**Document ID**: 03_18_08_1

**Date Received**: **Date Revised**: **Date Accepted**:

**Curriculum Topic Benchmarks**: S1.3.5, M3.3.7, M3.3.14 M3.3.12,
M4.3.3, M4.3.14

**Grade Level**: Middle School \[6-8\], High School \[9-12\]

**Subject Keywords**: solar energy, temperature, season, tilt,
inclination

**Rating**: Moderate

Why is Summer Hot?

**By**: Stephen J Edberg, Jet Propulsion Laboratory, California
Institute of Technology, 4800 Oak Grove Drive, M/S 301-486, Pasadena CA
91011

e-mail: Stephen.J.Edberg@jpl.nasa.gov

**From**: The PUMAS Collection http://pumas.jpl.nasa.gov

©2008, Jet Propulsion Laboratory, California Institute of Technology.
ALL RIGHTS RESERVED.

It is quite common for people to believe that summer is warmer than
winter, basing the explanation on the belief that Earth is closer to the
Sun during the summer than in the winter. Even a sizable fraction of
Harvard graduates carry this belief (Schneps, 1987, mentioned in Green,
2003). In reality, this is exactly opposite the situation in the
northern hemisphere. The separation of Earth and Sun is greatest at the
beginning of July and least at the beginning of January. More direct
sunlight and the greater duration of daytime in summer months makes
summer warmer than winter. This activity, effective outdoors or indoors,
will demonstrate how more direct sunlight leads to seasonal temperature
variations.

This activity demonstrates how insolation is affected by latitude by
using a pair of thermometers, each taped to some cardboard, placed
outside on a sunny day.  A globe can also be used, outdoors or indoors.

**OBJECTIVE:** Understand seasonal variations in temperature are the
result of the heating of the Sun as a function of its peak angle and
length of the day.

**APPARATUS:**

\(1\) Two **laboratory thermometers** that can be read to 1˚ C.

(2) **Corrugated cardboard** strip, long enough and wide enough to mount
    two thermometers to it lengthwise (Fig. 1). Approximate length 1 m,
    width 5 cm. The corrugation should be parallel to the width of the
    strip, so folding the cardboard makes a hinge. A more elaborate and
    permanent design can be made with materials such as wood or plastic,
    with good metal hinges, if desired.

(3) **Tape** or other material (aquarium cement, for example) to fix the
    thermometers to the cardboard backing (or the globe, below).

(4) **Short flat head nail** (optional), about 5 cm long, to indicate
    the orientation of a thermometer towards the Sun by minimizing its
    shadow.

Fig. 1. This side view shows the cardboard thermometer mounting strip in
its measurement position. Thermometers are attached to the middle
section and the ground section. The prop section holds the middle
section so it intercepts maximum sunlight. A (stylized) nail is pushed
through the cardboard below the middle section's thermometer for use in
orienting the assembly directly towards the Sun by minimizing the nail's
shadow. Dimensions are roughly 30 cm per section but they only need to
surround and protect the thermometers with some margin; size the strip
and its sections based on the length of the thermometers.

(5) **Globe** (12 inch \[30 cm\] or greater diameter); optional. A large
    ball can also be used, but having oceans and continents visible
    reduces the abstraction of this demonstration.

(6) **Cardboard sheet,** optional, with a circular hole closely matching
    the diameter of the globe. This will be used to provide a plane to
    mimic the horizon.

(7) **String,** optional, length somewhat greater than one-half of the
    circumference of the globe (i.e., \> π x \[globe radius\]).

(8) **Ruler** or **meter stick** for measuring the length of the string.

(9) Five (or more) **small thermometers** (no larger than 2-4 cm
    length), optional. The small thermometers are attached to the globe
    at the equator and at two higher latitudes in each hemisphere.
    Aquarium and pet stores sell small LCD thermometers (with limited
    temperature range, so test one first to confirm the temperature
    range is adequate). Very short dyed-alcohol thermometers can also be
    found.

(10) **Desk lamp with tungsten bulb** (optional, to do this experiment
     indoors during inclement weather). Fluorescent and LED lamps do not
     emit enough heat (they're too efficient at generating light!) to
     warm the thermometers.

**PROCEDURE:**

Fold the cardboard strip into three sections, roughly equal in length
(Figure 1). One end section becomes the prop to hold the middle section
thermometer oriented toward the Sun. The other end section is the
"ground section" that holds a thermometer flat on the ground. Attach the
thermometers to the middle section and ground section with tape, giving
them a few centimeters of space from the ends of their sections. A short
nail, if desired, can be pushed through the back of the middle section.
Avoid interference with the thermometer or shadowing the thermometer
during the experiment.

Lay the cardboard strip on the ground with the ground section end
towards the Sun. Elevate the middle section with the prop section. Use
the shadow of the nail to check the orientation. When the nail's shaft
shadows only itself, not the cardboard, the middle section is
perpendicular ("normal") to the direction to the Sun. Give the
thermometers a chance to equalize: each thermometer's working fluid
should settle at one temperature, after a minute or so. Observe that the
propped thermometer is much warmer than the one on the ground.

