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 =1.60 x 10^6 m/s. Relative to the center, the tangential speed is vT = 5.00 x 10^5 m/s for locations A and 8, 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 X 10^14 Hz. Find the measured frequency for the light from each of the following. (a) region A Hz (b) region B Hz

Explanation / Answer

a)

The speed at location A is calculated as follows:

VA = uG - vT = (1.60x106 m/s)- ( 5.00x 105 m/s) = 11 x 105 m/s
The speed at location B is calculated as follows:
VB = uG + vT = (1.60x106 m/s) + ( 5.00x 105 m/s) = 21 x 105 m/s
The frequency at A is calculated as follows:

fA = fs ( 1 - VA /c) = (6x 1014 Hz) ( 1 - (11 x 105 m/s) /( 3 x 108 m/s) ) = 5.978 x 1014Hz

b)

The frequency at B is calculated as follows:
fB = fs ( 1 - VB /c) = (6 x 1014 Hz) ( 1 - (21x 105 m/s) /( 3 x 108 m/s) ) = 5.958 x 1014Hz

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