
What are the benefits of each? What are some drawbacks?
Web References
http://solarscience.msfc.nasa.gov/SunspotCycle.shtml
http://umbra.nascom.nasa.gov/index.html/
http://sohowww.nascom.nasa.gov/
http://solar-center.standford.edu
http://science.nationalgeographic.com/science/space/solar -
system/sun-article/
http://nineplanets.org/sol.html
Appendix: Sample electricity bill
Unit III Assignment Worksheet
Background Information
The Ruby Red Movie Theater in town is in jeopardy of having
to close its doors because it is unable to generate enough total
revenue. In an effort to generate more total revenue, the movie
theater manager decided to change the prices this month for
drinks, popcorn, candy, hot dogs, and movie tickets.
The manager would like for you to analyze the data that has
been collected to help decide if the decisions to change the

7. prices were correct and, if not, what should be done to prices to
generate more total revenue. Be sure to answer all of the
questions in this worksheet.
Question 1
Information regarding the community’s average income and
movie ticket sales at the Ruby Red Movie Theater for both last
year and this year are presented below. Use this information
when answering questions A–C, below.
Last Year
This Year
Community’s Average Income
$55,800
$57,474
Movie Ticket Sales
4,980
5,021
A. Calculate the Income Elasticity of Demand for movie tickets.
(Show your work. You can type it in the box below, or write it
out by hand, take a picture, and insert the picture in the box.
Make sure it fits in the box. NOTE: These options apply to all
“Show your work” responses.)

8. B. Are movie tickets considered to be inferior goods, normal
goods, or unit (unitary) goods in this town? Explain why.

9. C. A new firm is relocating to the city and adding a large
number of above average salaries. Will the number of movie
ticket sales for the theater increase, decrease, or remain
constant? Base your answer on information you answered in
part B above.
Continue on next page
Question 2
The manager at Ruby Red Movie Theater decided to change the
prices of concession stand items as well as tickets this month in
an effort to increase revenues. Below, you are provided with
prices for last month and this month as well as the quantities
demanded for both months. Use this information when
answering questions A–H below.
Price

10. Quantity Demanded
Item
Last Month
This Month
Last Month
This Month
Large Drink
$6.00
$5.50
150
161
Large Popcorn
$7.50
$8.00
125
101
Small Drink
$2.50
$2.00
75
80
Small Popcorn

11. $5.00
$5.25
45
39
Candy
$4.00
$3.50
57
68
Hot Dog
$5.00
$5.25
35
36
Movie Ticket
$8.00
$9.00
428
300
A. Calculate the total revenues earned by the theater last month
and this month (Show your work.)

13. Total revenues last month =
Total revenues this month =
B. Calculate the price elasticity of demand for large drinks.
(Show your work.)

15. Is the price elasticity of demand for large drinks price elastic,
inelastic, or unit (unitary)? Briefly explain why in the box
below.
Answer =
Continue on next page
C. Calculate the price elasticity of demand for large popcorn.
(Show your work.)
Is the price elasticity of demand for large popcorn price elastic,
inelastic, or unit (unitary)? Briefly explain why in the box
below.
Answer =

16. Continue on next page
D. Calculate the price elasticity of demand for small drinks.
(Show your work.)
Is the price elasticity of demand for small drinks price elastic,
inelastic, or unit (unitary)? Briefly explain why in the box
below.
Answer =
Continue on next page
E. Calculate the price elasticity of demand for small popcorn.
(Show your work.)
Is the price elasticity of demand for small popcorn price elastic,
inelastic, or unit (unitary)? Briefly explain why in the box
below.

17. Answer =
Continue on next page
F. Calculate the price elasticity of demand for candy. (Show
your work.)
Is the price elasticity of demand for candy price elastic,
inelastic, or unit (unitary)? Briefly explain why in the box
below.
Answer =

18. Continue on next page
G. Calculate the price elasticity of demand for hot dogs. (Show
your work.)
Is the price elasticity of demand for hot dogs price elastic,
inelastic, or unit (unitary)? Briefly explain why in the box
below.
Answer =
Continue on next page
H. Calculate the price elasticity of demand for movie tickets.
(Show your work.)
Is the price elasticity of demand for movie tickets price elastic,
inelastic, or unit (unitary)? Briefly explain why in the box
below.
Answer =

19. Continue on next page
Question 3
Based on the relationship between price elasticity of demand
and total revenues, evaluate whether the individual price
changes the manager made were correct or not. Remember,
Ruby Red Movie Theater wants to increase total revenue.
A. Was the decision to decrease the price of large drinks
appropriate to increase total revenues? Why, or why not?
Briefly explain in the box below.
Answer =
B. Was the decision to increase the price of large popcorn
appropriate to increase total revenues? Why, or why not?
Briefly explain in the box below.
Answer =

20. C. Was the decision to decrease the price of small drinks
appropriate to increase total revenues? Why, or why not?
Briefly explain in the box below.
Answer =
D. Was the decision to increase the price of small popcorn
appropriate to increase total revenues? Why, or why not?
Briefly explain in the box below.
Answer =
E. Was the decision to decrease the price of candy appropriate

21. to increase total revenues? Why, or why not? Briefly explain in
the box below.
Answer =
F. Was the decision to increase the price of hot dogs appropriate
to increase total revenues? Why, or why not? Briefly explain in
the box below.
Answer =
G. Was the decision to increase the price of movie tickets
appropriate to increase total revenues? Why, or why not?
Briefly explain in the box below.
Answer =