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Or, more simply, would something 200 times wider look smaller from 300 times farther? I cannot give you the math, but expect the answer to be "yes."

Wait, I told a sincere falsehood (so NOT a lie! ) The relationship is linear, so the answer IS "yes." Take two objects of identical length and hold one at arms length, in line with the other at half an arms length: The farther will appear exactly half as long. So if distance increases more than size, the farther larger object appears smaller than the closer smaller one. In this case, ⅔-¾ as large, depending on time of month.