Pulse of the Planet: Calculating Sun Angles
Students use a formula to calculate sun angles, the key to knowing why Earth's seasons
change and the key to knowing how to orient shading to save energy.
Author
Grade Level
Duration
National Geography
Standards
ELEMENT THREE:
PHYSICAL
SYSTEMS
7. The physical
processes that shape the
patterns of Earth’s
surface.
Denise Dorn and Ron Dorn
6-7
2 class period
Arizona Geography
Strand 4
CONCEPT 1
World in Spatial Terms
GRADES 6, 7, and 8
PO 2 Identify purposes of, and
differences among, maps,
globes, aerial photographs,
charts, and satellite images.
CONCEPT 3
Physical Systems
Science Strand 6 Concept 2
GRADE 6
Explain the water cycle and
factors that affect climate.
Science Strand 6 Concept 3
GRADE 7
Explain the relationships
between the Earth and other
objects in the solar system.
Overview
Seasons affect so much of our lives, from what
we wear to when crops are planted. This lesson
explains the basic reason behind seasons, using
math to help explore relationships between axial
tilt and solar flux.
Background for Teacher
All of the background needed to understand
seasons can be found in the two movies that are
linked to the lesson home page. There is also a
PowerPoint presentation linked to the lesson
home page. This presentation explains the
mathematics of this lesson.
Answers to Tough Questions
Arizona Math Standard
STRAND 1 Number Sense and Operation
CONCEPT 1 Number Sense
GRADE 7
PO 4 Model and solve simple problems involving
absolute value.
CONCEPT 2 Numerical Operations
GRADE 7
PO 1 Add, subtract, multiply, and divide integers.
STRAND 4 Geometry and Measurement
CONCEPT 1 Geometric Properties
GRADE 6
PO 2 Solve problems using properties of supplementary,
complementary, and vertical angles.
GRADE 7
PO 1 Recognize the relationship between central angles
and intercepted arcs; identify arcs and chords of a circle.
Question: Why is it summer after the June
22nd solstice? Why isn’t it summer a month
and a half before and after the solstice?
Answer: It takes a long time for Earth to heat up
and cool down. So the 3 months after the time
of most sunlight is the time when Earth has
already heated up. There is also a “lag effect”
after the winter solstice (December 22nd).
Question: Earth is closest to the sun
(perihelion) in January, and Earth is farthest
from the sun (aphelion) in July. So why is it
summer in June and winter in January?
Answer: Earth is 3 million miles closer in
January. It is still winter (in the northern
hemisphere), because the sun angles are so low
and because the day lengths are so short.
Pulse of the Planet: Calculating Sun Angles
[Students may follow this up by asking if
seasons are harsher in the southern hemisphere
because perihelion (closest) occurs during their
summer solstice (longer days, higher sun
angles). The answer is yes. The sunlight is more
intense in their summer and less intense in their
winters. Another point to make is that having
perihelion occur in winter makes our winters
less harsh and our summers less intense.
Purpose
Students need to learn about why the Earth has
seasons. This is a core concept in physical
geography and has implications for all parts of
learning about Earth and its peoples.
Materials

Teacher Information

CD to play the movies and means to project
the movie on the CD (either on classroom
TV or via projector)

Student Note Taking Guide Worksheet and
Teacher Key

Student Activity Sheet and Teacher Key

Paper (construction, plain, or colored)

