What geometric principle dictates the rapid decrease in received energy from distant stars?
Answer
The inverse-square law.
The inverse-square law is the fundamental physical limitation governing how brightness diminishes over vast distances in three-dimensional space. As light spreads outward from a source, the total energy is distributed over an ever-increasing spherical surface area. Since the surface area of a sphere is proportional to the square of its radius (distance), the intensity of the light energy detected per unit area decreases proportionally to the square of the distance traveled. This geometric reality means that for objects billions of light-years away, the arriving signal drops to extremely low levels, sometimes just a few photons per second, making detection profoundly challenging.
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