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 = 2.20 × 106 m/s. Relative to the center, the tangential speed is vT = 0.350 × 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 8.084 × 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

Here, we need to remember the equation for dopler effect :

F = sqrt(c - u / c + u ) Fo

Fa - Fb = 8.084 x 10^14 Hz

Fa = sqrt[(2.20 x 10^6 - 0.350 x 10^6) Fb

Fa / Fb = 1.85

Fa = 1.85*Fb

1.85Fb - Fb = 8.84 x 10^14

Fb = 10.4 x 10^14 Hz

Fa = 19.24 x 10^14 Hz

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