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INVERSE SQUARE LAW

Electromagnetic energy (light, heat) from the Sun decreases very quickly with distance. The Sun is roughly a sphere, and the surface area of any sphere is,

*Surface Area of Sphere = 4pR ^{2}*

where R is the radius of the sphere, or in our case, the distance from the center of the Sun. As we move away from the Sun, this surface area increases because the radius, R, increases. In the figure at right, R_{1} is the distance to the Sun’s surface. R_{2} is the distance somewhere beyond the Sun’s surface…maybe where the Earth is! We see that R_{2} is greater than R_{1}. You can see that the power at the surface of the Sun has to spread out across the larger spherical surface at R_{2}.

To describe this effect mathematically we define a quantity called **Intensity**. Intensity is the power spread out over an area, or

*I = * Power ÷ Area

As discussed above, the area of a spherical surface is 4pR^{2}, so we have:

*I =* Power ** ÷** 4pR^{2}

At its surface, the Sun's power is approximately 383 billion billion megawatts, or 3.83 x 10^{26} watts. Therefore, by the time this reaches Earth (see diagram), it is spread out over an enormous spherical surface. At the Earth's distance from the Sun (93 million miles, or 1.496 x 10^{11} meters) the intensity drops to:

*I*_{at}_{ Earth}_{} = [3.83x10^{26} watts]
** ÷ **[4p(1.496 x 10^{11} meter)^{2}]

*I*_{at}_{ Earth}_{} = 1360 watts per m^{2}

**
Calculate the solar intensity at Jupiter's distance from the Sun!
**The average distance from the Sun to Jupiter is 483 million miles, or 7.78 x 10

In the diagram at left you can see how quickly the Sun's energy decreases as you move to the outer planets.

The inverse-square law applies to other quantities in physics, provided the source is a sphere. Among them are gravity, static electric fields, and electromagnetic fields (light).