A distant galaxy is simultaneously rotating and receding from the earth. As the

Question

A distant galaxy is simultaneously rotating and receding from the earth. As the drawing shows, the galactic center is receding from the earth at a relative speed of uG = 1.6 x 106 m/s. Relative to the center, the tangential speed is vT = 0.57 x 106 m/s for locations A and B, which are equidistant from the center. When the frequencies of the light coming from regions A and B are measured on earth, they are not the same and each is different from the emitted frequency of 8.327 x 1014 Hz. Find the measured frequency for the light from (a) region A and (b) region B. (Give your answer to 4 significant digits. Use 2.998 x 108 m/s as the speed of light.)

Explanation / Answer

A. Tangential speed at A is toward earth: v = 1.34E6 m/s ß = v/c = 4.46964643095397E-3 fA/f0 = sqrt((1+ß)/(1-ß)) = 1.00447968009762 fA = 9.27235192698113E13 Hz B. Tangential speed at B is away from earth: v = -2.06E6 m/s ß = v/c = -6.87124749833222E-3 fB/f0 = sqrt((1+ß)/(1-ß)) = 0.993152198143301 fB = 9.16778794106081E14 Hz

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