Sunlight, Axial Tilt and Zenith Angle: Practice Problem Solutions

1. They add up to 90 degrees: zenith angle = 90 degrees - altitude.

2. 90 - 30 = 60 degrees.

3. The same beam is spread over a larger area of ground when the Sun is low, so each square meter receives less energy (the area is larger by 1 / sin of the altitude). Low sunlight also passes through more air.

4. a = 90 - |33.5 - (-23.5)| = 90 - 57 = 33 degrees.

5. a = 90 - |33.5 - 23.5| = 90 - 10 = 80 degrees.

6. sin(80) = 0.985 and sin(33) = 0.545. June is stronger by 0.985 / 0.545, about 1.8 times.

7. Alabama is north of the Tropic of Cancer (23.5 degrees north), and the Sun's declination never goes higher than +23.5, so it is always at least about 9 degrees from straight overhead.