Pencil

Protractor

Optional: flashlight and globe

Wall Map
Objectives
The student will be able to:
1. Explain the relationship between sun angles
and seasons
2. Use information on the time of year and
specific latitude to calculate the noon sun angle.
Procedures
Students should have had experience in angles
and subtraction.
1. Introduce the lesson by showing Snow and
Vegetation Seasons Movie
(SeasonChangeGlobe.mpg) . Show this on a
“loop” as the set for lesson. Ask students to
describe what they are seeing. This movie shows
seasonal changes as seen by NASA satellites.
2. Put up Word Wall of key vocabulary terms.
It is helpful for ELL students to review key
terms (seasons, tilt, fall, winter, spring, summer,
solstice, equinox).
3. Have students work in groups of 3 – 4. Give
each group a piece of paper (plain, construction,
colored). Tell students to work in pencil
because they may need to make corrections to
their notes. Have one student in each group,
make 4 fold, and label top with seasons. Ask
students, in their groups, to make short list of
things that they do differently in each season
(food, activities, clothing, etc). Have groups
share their answers.
4. Discuss how seasons affect the planet– what
did they notice in the movie that was playing
when they came into class? They should list
things like weather and vegetation patterns.
They may be able to extend this to migration
patterns of animals.
5. Show Pulse of the Planet Movie
(PulsePlanetGSFC.mpg) - discuss images. Use
Notes for Pulse of the Planet Video for extra
information.
6. Distribute Note Taking Guide Worksheet or
have students take notes on notebook paper.
Your class may have prior knowledge about the
location of the Arctic and Antarctic Circle, the
Equator, and the Tropics of Cancer and
Pulse of the Planet: Calculating Sun Angles
the sun. On this day there are 12 hours
daylight/12 hours night entire globe. Vernal
Equinox occurs on March 22nd. The first day of
spring. Autumnal Equinox occurs on September
22nd. The first day of fall.
Capricorn. If this is the case, give them a few
minutes to fill in the diagram on page one of the
Note Taking Guide.
7. Provide direct instruction about causes of
seasons.
o Explain that the basic of idea of seasons
is easy to understand. Summer occurs
when more sunlight hits that place on
Earth. Winter occurs when less sunlight
hits that place.
o Earth’s orbit is nearly circular NOT an
ellipse (draw on board). Our seasons
ARE NOT the result of our distance
from the sun!
o Earth average distance from sun is about
93 million miles. Earth is 3 million miles
closer to sun in January (perihelion) -winter in N. Hemisphere. Earth is further
away from sun in July (aphelion) –
summer in N. Hemisphere
8. Show Day length Movie
(DayLengthGSFC77_2.mpg). This video
explains the role of the tilt Earth’s axis in
causing our seasons.
9. Review the DayLength Movie – have students
construct notes or fill out diagram on Note
Taking Guide Worksheet. Have students
brainstorm a list of things they learned from the
video. Write results of brainstorming on the
board. Put this information into the categories
Vernal Equinox, Summer Solstice, Autumnal
Equinox, Winter Solstice. Provide missing
information. Have student fill in Note Taking
Guide. Have partners trade Note Taking Guides
to check work.
Key Points
o
o
o
o
o
Summer occurs when more sunlight hits Earth
Winter occurs when less sunlight hits Earth
Earth is tilted on its axis (23.5o) toward the Plane
of the Ecliptic (or the orbital path of the Earth)
It is the tilt that affects the length of our days and
causes the changes of our seasons
On both the vernal and autumnal equinox the
poles are not pointing towards, nor away from
o
Summer Solstice. The first day of summer.
Occurs on June 22nd. The North Pole is tilled
towards the sun, and the South Pole is tilled away
form the sun. On this day there are 24 hours
daylight above Arctic Circle and 24 hours of
darkness below Antarctic Circle. On this day,
places in the N. Hemisphere receive more than
12 hours of daylight. On this day, places in S.
Hemisphere receive less than 12 hours of
daylight.
o
Winter Solstice. The first day of winter. Occurs
on December 22nd. The South Pole is tilled
towards the sun, and the North Pole is tilled away
form the sun. On this day there are 24 hours of
daylight below the Antarctic Circle and 24 hours
of darkness above Artic Circle. On this day,
places in the S. Hemisphere receive more than 12
hours of daylight and places in N. Hemisphere
receive less than 12 hours of daylight.
10. Discuss sun angle
Ask: When you go outside today at NOON
where is the sun? Point to where you think it
will be. Talk to your neighbor and decide
what angle you have each shown. When you
go outside at NOON the day before winter
break, where is the sun? Point to its location.
Talk to your neighbor and decide what angle
you have each shown.
Tell students: Most people think the sun is
directly overhead at noon. The truth is this
rarely happens. There are many places where
it never happens! The angle the sun’s rays
make when striking the earth play an
important roll in our seasons.
11. Show Sun Angle Movie.
(SunAngleGSFC77_3.mpg )
12. Review the information presented in the Sun
Angle movie. – have students construct notes or
fill out diagram on Note Taking Guide
Pulse of the Planet: Calculating Sun Angles
Worksheet. Have students brainstorm a list of
things they learned from the video. Write results
of brainstorming on the board. Student can then
answer the questions on the Note Taking Guide.
Have partners check/discuss their answers.
Key Points
o
The sun emits light and heat in all directions.
Solar flux is the term used to describe the
amount of sunlight striking a given area. If
small amount of light hits the area, the solar
flux is low. If a lot of light hits the area
solar flux is high. Solar flux affects
temperature because the sun emits both light
and heat. Low soar flux means temperatures
are cold, high solar flux means temperatures
are warm. When a surface is tilted, fewer
sunrays strike it so solar flux decrease and
temperature drops. Because the Earth is a
sphere, the ground near the poles is tilted
and receives less light. Solar flux is low and
so temperatures are cool. Near the equator,
the surface faces more directly towards the
sun. Solar flux is high and temperatures are
warmer.
Explain that summer occurs when two things
happen together: (1) days are longer, so more
sunlight hits the Earth at that place; (2) sun
angles are higher (45o – 90o), so sunlight is more
intense.
After this video, it is sometimes useful to use a
flashlight to make the point. If you shine a
flashlight directly down on a spot, the light is
most intense – as in summer. The angle formed
between the light source and the surface is 90o.
Then, shine the light at an oblique angle. The
angle formed between the light source and the
surface is less than 90o. Explain that the light is
spread out over a larger area and is much less
intense — as in winter.
13. Show Sunlight Striking Earth
(UV_EarthGSFC2218.mpg). This movie shows
sunlight received at different latitudes, in the
Western Hemisphere, zooming into North
America. Red means more sunlight. Explain to
the students that the ups and downs of the red
are the seasons. Reinforce idea of warm at
equator/cooler towards the poles.
14. Complete Note Taking Guide Worksheet
15. Complete Sun Angle Worksheet. Model for
the student how to calculate noon sun angle.
There is PowerPoint presentation on the CD that
is intended to reinforce the idea behind seasons
and sun angles, and to model the mathematics of
the lesson. Its use is optional.
16. Complete Geography Assessment
Assessment
The student activity sheet serves as the
assessment for the mathematics performance
objectives. Mastery will be considered 80% or
higher.
There is a multiple-choice assessment of the
geography objectives of this lesson. Four out of
five correct will be considered mastery.
Extensions
Have students use protractors to draw the angles
they calculate on the student worksheet.
Coordinate this lesson with science, perhaps
using flashlights and globes for kinesthetic
learners. This may also fit with studies in
science on the solar system.
Another extension is to learn about climographs,
so students can see how seasons play out at
different places on Earth.
Use this lesson to introduce the need for
different clothing styles, house types,
vegetation, etc. around the world.
For another explanation about Earth-Sun
relationships, students can read the NGS
Reading Expeditions book Earth, Sun, Moon
by Glen Phelan. ISBN 07922-4573-3.
Pulse of the Planet: Calculating Sun Angles
Sources
All of the videos are courtesy of NASA’s
Goddard Space Flight Center and their
visualization group.