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 = 2.00 106 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.

(a) region A ? Hz

(b) region B ? Hz

Explanation / Answer

Hi. I don't see the diagram but I assume that A and B points are on the radius of the galaxy and on opposite directions.

We have here change at light frequency (red shift and blue shift) due to the relative moving of the galaxy in earth frame of reference.

emitted frequency fs=6*1014 Hz

velocity of point A is va=Ug+Vt=2.5*106 m/s

velocity of point A is va=Ug-Vt=1.5*106 m/s

The frequency observed at eatrh will be diffrerent from the transmitted one, and is given by following formula:

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