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# problem_1 - ASTRONOMY 294z History of the Universe...

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ASTRONOMY 294z History of the Universe Professor Barbara Ryden Problem Set # 1 Due Tuesday, January 15 AT CLASS TIME NAME (please print clearly): SCORE (instructor use only):

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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. [Hint: This is essentially the method of Eratosthenes for measuring the circumference of the Earth, as described in the lecture for January 3; we’ve merely transferred it from Earth to Mars.]
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. Draw an accurate diagram of the positions of Earth, Moon, and Sun necessary for this measurement to be correct. In this case, what is the ratio of the Earth – Sun distance to the Earth – Moon distance? [Hint: to

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problem_1 - ASTRONOMY 294z History of the Universe...

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