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 = 5.00 105 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 than the emitted frequency of 6.00 1014 Hz. Find the measured frequency for the light from each of the following.

Explanation / Answer

For A --> tangential speed towards earth

v = (1.5 x106) - (5 x 105) = 106 m/s

= v/c = (106 m/s)/(2.998 x 108 m/s) = 0.3335 x10-2

fA/fo = ((1+)/(1-)) = (1.003335/0.996665) = 1.006692 = 1.0033

fA = (6 x 1014)(1.0033) = 6.0198 x 1014 Hz

For B --> tangential speed away from earth

v = -(1.5 x106) - (5 x 105) = - 2 x 106 m/s

= v/c = (- 2 x 106 m/s)/(2.998 x 108 m/s) = 6.67 x 10-3

fB/f0 = ((1+)/(1-)) = (1.00667/0.99333) = 1.01342 = 1.0066

fB = (6 x 1014)(1.0066 ) = 6.0396 x 1014 Hz

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