Name:________________________________
lAltitude and Azimuth Worksheet
Everyone uses directions to describe the locations of objects in the sky. Nonscientists use the directions around the horizon (e.g., north, southeast) and
fractional distances above the horizon (e.g., half-way up). Scientists use much more
precise angular distances around horizon (azimuth with 0o north and 90o east) and
above the horizon (altitude with 0o at the horizon and 90o at the zenith). To
exhibit your understanding of both systems of location, answer the following
questions.
altitude
CARDINAL DIRECTIONS:
1. You are facing south. Which direction is behind you? _____
2. You are facing west. Which direction is to your left? ______
3. You are facing east. Which direction is to your right? ______
ALTITUDE AND AZIMUTH:
4. The sun is located half-way up in the southwest. What is its altitude?
5. The sun is located half-way up in the southwest. What is its azimuth?
45*
225*
LOCATION OF POLARIS: Earth’s rotation axis points nearly at the star Polaris,
the North Star. As a result, the star stands nearly still in the sky and its azimuth
is nearly 0o for all observers in the northern hemisphere. The altitude, however,
depends upon where one is located on the earth. The altitude of the North Star
is equal to one’s latitude.
6. You are located at Earth’s north pole, 90o north
latitude. Give the azimuth and altitude of the
North Star as seen from this location.
Azimuth = 0*
Altitude = 90*
7. Describe in words where you would look to find Polaris, the North Star.
Polaris would be directly at my Zenith.
8. You are located at home, about 40o north latitude.
Give the azimuth and altitude of the North Star
as seen from this location.
Azimuth = 0*
Altitude = 40*
9. Describe in words where you would look to find
Polaris, the North Star.
To find Polaris, you would have to look towards
more to the north with a 40* Altitude.
10. You are located at Earth’s equator, 0o latitude.
Give the azimuth and altitude of the North Star
as seen from this location.
Azimuth = 0*
Altitude = 0*
11. Describe in words where you would look to find
Polaris, the North Star. You can find Polaris over
the horizon.
12. Imagine that you are located at Earth’s south pole. Where would you point if
you were asked to indicate the location of the North Star?
It would be at my Nadir so I would not be able to see it.
Application: Photovoltaic Cell Effectiveness
A sun chart can be used to help determine possible obstructions that will affect a
PV (Photovoltaic) system’s performance over the course of a year. A sun chart is a
graph of solar azimuth and solar altitude. Azimuth is the sun’s location from north
towards east in the sky. Solar altitude is a measure of the sun’s location in degrees
above the horizon. The chart can help to determine if there are critical times of the
day and year when the PV system will receive too much shading to make the
installation worthwhile.
The sun chart below shows the movement of the sun across the sky over the course
of the day for an entire year. Charts vary depending on what latitude and longitude
is used. The chart below represents the sun’s path across the sky at latitude 45 and
longitude -120. Using the sun chart provided, complete the exercise by answering
the questions below.
1. The first day of summer (June 21st), the azimuth at sunrise is 55°. What is the
azimuth at 9 a.m. on the same day?
A. 100°
B. 95°
C. 110°
D. 105° This one
2. What is the approximate maximum altitude the sun reaches on March 20th?
A. 40°
B. 45° This one
C. 50°
D. 55°
3. Assume that the PV will be shaded if the altitude is less than 30° when the azimuth
is 120°. The months of the year when the array will be shaded between 9 a.m. and
3 p.m. include:
A. April, May, June
B. January, February, March
C. November, December, January This one
D. December
4. The maximum, annual solar altitude (elevation) between 9 a.m. and 3 p.m. sun
time is closest to:
A. 30
B. 50
C. 60
D. 70 This one
5. The minimum, annual solar altitude (elevation) between 9 am and 3 pm sun time is
closest to:
A. 10 This one
B. 20
C. 30
D. 40