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 = 1.50 × 106 m/s. Relative to the center, the tangential speed is vT = 0.380 × 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 6.091 × 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

For A --> tangential speed towards earth

v = (1.5 x106) - (3.80 x 105) = 1.12x106 m/s

= v/c = (1.12x106 m/s)/(2.998 x 108 m/s) = 0.373 x10-2

fA/fo = ((1+)/(1-)) = 1.0037

fA = (6.091 x 1014)(1.0037) = 6.113 x 1014 Hz

For B --> tangential speed away from earth

v = -(1.5 x106) - (3.80 x 105) = - 1.88 x 106 m/s

= v/c = (- 1.88 x 106 m/s)/(2.998 x 108 m/s) = 6.27 x 10-3

fB/f0 = ((1+)/(1-)) = 1.0062

fB = (6.091 x 1014)(1.0062 ) = 6.128 x 1014 Hz

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