The galactic center is receding from the earth at a relative speed of u G = 1.30

Question

The galactic center is receding from the earth at a relative speed of uG = 1.30 × 106 m/s. Relative to the center, the tangential speed is vT = 0.360 × 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 8.656 × 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

A. Tangential speed at A is toward earth:
v = 0.94E6 m/s
ß = v/c = 3.1354E-3
fA/f0 = sqrt((1+ß)/(1-ß)) = 1.003140331
fA = 8.683182E14 Hz
B. Tangential speed at B is away from earth:
v = -1.66E6 m/s
ß = v/c

= -5.53702E-3
fB/f0 = sqrt((1+ß)/(1-ß)) = 1.005552435
fB = 8.704061E14 Hz

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