Homework 2 - sanchez(ds28677 homework 02 Turner(58220 This...

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sanchez (ds28677) – homework 02 – Turner – (58220) 1 This print-out should have 12 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 The radius of the moon is 1 . 74 × 10 6 m , the radius of the sun is 6 . 96 × 10 8 m, the average moon-earth distance is 3 . 84 × 10 8 m , and the average sun-earth distance is 1 . 496 × 10 11 m. What is the apparent angle the diameter of the moon subtends, as seen from the earth? Correct answer: 0 . 0090625 rad. Explanation: If you have an angle θ that is very small ( 1 ) in measure, then θ tan θ, for θ measured in radians. r earth moon r earth moon d moon θ 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 θ tan θ = diameter distance AlternateSolution: The definition of an- gular displacement is the arc length divided by the radius. The angular displacement us- ing this definition is labeled using rad (actu- ally a pure number). For this problem, the “arc length” is ap- proximately 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 “distance” R earth moon = 3 . 84 × 10 8 m from the earth to the moon. Thus θ arc length radius = 2 R moon d EM = 2 (1 . 74 × 10 6 m) 3 . 84 × 10 8 m = 0 . 0090625 rad .
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