A distant galaxy is simultaneously rotating and receding fro

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 U_G = 1.50 Times 10^6 m/s. Relative to the center, the tangential speed is V_T = 0.520 Times 10^6 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 5.707 Times 10^14 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 Times 10^8 m/s as the speed of light.) Number Unties Number Units

Solution

A. Tangential speed at A is toward earth:
v = .98E6 m/s (1.50 -.520 *10^6)
ß = v/c = 3.268845*10^-3
fA/f0 = sqrt((1+ß)/(1-ß)) = 1.00655913078
fA = 5.744432 *10^14 Hz
B. Tangential speed at B is away from earth:
v = -2.02*10^6 m/s
ß = v/c = -6.73782*10^-3
fB/f0 = sqrt((1+ß)/(1-ß)) = 0.9932884
fB = 5.6686E* 10^14 Hz