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# solution_1 - ASTRONOMY 294Z The History of the Universe...

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ASTRONOMY 294Z: The History of the Universe Professor Barbara Ryden SOLUTIONS TO PROBLEM SET # 1 1) [20 points] Two Martian astronomers, Marvin and Marla, are located due north and south of each other on the planet Mars. Marvin sees the Sun directly overhead (at the zenith) at noon. At the same time, Marla sees the Sun 6 degrees away from the zenith. Marla is 355 kilometers north of Marvin. Compute the circumference of the planet Mars. Since this is the method of Eratosthenes transplanted to Mars, I can reuse the “Eratosthenes” slide from the lecture of January 3, with a bit of relabeling (see above). The angle α is equal to 6 . Since the angle α is equal to the angle β , the angle β is also equal to 6 , or 1 / 60 of a full circle. Thus, the distance D = 355 km is equal to 1 / 60 of the circumference of Mars. The circumference C of the planet Mars is then C = 60 D = 60(355 km) = 21 , 300 km . (1)

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2) [20 points] Suppose that Aristarchus had measured an angle of 45 degrees between the Sun and the Moon when the Moon was in its first quarter phase.
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