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

speed at location A is

VA = uG - vT = (2.2x10^6 m/s)- ( 0.350x 10^6 m/s) = 1.85 x 10^6 m/s

speed at location B is

VB = uG + vT = (2.2x10^6 m/s)+ ( 0.350x 10^6 m/s) = 2.55 x10^6m/s

a) The measured frequency at A is
fA = fs ( 1 - VA /c) = (8.084x 1014 Hz) ( 1 -   (18.5 x 105m/s) /( 3 x 108m/s) ) = 8.034 x 1014Hz

b) frequency at B is
fB = fs ( 1 - VB /c) = (8.084 x 1014 Hz) ( 1 -   (25.5 x 105m/s) /( 3 x 108m/s) ) = 8.015 x 1014Hz

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