Question

A distant galaxy is simultaneously rotating and receding from the earth. As the drawing shows, the...

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 up = 1.6 x 10^6 m/s. Relative to the center, the tangential speed is vr = 0.4 x 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 emitted frequency of 6.200 x 10^14 Hz. Find the measured frequency for the light from (a) region A and (b) region B.

Homework Answers

Answer #1

(a)

At location A, the relative speed of the galaxy and the tangential velocity are opposite in direction to each other.

Therefore, the velocity of the galaxy at location A is,

VA = uG - vr = 1.6*106 - 0.4*106 = 1.2*106 m/s

The expression for the observed frequency when the source is moving away is,

fo = fs*(1 - VA/c)

fo = 6.2*1014*(1 - 1.2*106/3*108)

fo = 6.17*1014 Hz

(b)

VB = uG + vr = 1.6*106 + 0.4*106 = 2*106 m/s

The expression for the observed frequency when the source is moving away is,

fo = fs*(1 - VB/c)

fo = 6.2*1014*(1 - 2*106/3*108)

fo = 6.15*1014 Hz

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