Why Is Alaska So Cool?
Solar Angle and Solar Noon
Activity 5: Finding Solar Angle and Solar Noon
Guiding Question
How high above the horizon does the sun get on the summer solstice?
Predicting Results
Look at the diagram below.
sun
angle
you
horizon
Then predict the highest angle above the horizon the sun will be during June 20, the
date of the summer solstice. Do not look this information up in any references. Write
your hypothesis (best guess) in Data Table 3 on page 8 of these lesson plans.
Warning! DO NOT look directly at the sun. Serious eye damage can occur.
Objectives
The objectives of this activity are to:
 be able to measure the solar angle; and
 determine solar noon for your location.
Materials Needed
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sunshine – you must be able to see a distinct shadow
a place outdoors that receives unobstructed sunshine from 11 am to 2 pm or a
window through which you can see the sun during this entire time
level surface (check with a level if you have one)
wooden dowel or stick (outdoors) or pencil (indoors), or other slender object
hammer (outdoors) or tape (indoors)
clock or watch
ruler or tape measure
TI-83 Graphing Calculator
protractor
thread, string, or fishing line
Vocabulary:
Solar Angle - the angle of the sun above the horizon.
Solar Noon - the time of day at which the solar angle is greatest. This may or may not
correspond to noon on your clock or watch.
Activity 5
Page 1
Solar Angle and Solar Noon
Why Is Alaska So Cool?
Procedure
Begin the set-up of this activity about 10:00 am so that you will have all of your
equipment ready to begin your data collection at 11 am.
You may need to modify the materials to fit your circumstances, but do your best to
measure accurately. If done carefully, you should be able to determine the solar angle
accurately to within a degree or two.
The first requirement is that you have clear skies from about an hour before noon to an
hour or two after noon. The sky does not need to be cloudless, but it should be clear
enough that objects cast a distinct shadow.
Make a reasonable attempt to do this activity outdoors. Use a hammer to pound a
dowel or stick into the ground. If you must work indoors, tape a pencil or other object
to the end of a table near a window that faces south. This window should get light from
the sun from about an hour before noon to an hour or two after noon. If outdoors, you
can pound a stake into the ground. The pencil or stake is represented by A in the figure
below. B represents the shadow that the dowel or stick casts.
In either case, use your
protractor to ensure that
your object is
perpendicular to the
ground (that is, it should
make an angle of 90
with the horizontal
surface on which the
shadow falls).
Two different methods of determining the solar angle are explained on the following
pages. Read them both carefully. Then choose one method to use. Use the same method
for all your observations. Although Method 2 may seem more complicated, it is an easy,
accurate method for making solar angle measurements.
Page 2
Activity 5
Why Is Alaska So Cool?
Solar Angle and Solar Noon
Method 1: Using a Protractor to Determine Solar Angle
Remember, DO NOT look directly at the sun. Serious eye damage can occur.
In this method, you will use a protractor to directly measure the solar angle. You will
need a helper.
1. Align the shadow of the stick with the baseline of the protractor.
Make sure that your protractor is level and that the baseline of the protractor (a line
between the 0 and 180 marks) are in the same horizontal plane as the shadow your
object casts. Many protractors, as does the one shown below, have some space
between the bottom of the protractor and the scale. If outdoors, you may need to
push your protractor into the ground a bit to align the shadow and protractor scale.
Indoors, you may need to add layers of cardboard or some other flat material
beneath your shadow to get the protractor and the shadow to be in the same
horizontal plane.
2. Center the end of the shadow in the crosshairs of the protractor and have your
helper tape the end of a string or fishing line to the crosshairs.
3. Practice making angle measurements. Ask your
helper to stretch the string or fishing line tightly to
the top of the dowel or stick. Read the angle as
accurately as you can. Can you read most
accurately to the nearest degree? two degrees? five
degrees? Practice several more measurements until
you are confident in your ability to measure
accurately.
2. Make your solar angle observations. Take your first solar angle reading at 11:00 am.
Write your angle measurement in the column called "Observed Solar Angle" in
Table 1 on page 8. Make additional observations every twenty minutes. Continue as
long as your solar angle readings are the same or bigger. Stop making observations
once your solar angle readings decrease twice in a row.
Activity 5
Page 3
Solar Angle and Solar Noon
Why Is Alaska So Cool?
Method 2: Solar Angle Determination Using Geometry
In this method, you will use a tape measure or ruler to measure the height of your
dowel or stick and the length of its shadow. You will then use the TI-83 calculator to
calculate the solar angle from this information.
1. Measure the height
of your dowel or
stick (A in the
diagram). Write this
height in Table 2
found on page 8 of
these lesson plans.
2. Beginning at 11:00 am, measure the length of the shadow (B in the diagram) the
dowel or stick casts every twenty minutes. Record the length B in Table 2 on
page 8. Continue to make measurements and record them as long as the shadow
lengths are the same or decreasing. Stop making observations once the shadow
lengths increase twice in a row.
3. Use your calculator to find the solar angles. You may do this between shadow
length measurements or after you have finished all your measurements.
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Find the ratio of A
A
to B,
(or AB).
B
This ratio is the
tangent of the
solar angle,
labeled  (theta) in
the diagram to the
right. Write the value for this ratio in Table 2 on page 8.
