SOLAR ENERGY AND SUN ANGLE
5 points (-1 pt for every 3 questions missed)
Name____________________
Introduction:
In order to understand the changing heat patterns on Earth, we have to understand the relationship
between Earth and the external source of heat, the Sun. Variations in the amount of solar energy intercepted at
the Earth’s upper atmospheric surface (insolation) are a result of the geometric relationship between Earth and
Sun.
Outside: Figuring out north without a compass. This method works for locations in the NH above 23.5
degrees latitude.
Hold your watch horizontal.
Point the hour hand at Sun.
Halfway between that point and 12 is south.
So north is at the other end of the line.
Local solar noon is the time when the sun crosses the meridian of longitude of a particular place. The shadow
of a vertical object like a flagpole will point either directly north or south depending on latitude and season.
Sun angle is measured from the sun to the horizon. The typical adult four fingers (open palm) held horizontally
represents about 6 degrees of arc which is one hour. Count the number of palms between the horizon and the
base of the sun___________x 6 = _______________sun angle right now.
Section 1: Revolution and Rotation
Earth revolves around the Sun in an elliptical path. Earth rotates about a geographic axis. This diagram is not
to scale.
1. Label the monthly positions where the two unique points in the orbit known as aphelion and perihelion
occur.
2. While looking at the North Pole on the globe, rotate the globe about its axis in a counterclockwise direction.
The speed of rotation can be measured in angular velocity or linear velocity. Angular velocity is measured in
degrees of arc per time unit.
How many degrees are in a circle? ______
How many hours are in a day? ________
Number of degrees divided by hours in a day equals an angular velocity of ________.
During this class period today, approximately how many degrees of longitude will the Earth have rotated
through? _______
3. How does this angular velocity relate to the time zone concept used in the United States and most of the
world?
4. Linear velocity changes with latitude. Place your finger on the globe at the Equator and spin the globe
counterclockwise. Repeat with your finger at a latitude of 45 degrees North. The distance traveled by your
finger at the Equator is greater than the distance traveled by your finger at 45 degrees North. Linear velocity is
calculated by dividing the length of the parallel of latitude by the number of hours in a day. Calculate the linear
velocity for the following latitudes:
Latitude
0
30
60
90
Approximate length(km)
40074
34835
20085
0
Hours/Day
24
24
24
24
Linear velocity (km/h)
5. The Earth’s axis of rotation runs through the North Pole, the center of the Earth, and through the South Pole.
Look at the globe and notice the axis is not vertical. It is tilted 23.5 degrees from the vertical to the plane of the
ecliptic (the orbital plane of Earth). The axis remains parallel as Earth revolves around the Sun. On the
December and June solstice diagrams (on the first page) of the Earth label:
North and South Poles
Arctic and Antarctic Circles
Equator
Tropics of Cancer and Capricorn
Section 2: Sun Angle
Since the Earth presents a curved surface to the Sun’s rays, there is an uneven distribution of solar energy
from the Equator to the Poles. The subsolar point is the place that receives insolation from directly overhead
(90 degrees) on a given day. Any other latitude on Earth receives solar energy at lower angles of incidence as
the distance from the subsolar point increases. The solar energy is spread out over a larger area and is more
diffuse. At the subsolar point, the solar energy would be intense or concentrated. Refer to the previous diagram
of Earth’s revolution about the Sun.
1. For the June Solstice diagram of Earth on the first page, draw a line from the center of the Sun to the Tropic
of Cancer. For the December Solstice diagram of Earth, draw a line from the center of the Sun to the Tropic
of Capricorn. These are the respective subsolar points for those dates. They are the points farthest from the
Equator where the Sun is directly overhead.
2. During the March and September Equinoxes, the subsolar point is at the Equator. Is the subsolar point ever
at Dallas, Texas? Why or why not?
Section 3: Calculating Sun Angle
The Sun’s angle of incidence for a place at a particular date can be determined by the equation:
Sun Angle = 90 degrees – (latitude of a place + declination)
Declination is the latitude where the sun is directly overhead for that date. You drew these on the Earth-Sun
diagram on page 1. So after determining latitude from the globe, the only unknown is sun angle.
Here is an easier way to express that equation that removes the problem of whether to add or subtract the
declination:
Sun Angle = 90 degrees – (how many degrees are there between the latitude of the place and the latitude
where the subsolar point is on that day)
1. The latitude for Donetsk, Ukraine is_________________. Look by the Black Sea between Turkey and
Russia. Why has Donetsk been in the news?
Calculate the local solar noon sun angle for Donetsk on the following dates:
June Solstice
December Solstice
March Equinox
September Equinox
2. The latitude for Rio de Janeiro, Brazil is____________. Why was Rio de Janeiro in the news this summer?
Calculate the noon sun angle for Rio de Janeiro, Brazil on the following dates:
June Solstice (which is their winter)
December Solstice (which is their summer)
March Equinox
September Equinox
3. The latitude of any place at the Equator is____________. Calculate the noon sun angle for the Equator on
the following dates:
June Solstice
December Solstice
March Equinox
September Equinox
4. Find the latitude for your favorite location. Determine the sun angle at that location for each solstice and
each equinox. Label each answer. Show your math.
My favorite place is_________________.
The latitude is_____________________.
Sun angle for June Solstice
Sun angle for December Solstice
Sun angle for March Equinox
Sun angle for September Equinox
5. We can rework the equation to find the latitude of a place if the sun angle and the
declination of a particular date are known. It would look like this:
Latitude of a place = 90 degrees – (sun angle + declination)
or an easier way to express it:
Latitude of a place = 90 degrees – (how man degrees are there between the sun angle and the latitude
where the subsolar point is on that day)
One of my favorite mountain ranges has a longitude of 150 degrees West. The latitude is a mystery. But the
sun angle on the June Solstice was 46.5. This is the highest sun angle that this location ever receives. What is
the latitude of my favorite mountain range?
The mountain range is
7. What is the latitude of a place where the noon sun angle is 59.5 degrees above the northern horizon on the
December Solstice? Hint: if the sun is to the north on the December Solstice, think about what hemisphere the
mystery location is in.