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 = 1.40 × 106 m/s. Relative to the center, the tangential speed is vT = 0.430 × 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 8.521 × 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 × 108 m/s as the speed of light.)

Explanation / Answer

A. Tangential speed at A is toward earth:
v = 0.97E6 m/s
ß = v/c = 3.2333E-3
fA/f0 = sqrt((1+ß)/(1-ß)) = 1.0032385
fA = 8.5485952585E14 Hz

B. Tangential speed at B is away from earth:
v = -1.83E6 m/s
ß = v/c = -6.1E-3
fB/f0 = sqrt((1+ß)/(1-ß)) = 0.99391849
fB = 8.46917945329E14 Hz

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