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 = 1.30 × 106 m/s. Relative to the center, the tangential speed is vT = 0.460 × 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 8.894 × 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) For location A, speed
VA= UG - VT = 1.3*106 - 0.46*106 = 8.4*105 m/s
For location B, speed
VB = UG + VT =  1.3*106 +0.46*106 = 1.76*106 m/s
emitted frequency fS = 8.894*1014 Hz
(a) fA = fS(1- VA /C) = 8.869*1014 Hz
(b) fB = fS(1- VB /C) = 8.842*1014 Hz

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