p01_040 - 40. (a) When is measured in radians, it is equal...

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40. (a) When θ is measured in radians, it is equal to the arclength s divided by the radius R .F o ra very large radius circle and small value of θ ,sucha sw edea lw i thinF ig .1 -9 ,thea rcmaybe approximated as the straight line-segment of length 1 AU. First, we convert θ = 1 arcsecond to radians: (1 arcsecond) µ 1arcminute 60 arcsecond ¶µ 1 60 arcminute ¶µ 2 π radian 360 which yields θ =4 . 85 × 10 6 rad. Therefore, one parsec is R o = s θ = 1AU 4 . 85 × 10 6 =2 . 06 × 10 5 AU . Now we use this to convert R = 1 AU to parsecs: R =(1AU) µ 1pc 2 . 06 × 10 5 AU =4 . 9 × 10
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