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

Question

A distant galaxy is simultaneously rotating and receding from the earth. As Figure shows, the galactic center is receding from the earth at a relative speed of uG=1.6×10^6 m/s. Relative to the center, the tangential speed is vT=0.4×10^6 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 6.200×10^14 hertz. Find the measured frequency for the light from (a) region A and (b) region B .

Explanation / Answer

A. Tangential speed at A is toward earth:

v = 1.2E6 m/s

ß = v/c = 4.E-3

fA/f0 = sqrt((1+ß)/(1-ß)) = 1.00400803

fA = 6.224849E14 Hz

B. Tangential speed at B is away from earth:

v = -2.00E6 m/s

ß = v/c = -6.6666666E-3

fB/f0 = sqrt((1+ß)/(1-ß)) = 0.99335540

fB = 6.158803E14 Hz

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