Caveats:  This demonstration is much more effective on cold sunny days
than on warm sunny days.  It is better done early or late in the day
when the Sun is closer to the horizon, not around noon. On warm days and
at mid-day heating by conduction from the ambient air can reduce the
apparent difference between warming caused by sunlight radiating
directly onto a thermometer and warming due to sunlight falling at an
angle.

You can actually do this experiment indoors on a rainy day if you use a
good spotlight (make sure you use a tungsten bulb, not fluorescent or
LED) equidistant from the two thermometer bulbs with the geometry
otherwise copying natural solar illumination.

[Variation]{.underline}: Use some small thermometers and a globe. Tape
small thermometers to the equator, to similar mid-latitudes in both
hemispheres, and to similar polar latitudes in both hemispheres on the
same meridian of longitude on the globe. Illuminate the globe with
sunlight outdoors or with a close spotlight or desk lamp indoors; make
sure you use a tungsten bulb, not fluorescent or LED.

Start with artificial or actual sunlight falling on the equator (vernal
and autumnal equinox). (If artificial lighting is being used, maximize
the distance between source and globe. This minimizes the warming
resulting from the globe's bulge \[due to its spherical shape\] being
closer to the lamp.) Allow the thermometers to equilibrate (probably
less than two minutes for LCD thermometers). The difference in
temperatures at different latitudes will be apparent. Now tilt the globe
with one pole towards the light source (or move the lamp) and wait for
the thermometers to equilibrate again (Figure 2). The hemisphere getting
more direct light (summer solstice) will be warmer than before while the
thermometers in the opposite hemisphere will be cooler. Repeat with the
same pole tilted away (winter solstice) from the source. The
thermometers will change their temperatures to match the change in
desktop-season. Since the distance from light source to globe has not
changed, the changes in temperature must be due to the angle of the
sunlight falling on the thermometers, and hence Earth's surface.

It is important to point out that Earth does not change its orientation
with respect to the stars; its rotation axis always points towards
Polaris, the North Star. Earth's orbital motion makes the Sun change its
apparent maximum height at local noon as Earth goes around the Sun
annually. This is due to the tilt of Earth's rotation axis with respect
to the plane of its orbit around the Sun (Figure 2).

> ![](media/image1.png){width="1.5133858267716536in"
> height="1.4598425196850393in"}![](media/image2.png){width="0.7311023622047244in"
> height="1.4145669291338583in"}![](media/image1.png){width="1.5133858267716536in"
> height="1.4598425196850393in"}![](media/image2.png){width="0.7311023622047244in"
> height="1.4145669291338583in"}
>
> Fig. 2. Earth's hemispheres experience summer and winter on opposite
> sides of Earth's orbit around the Sun. The tilted white line
> represents Earth's rotation axis, which maintains the same orientation
> (towards the North Star, Polaris) as Earth goes around the Sun. During
> northern summer, the northern hemisphere is tilted towards the Sun and
> receives more direct sunlight. The north polar region is in continuous
> sunlight. During northern winter, on the other side of Earth's orbit,
> the northern hemisphere is tilted away from the Sun and receives less
> direct sunlight. The north polar region is in continuous night.

**THE UNDERLYING PRINCIPLES:**

Solar energy falls on Earth's surface and is absorbed, warming the
surface. If the energy falls with an angle of incidence that is not
perpendicular (i.e., not normal) to the surface, the energy is spread
over a larger area and will not warm the surface as rapidly. This is
illustrated in Figure 3. At the equator during the vernal and autumnal
equinoxes sunlight falls straight down on the surface. Sites at
latitudes off the equator experience different levels of less-direct
illumination. They always have the same amount of energy, per unit area
coming from the Sun, but it is spread over a larger area than at the
equator. The increase in area is a function of the latitude, φ. The
length of the side of the triangle, h, represents the increase in area
due to the latitude. Assuming a square with a 1 m side, the definition
of cosine tells us that

> h = 1/(cos φ) (1)

The **Extension** describes how to make a paper cylinder that
illustrates the size of the illuminated area off of the equator.

> Fig. 3. An area on Earth's surface intercepting solar energy is warmed
> by it. If the receiving area is tilted with respect to the incoming
> rays, a larger area is warmed by the same amount of energy, so it
> warms more slowly. Higher latitudes warm more slowly than the equator.
> The triangle in the lower right is an enlargement of the high latitude
> triangle. The hypotenuse, h, is representative of the increase in area
> intercepting energy, compared to the equatorial value represented by
> the dashed line.

**DISCUSSION:**

More direct sunlight falling on a hemisphere warms it more than less
direct sunlight. The duration of daylight also plays a role: longer days
mean more sunlight and more warming during the summer. Longer days can
be demonstrated with string and a horizon plane (one may be built right
onto your globe stand, or it can be made from cardboard). Figure 4
illustrates on flat paper three situations (that are better demonstrated
with the globe) and are described below.

