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Unformatted text preview: pels (kcp389) Homework 1 hill (666) 1 This print-out should have 51 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 4) 10.0 points Consider the following accepted constants: Radius of the moon=1 . 74 10 6 m. Radius of the sun=6 . 96 10 8 m. Average moon-earth distance=3 . 84 10 8 m. Average sun-earth distance=1 . 496 10 11 m. a) What is the apparent angle the diameter of the moon subtends, as seen from the earth, in radians? Correct answer: 0 . 0090625 rad. Explanation: If you have an angle that is very small ( 1 ) in measure, then tan , for measured in radians. r earth moon r earth moon d moon Since the distance from the earth to the moon or the sun than the diameters in- volved, the angle can thus be approximated by its tangent, and tan = diameter distance Alternative Solution: The definition of angular displacement is the arc length divided by the radius. The angular displacement us- ing this definition is labeled using rad. How- ever, angular displacement should be unitless, i.e. , rad is not a unit but denotes a pure num- ber. For this problem, the arc length is approximately the diameter (2 R moon = D moon = 2 (1 . 74 10 6 m) = 3 . 48 10 6 m) of the moon and the radius is the dis- tance from earth to the moon ( R earth moon = 3 . 84 10 8 m). Thus arc length radius moon s diameter distance of earth to moon = 2 (1 . 74 10 6 m) (3 . 84 10 8 m) = . 0090625 rad . 002 (part 2 of 4) 10.0 points b) What will the result be in degrees? Correct answer: 0 . 519243 . Explanation: Conversion from radians to degrees: A conversion factor for degrees and radians is rad = 180 so that rad 180 rad = degrees Another conversion factor is 1 rad = 57 . 3 . moon = (0 . 0090625 rad) parenleftbigg 180 parenrightbigg = . 519243 . 003 (part 3 of 4) 10.0 points c) What is the apparent angle the diameter of the sun subtends, as seen from the earth, in radians? Correct answer: 0 . 00930481 rad. Explanation: The apparent angular diameters are ap- proximately the same for the sun and the moon, as seen from the earth, which agrees with our visual observation, and is the reason eclipses are as spectacular as they are. 004 (part 4 of 4) 10.0 points d) What will the result be in degrees? Correct answer: 0 . 533127 . Explanation: Same analysis applies as that of the Earth- Moon. r earth sun r earth sun d sun pels (kcp389) Homework 1 hill (666) 2 Thus arc length radius sun s diameter distance of earth to sun = 2 (6 . 96 10 8 m) (1 . 496 10 11 m) = 0 . 00930481 rad = . 533127 ....
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