<i>&gt; As the Earth&#x27;s distance from a star increases, it subtends a decreasing angle in that star&#x27;s &quot;sky.&quot; </i><p>But the number of stars at a given distance increases as the distance increases, and this increase exactly cancels out the decrease in the amount of light from a given star that reaches the Earth. So your argument does not explain why the night sky is dark.<p><i>&gt; Now divide the surface area of the dot, by the surface area of the sphere (4)(pi)(r^2). That&#x27;s how much of that star&#x27;s energy our planet catches.</i><p>Now do it the other way: draw a sphere around the Earth with some radius r. Calculate how many stars are on that sphere. The number increases as r^2; and, as you have shown, the amount of light reaching Earth from a given star decreases as r^2. So, as I said above, the increase in the number of stars exactly cancels out the decrease in the amount of light from each star that reaches the Earth; thus, the total starlight reaching Earth from a given radius r is a constant, independent of r.