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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 = 1.90 106 m/s. Relative to the center, the tangential speed is vT = 3.00 105 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 6.20 1014 Hz. Find the measured frequency for the light from each of the following.

region A=

region B=

This difference is due to the Doppler effect.
If fo is emitted frequency, the observed frequency f is
f=fo(c + v(r))/(c + v(s)),
where c is the velocity of waves in the medium;
v(r) is the velocity of the receiver relative to the medium; here v(r)= 0
v(s) is the velocity of the source relative to the medium; positive if the source is moving away from the receiver.
The frequency is decreased if either is moving away from the other.
v(s)1 = u(G) –v(t) = 1.9•10^6-3•10^5 = 1.6•10^6 m/s
v(s)2 = u(G) –v(t) = 1.9•10^6+3•10^5 = 2.2•10^6 m/s
c= 3 •10^8 m/s
f 1=6.167•10^14 Hz
f2 =6.155•10^14 Hz