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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 = 4pR2

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, R1 is the distance to the Sun’s surface.  R2 is the distance somewhere beyond the Sun’s surface…maybe where the Earth is!  We see that R2 is greater than R1.  You can see that the power at the surface of the Sun has to spread out across the larger spherical surface at R2.

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 4pR2, so we have:

                                                                        I  =  Power ÷ 4pR2

At its surface, the Sun's power is approximately 383 billion billion megawatts, or 3.83 x 1026 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 1011 meters) the intensity drops to:

Iat Earth =   [3.83x1026 watts] ÷ [4p(1.496 x 1011 meter)2]

Iat Earth  =  1360 watts per m2




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 1011 meters. (answer!)

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).