1. For Every Season: Tilt, Tilt, Tilt
Why do seasons happen?

2. Density Diminishes With Distance
Shower/Spray Bottle Analogy
Water is spreading out in a cone as it leaves the nozzle.
All slices of cone of spray contain the same amount, but different densities of water.
Same amount of water
Different densities of water
Water Balloon Analogy
If the water were sprayed out in all directions at once, like an exploding water balloon, then the spray would be in the shape of a sphere.
The slices would be hollow spheres (3D).
Each hollow sphere would contain the same amount, but different densities of water.

3. Origin of Inverse Square Law
Surface Area of a Sphere = 4 π r2
So for r = 1,
Surface Area = 4 π (1)2 = 4 π
For r = 2,
Surface Area = 4 π (2)2 = 4 π (42) = 16 π
So by doubling the radius, r, we quadruple the surface area. 1
Density of Water on Spheres 
“” Is read “proportional to” r2
If the same amount of water is on each sphere, then the density of the water on the larger sphere is one quarter the density of the water on sphere half its size.
In other words, the density of water is proportional to the inverse square of the radius of the sphere.

4. Inverse Square Law with Sunlight
Like the water from the water balloon, the same amount of light from the sun is used to illuminate (and heat) each of the successive spheres.
As the surface area increases, the total amount of heat energy stays the same.
So temperature at each sphere follows an inverse square law.
Hence the closer the Earth is to the Sun, the warmer it would be.
From page 257 of your lecture text: Astronomy: A Beginner’s Guide to the Universe

5. Elliptical Orbit Does Not Do the Job
Hypothesis:
The Earth is closer to the Sun in summer and farther away from the Sun in winter. After all the Earth’s orbit is an ellipse.
Earth during summer
Earth during winter
Observations:
Northern hemisphere experiences summer while the southern hemisphere experiences winter.
We experience a seasonal change in temperature of about 35 Celsius degrees (63 Fahrenheit degrees).
Earth’s elliptical orbit only accounts for about 5 Celsius degree change. Moreover, Earth is closer to Sun during northern hemisphere’s winter.

6. Rethinking the Water Analogy
Shower/Spray Bottle Analogy
What if we change the angle of our target?
Again, both slices receive the same amount of water.
The tilted target spreads the water out over a greater surface area.
So the tilted target has just as much water on it, but on average a given spot on the tilted target is drier.

7. Applying Tilt to Light Flashlight Analogy
Both slices receive the same amount of light.
The tilted target spreads the light out over a greater surface area.
Hence, tilted target is dimmer overall.
Now imagine yourself on the targets.
For the circular (non tilted) target the light/Sun is directly overhead.
For the tilted target the light/Sun is not directly overhead.

8. Earth is Round
Since the Earth is round, your latitude determines the height of the Sun in the sky.
The higher in the sky the Sun is, the less tilted your part of the Earth is to the sunlight.
Sun is on horizon.
Sun is 45º above horizon.
Sun is 90º above horizon (directly overhead).
This explains why it is hotter at the equator and colder at the poles, but not seasons.

9. The Tilt of the Earth
The rotational axis of the Earth is not perpendicular to plane of the orbit of the Earth around the Sun. This tilt is 23.5º.
The rotational axis of the Earth points toward the north star all year.
The result is that the Sun’s light falls on a given part of the Earth at a different angle during the year.
Seen from side angle, not above.
December
Winter Solstice
June
Summer Solstice
March
Spring Equinox
September
Autumnal Equinox

10. The Tilt of the Earth
December
Winter Solstice

11. What if the Earth had no tilt?
Sun would never change its noon “height” in the sky.
Sun would always be on horizon at the poles
Sun would never change its noon height.
Sun would always be directly overhead at equator.

12. Rethinking the Analogies
Hypothesis:
The Earth is closer to the Sun in summer and farther away from the Sun in winter. After all the Earth’s orbit is an ellipse.
Earth during summer
Earth during winter
Observations:
Northern hemisphere experiences summer while the southern hemisphere experiences winter.
We experience a seasonal change in temperature of about 35 Celsius degrees (63 Fahrenheit degrees).
Earth’s elliptical orbit only accounts for about 5 Celsius degree change. Moreover, Earth is closer to Sun during northern hemisphere’s winter.