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Yes, it's definitely r^4. If we assume that the planet is far from the sun compared to the earth, such that the earth-planet distance and the sun-planet distan
by bzbarsky 11y ago
Yes, it's definitely r^4. If we assume that the planet is far from the sun compared to the earth, such that the earth-planet distance and the sun-planet distance are both approximately r, then the amount of light the planet gets from the sun is proportional to 1/r^2. Then the planet reflects that light in all directions, and the fraction of it that comes back to us on earth is also proportional to 1/r^2. 1/r^2 * 1/r^2 = 1/r^4.