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Check to see that your TI-83 calculator is in the degree mode rather than the
radian mode. (Remember to use the mode key and then 2nd [QUIT].)
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Determine  (the angle whose tangent is
entering the value you calculated for
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Page 4
A
) by pressing 2nd [TAN-1], then
B
A
.
B
Write the value for the solar angle, , in Table 2 on page 8.
Activity 5
Why Is Alaska So Cool?
Solar Angle and Solar Noon
Analyze and Compare
1. Write the date in Table 3.
2. In Table 3, write the name of the town in which you live or the town nearest
to your location.
3. Write the latitude and longitude of your town or the town nearest to you in
Table 3. Use your local resources to find your latitude and longitude. If you
have access to the Internet, log on and go to the USGS Geographic Names
Information System (GNIS) at
http://geonames.usgs.gov/pls/gnis/web_query.gnis_web_query_form
You need only three pieces of information to find the latitude and longitude
of places in the US and its territories: the name of the place (called “feature
name” on the menu, the state or territory, and the feature type. Be sure to
spell correctly and to identify the name of the feature correctly. In most cases,
“populated place” is the correct choice for the feature type.
4. Look through Table 1 or Table 2 on page 8 of these lesson plans to find the
largest solar angle you observed or calculated. Write this value in Table 3.
5. Solar noon is the time of day when the solar angle is largest. Use the data you
collected in Table 1 or Table 2 on page 8 of these lesson plans to find solar
noon. You probably observed that you recorded the largest solar angle more
than once. If so, solar noon would be median of the times you made this
measurement. See the example below.
Activity 5
Page 5
Solar Angle and Solar Noon
solar noon
Time*
11:00 am
11:20 am
11:40 am
12:00 noon
12:20 pm
12:40pm
1:00 pm
1:20 pm
1:40pm
Why Is Alaska So Cool?
Observed Solar Angle
47
48
49
50
51
52
52
52
51
6. Compare your values for the solar angle with the official US Naval
Observatory calculations. To find these official values, log on to the Internet,
then go to the U.S. Naval Observatory Astronomical Observations site at
http://aa.usno.navy.mil/AA/data/docs/AltAz.html.
First try Form A.
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Type in the year, month, and day on which you made your
measurements.
Change the tabular interval to 20 minutes
Select your state in the "State or Territory" field
Type in the name of the town in which you live or is closest to you.
Press "compute table."
Find the angle values that correspond to the times you made your
observations. These are found on the web site in a column labeled
"Altitude" rather than solar angle. Write the values from the web site in
the correct column of Table 1 or Table 2 on page 8 of these lesson
plans.
Use Form B if you get a message that says "Unable to find location in our file.
Try another location." See the next page for instructions.
Page 6
Activity 5
Why Is Alaska So Cool?
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Solar Angle and Solar Noon
Type in the year, month, and day on which you made your
measurements.
Change the tabular interval to 20 minutes
Type in the name of the town in which you live or is closest to you.
Enter the longitude and latitude. (See Table 3 found on page 8.)
Enter "8" in the time zone field. (Alaska time is eight hours west of
Greenwich time during Daylight Savings Time. Use the link to the
Time Zone Map if you need to calculate a different time zone.)
Press "compute table."
Find the angle values that correspond to the times you made your
observations. These are found on the web site in a column labeled
"Altitude" rather than solar angle. Write the values from the web site in
the correct column of Table 1 or Table 2 on page 8 of these lesson
plans.
7. Use the values you found on the Naval Observatory site to determine the
actual time of solar noon. Write this time in Table 3 found on page 8 of these
lesson plans.
Activity 5
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Solar Angle and Solar Noon
Why Is Alaska So Cool?
Record Your Data
You should have data for Table 1 OR Table 2. You did not need data for both.
Table 3 should be filled out completely.
Table 1: Using a Protractor to Determine Solar Angle
Time*
Observed Solar Angle
Solar Angle from Website
11:00 am
11:20 am
11:40 am
12:00 noon
12:20 pm
12:40pm
1:00 pm
1:20pm
1:40 pm
2:00 pm
Table 2: Solar Angle Determination Using Geometry
Time*
Dowel
Height (A)
Shadow
Length (B)
A
B
Calculated
Solar
Angle
Solar
Angle
from
Website
11:00 am
11:20 am
11:40 am
12:00 noon
12:20 pm
12:40pm
1:00 pm
1:20pm
1:40 pm
2:00 pm
Table 3
Date:
Latitude and Longitude:
Predicted Solar Angle:
Largest Solar Angle Observed:
Largest Solar Angle from Website:
Page 8
Name of Your Town:
Solar Noon Observed:
Solar Noon from Website:
Activity 5
Why Is Alaska So Cool?
Solar Angle and Solar Noon
Concluding Questions
Answer the following questions.
1. Compare your results for the solar angle (Table 1 or 2) with the expected
results found on the Naval Observatory website. How similar are your results
to the results found there?
2. Which method did you use to determine the solar angle? Review the
procedure for this method. Which are some possible sources of inaccuracies
in the solar angle determinations you made?
3. Review Table 3. How does your prediction for the maximum solar angle
compare with the values for the solar angle you observed and found on the
Naval Observatory web site? Was your prediction close? Were you surprised
by your results?
Write your reflections on this activity in your daily log.
Activity 5
Page 9