Seasons Storyboard
Storyboard Text
- Slide: 1
- The seasons are dependent on the varying intensity of sunlight on different parts of the Earth at different times of year. For the purposes of this project, we will assume that the Sun's rays are perfectly parallel. Of course, this is not the case, but we can show that it is very close to the truth. The mean distance between the Earth and Sun is 149.6 million kilometers and the Earth's radius is 6378 kilometers. We would like to find the variation of the angle of sunlight between the Earth's center and its pole. Thus we are looking for the arctangent of 6378/149600000, which is approximately 0.002 degrees. The difference between the angle of sunlight between two antipodal points is twice this, 0.004 degrees, which is negligible.
- Slide: 2
- In order to continue our investigation of sunlight, we must find a way to measure the amount of sunlight that falls on surfaces of different slopes relative to the light. If we have a slope at a given angle theta, then the amount of impacting sunlight is proportional to the side length of the side opposite to angle theta. Thus the intensity of sunlight is proportional to the sine of theta.
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- Slide: 3
- We would like to find the intensity of sunlight over any latitude. Let the point at which the circle's radius intersect its circumference be A, and let the circle's center be O. Then the smaller angle between A, O, and the horizontal is equal to the latitude of A on the circle. Also, AO is perpendicular to the tangent line intersecting it. Because EB is parallel to the horizontal, angle AEB is the same as the angle between A, O, and the horizontal, or the same as A's latitude. Angle EAB is 90 degrees, so angle EBA is 90 minus A's latitude. The intensity of sunlight is then proportional to the sine of 90 minus A's latitude. The sine of 90 minus an angle is equal to the cosine of the angle, so we may claim that the solar intensity upon a point on the Earth's surface is proportional to the cosine of its latitude.
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