The major driver of Earth’s climate is the amount of solar energy it receives. Three laws relate the solar energy reaching Earth to the planet’s orientation with the sun.
The first is the cosine law, which explains many of the differences in climate between the equator and the poles. Sunbathers instinctively obey this law in orienting themselves perpendicular to the sun to maximize the interception of solar rays or more parallel to the sun to decrease interception. The more slanted (or oblique) the angle between the sunbather and the sun, the greater the area over which a given amount of solar energy is distributed and, thus, the smaller the energy per unit area. Moreover, at the oblique angle near the poles, solar energy passes a longer distance through the atmosphere and is more likely to be reflected or absorbed by gases or particles in the atmosphere before striking Earth’s surface. The reflectance of many materials increases at an oblique angle (e.g., sunsets reflecting off water). For these reasons, the poles receive less solar energy per unit area than the equator and are colder.
The cosine law also explains differences among the seasons. Earth rotates daily around an axis that is oriented at an angle of 23.4° away from its plane of orbit around the sun. At the equinoxes, the sun is directly over the equator, but at the solstices, June 21 and December 21, the sun is directly above the Tropic of Cancer (latitude 23.4°N) or the Tropic of Capricorn (latitude 23.4°S), respectively. Therefore, on June 21, the Tropic of Cancer receives full sunlight and experiences summer; the Tropic of Capricorn receives 68.5% of full sunlight and experiences winter. On December 21, the reverse applies.
The second law introduced here is Kepler’s second law, which states that gravitational bodies rotate through equal areas in equal time. Consequently, a line from Earth to the sun sweeps an equal amount of area in the orbital plane (the plane on which Earth is orbiting) every day, regardless of where the planet is in its orbit. Consequently, Earth moves faster when it is near the sun than when it is far from the sun because at the smaller distance it needs to trace a greater arc to cover the same area. This means that Earth spends less time orbiting close to the sun than far from it.
Kepler’s second law. Gravitational bodies in their orbits transcribe equal areas in equal amounts of time. Earth requires the same amount of time to rotate through the gray areas and, thus, moves faster when it is closer to the sun.
Third, and last, is the inverse square law. It treats the sun as a point source of light, one that distributes light energy evenly in all directions. Therefore, at a given distance from the sun, the sun’s energy is distributed over the surface area of a sphere. At twice the distance, its energy is distributed over 4 times the area, and so on. The inverse square law states that the amount of solar energy striking an area decreases with the square of the distance from the sun. This means that, at its farthest distance from the sun (aphelion), during the summer in the Northern Hemisphere, Earth receives only 93.5% of the solar energy that it receives at its closest distance (perihelion), during winter in the Northern Hemisphere. Nonetheless, the more perpendicular angle of the Northern Hemisphere to the sun during July more than compensates for the greater distance.
This is an excerpt from the book Global Climate Change: Convergence of Disciplines by Dr. Arnold J. Bloom and taken from UCVerse of the University of California.
©2010 Sinauer Associates and UC Regents