Consider a spiral gelexy that is moving directly away from Earth with a speed V
ID: 1585604 • Letter: C
Question
Consider a spiral gelexy that is moving directly away from Earth with a speed V -3.600 x 10 m/'s at its center, as shown in the figure. The galaxy is also rotating about its center, so that points in its vit·speed v-6.S00 x 105 m/s relative to the center. Ught with a frequency of 9.830 × 1034 Hz emitted in both arms ofthe galaxy, and this light detected by astronomers on Earth ) Does the arm near the top of the figure show a red shift (toward lower frequency) or a blue shit (toward higher frequency)? o red shit O blue shift Does the lower arm show a red or a blue shift? O red shin O blue shit Score: 1 out of 1 (b) what frequency i s detected by the astronomers observing the upper arm? (Enter your answer to 4 significant figures.) s detected by the astronomers observing the lower arm? (Enter your ansmer to 4 significant figures.)Explanation / Answer
The relative velocity of the upper arm is v_U = 6.5*10^5 m/s - 3.6*10^5 m/s = 2.9*10^5 m/s
The relative velocity of the lower arm is V _L = 10.1*10^5 m/s
a ) z = v / c = 2.9*10^5 m/s / 3.0*10^8 m/s = 0.00097 m
observed frequency = emmitted frequency (1+ z )
9.83 *10^14 Hz * ( 1.00097 ) = 9.84*10^14 Hz
b ) z = v / c = 10.1*10^5 m/s / 3.0*10^8 m/s = 0.00337 m
observed frequency = emmitted frequency (1- z )
9.83 *10^14 Hz * ( 0.9966) = 9.80*10^14 Hz