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solution_2 - 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 # 2 1) [20 points] With a telescope here on Earth, would we ever see Venus in a crescent phase? If so, sketch the relative positions of Venus, Sun, and Earth when that happens. To clarify the conditions under which a planet (or moon) appears as a crescent, I drew the above diagram. The planet is brightly illuminated on the hemisphere facing the Sun, and dark on the hemisphere away from the Sun. To see only the dark hemisphere (called the “new” phase), an observer must be along the dotted line labeled “new”. To see only the bright hemisphere (called the “full” phase), an observer must be along the dotted line labeled “full”. To see the planet half dark and half light, (called “first quarter” or “last quarter”), an observer must be along the dotted lines labeled “quarter”. To see the gibbous phase (mostly bright, with a little slice of dark), the observer must be in one of the two quadrants labeled “GIBBOUS”. Finally, to see the planet in its crescent phase (mostly dark, with a little slice of bright), the observer must be in one of the two quadrants labeled “CRESCENT”. To see a planet in its crescent phase, the observer must be farther from the Sun than the observed planet is. Since the Earth is farther from the Sun than Venus is, it is possible to see Venus in a crescent phase from the Earth. A diagram showing a configuration in which Venus would be a crescent is shown at the top of the next page.
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