Procedure

Opener

Ask students to think about what they know about the seasons. Then ask what they think is the underlying cause of the seasons. Does the entire planet experience the same seasons simultaneously? Accept all answers.  Students may offer various causes, such as the tilt of the Earth, the distance from the Sun, etc.

Discrepant event:

Present: Data on Perihelion and Aphelion Dates, which should indicate that Earth is closest to the Sun in January, farthest in July.

Discuss:  Is this information surprising?  What explanations for causes of seasons does this data eliminate?

Target Response:  this eliminates theories concerning the Earth-Sun distance as the cause of the seasons, since we know that, at least in the Northern Hemisphere, July is generally warmer than January.

Development:

Present: Data on Declination of Sun throughout calendar year, which should indicate that the Sun is at its northernmost declination in June, southernmost in December.  Declination is near zero in March and September. Have students briefly discuss this data among themselves.

Present: Data on average monthly temperatures for various world cities:  In Northern Hemisphere cities, temperature is max in July, min in Jan-Feb.  The opposite is the case for Southern Hemisphere cities.  Cities near the equator have very consistent temperatures all year round.  Have students briefly discuss this data among themselves.

Present: Data on hours of daylight per month in selected Earthly locations:  Daylight hours are max in June in the Northern Hemisphere, min in December.  The opposite holds for the Southern Hemisphere.  Near the equator, daylight hours are fairly consistent throughout the year. 

Discuss as a class: Does this data make sense? What theories regarding the cause of the seasons might this data support?  What theories does it refute? Does this data support the idea that a given season occurs simultaneously throughout the planet? What is the correlation between solar declination and the seasons?

Target Responses:  there seems to be a correlation between declination of the Sun and the seasons, as indicated by temperature and length of day. This data also appears to indicate that summer in the Northern Hemisphere coincides with winter in the Southern Hemisphere.  Thus, seasons probably do not occur simultaneously throughout Earth, but appear to depend on latitude. 

Closure

Return to the original question about the underlying cause of the seasons. Guide students to the realization that it is the angle at which solar radiation strikes the earth that determines the relative "intensity" (Power/Area) of this incoming radiation. The gradual change in this angle (solar declination) throughout the year, as a result of the tilt of Earth's rotational axis relative to the ecliptic (the plane that contains Earth's orbit about the Sun), is what causes the change in seasons.

Have the students make sample calculations for a general illustration of the effects of angle of incidence on intensity. For example, at noon on the equator the solar intensity is about 1000 W/m^2. At the same time, what is the intensity at a latitude of 45 degrees North, assuming the same longitude? Answer: At 45 degrees North, the angle of incidence is 45 degrees (90 - 45 = 45); thus, Intensity = 1000 sin (45) = 700 W/m^2. Thus we see the correlation between angle of incidence and intensity, the same effect that is at play in the changing seasons.

Refer to the declination table given earlier, and remind students that over that course of a year, the angle of incidence of the Sun changes by 46 degrees in non-Tropical locations (and by less in Tropical locations). The effect that this has on the intensity of incoming radiation is roughly proportional to sin (46) = 0.72. Thus, the intensity of solar radiation throughout the year varies by about 28%, due solely to changes in the angle of the Sun in the sky.

Refer next to the Perihelion/Aphelion data, and note that at its greatest distance from Earth the Sun is 152 million km, and 147 million km at its closest. Then ask the students to calculate the relative change in solar intensity due to Earth-Sun distance in the course of a year, using the relation that Intensity is proportional to 1/(distance)^2. They should find that distance alone causes a variation in intensity of only about 7%, relatively small compared to the effect of solar declination determined above.