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It has to do with the angle at which the light strikes the surface. The smaller the angle as which the light strikes Earth's surface, the more it is spread out. The steeper the angle, the more concentrated the light is. To illustrate this point, take a flashlight and shine in on a flat surface. Vary the angle at which the beam strike the surface. Note that when you shine the light straight at the surface it is a circle of light. However, as the angle with the surface decreases, this circle becomes more and more elongated. Finally note that as the beam becomes more spread out, the amount of light received by each square inch of area decreases.
So, how does this related to the temperature-latitude relationship? First of all, you you need to remember that Earth is a sphere. Because of this, in the tropics, the sun is nearly straight up. Therefore the Sun's energy is more concentrated, just like when the flashlight is aimed straight at the surface. So, these areas are more strongly heated. On the other hand, the sun is generally at a very low angle above the horizon at the poles. (For half of the year it is below the horizon.) So, the polar regions don't get as much heat. It actually works out so that about half of the energy Earth receives from the Sun falls between 30° N and 30° S latitude, about 3/8 of the energy is received between 30° and 60° both north and south and that only 1/8 of the energy is received above 60°. (These are the average fractions for the entire year.) So, this is why the equator is warmer than the poles.
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