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Suppose you wish to construct a scale model of the Solar System. The distance between the Earth and the Sun (one "Astronomical Unit" - ) is , and you represent it by 15 km, about the size of a reasonably big city. (a) What is the scaled distance of the dwarf-planet Pluto (39.5 au) ? (Hint: Use ratios here and elsewhere when possible!) (b) The Earth is about 12,800 km in diameter. How large is Earth on your scale? Compare its size with that of a common object. (c) The Sun's diameter is about . How large is it relative to Earth? (d) The nearest star, Proxima Centauri, is 4.2 light-years away (i.e., ). How far is this in your scale model? (e) Compare your answer in part (d) with the true distance to the Moon, . Comment on whether this gives you some idea of the enormous distances of even the nearest stars.