Set up the plane so the globe's center is in the plane. The orientation
of the plane should be varied: try the measurements described with the
Earth's (globe's) poles in the horizon plane, with the horizon plane at
some angle between the poles and equator, and the equator in the same
plane as horizon plane. These positions correspond to an observer placed
on the equator, placed at a middle latitude, and placed on the North
Pole or South Pole (be sure to specify which during the demonstration
and discussion).

For each position of the plane, use the string and a ruler or meter
stick to measure the length of the latitude arc from one side of the
horizon plane to the other. Lay the string along the "great circle" of
the equator and along the "small circles" at 23.4˚ north and south of
the equator (the Tropic of Cancer and the Tropic of Capricorn,
respectively).

**EXTENSION:**

**1)** Students can construct a cylinder with a square cross-section to
illustrate the effect of changing the angle of illumination (Figure 5
and Student Construction Sheet at the end of this activity). Inspection
will immediately show that the area of the square end of the cylinder is
smaller than the area of the end which has been sliced off at an angle.
Alternatively, the square end can be placed on the rectangular portion
of the discarded section to compare the areas.

The areas of the open ends of the cylinder can be calculated by
measuring the length and width of the square (length = width) and of the
rectangle and multiplying them:

> Area = (length) x (width) (2)

Divide the area of the rectangle into the area of the square to see the
ratio of the areas.

> Area Ratio = (area of rectangle)/(area of square) (3)

To see the effect of the increased area at high latitudes, divide the
Area Ratio into the solar constant (i.e., the solar energy per unit area
reaching the top of Earth's atmosphere), 1.37 kW/m^2^ (Bishop, 2007):

> Solar Energy Flux at Latitude = 1.37 \[kw/m^2^\]/(Area Ratio) (4)

The solar energy will be less than 1.37 kW/m^2^ for any latitude off of
the equator.

For a more mathematically advanced treatment of the situation the angle
of the slice can be measured with a protractor or it can be calculated
by measuring the length and width of the rectangular opening (since the
cylinder is a square). The computed angle is:

> Angle = sin^-1^(width/length) (5)

The angle from (5) can be used with Equation (1) and the solar constant
to determine the insolation at the latitude demonstrated by the square
cylinder.

**2)** According to Kaufmann (1991), Earth's

Mean distance from the Sun: 1.496x10^8^ km

Maximum distance from the Sun: 1.521x10^8^ km

Minimum distance from the Sun: 1.471x10^8^ km

Students can calculate the percentage difference in Earth's distance
compared to its mean distance. The answer is 1.7%, a small amount
compared to the effect of illumination angle and duration of daylight
between summer and winter solstices and the equinox everywhere except
for a narrow band centered on the equator. (How narrow is the band?)

> Fig. 5. Students can prepare a regular 8.5"x11" piece of paper to
> explore the effects of the angle of illumination on heating. Three
> folds are made (along the dashed lines) and two diagonal lines are
> penciled in (solid lines). Scissors are used to cut along the bold
> lines. See the Student Construction Sheet at the end of this activity
> for detailed instructions.

**REFERENCES:**

Bishop, R., 2007, "Some Astronomical and Physical Data" in *Observer's
Handbook 2008***,** P. Kelly, ed., Royal Astronomical Society of Canada,
Toronto.

Green, P. J., 2003, *Peer Instruction for Astronomy*, Pearson Education,
Inc., Upper Saddle River, NJ.

Kaufmann, William J, *Universe*, 3rd Edition, W.H. Freeman, 1991.

Schneps, M. H., 1987, *A Private Universe*, a film available from
Pyramid Films and Video, 2801 Colorado Avenue, Santa Monica, CA 90404.

**ACKNOWLEDGMENT:**

This publication was prepared by the Jet Propulsion Laboratory,
California Institute of Technology, under a contract with the National
Aeronautics and Space Administration.

Reference herein to any specific commercial product, process, or service
by trade name, trademark, manufacturer, or otherwise, does not
constitute or imply its endorsement by the United States Government or
the Jet Propulsion Laboratory, California Institute of Technology.

STUDENT CONSTRUCTION SHEET

![](media/image3.wmf){width="8.541666666666666in"
height="8.427083333333334in"}To construct a square cylinder: First fold
the paper into quarters along the dashed lines. Start by making the
middle fold. Open the sheet. Now fold each outer edge inwards to the
first fold. All the creases should be "hinged" to bring the paper faces
together in the same direction.

With a ruler, draw straight diagonal lines across two quarters of the
paper, as shown. Draw a connecting straight line from the intersection
of the creases and the diagonal lines.

Use scissors to carefully cut the diagonal and connector lines.

Fold the outer two sections in to the original center-crease and tape
them to each other at the top and bottom. Open the flattened paper into
a cylinder with a square cross-section.