Consider a spiral galaxy that is moving directly away from Earth with a speed v1
ID: 1697813 • Letter: C
Question
Consider a spiral galaxy that is moving directly away from Earth with a speed v1 = 4.100×105 m/s at its center, as shown in the figure . The galaxy is also rotating about its center, so that points in its spiral arms are moving with a speed v2 = 6.500×105 m/s relative to the center.A.) If light with a frequency of 8.260×1014 Hz is emitted in both arms of the galaxy, what frequency is detected by astronomers observing the arm that is moving toward the Earth? (Measurements of this type are used to map out the speed of various regions in distant, rotating galaxies.)
B.) If light with a frequency of 8.260×1014 Hz is emitted in both arms of the galaxy, what frequency is detected by astronomers observing the arm that is moving away from Earth?
Explanation / Answer
The relative velocity of the upper arm is v_U = 6.5*10^5 m/s - 4.10*10^5 m/s
= 2.4*10^5 m/s
The relative velocity of the lower arm is V _L = 10.6*10^5 m/s
a ) z = v / c
= 2.4 *10^5 m/s / 3.0*10^8 m/s
= 0.0008 m
observed frequency = emmitted frequency (1+ z )
8.26 *10^14 Hz * ( 1.0008 )
= 8.266*10^14 Hz
b )
z = v / c
= 10.6 *10^5 m/s / 3.0*10^8 m/s
= 0.00353 m
observed frequency = emmitted frequency (1+ z )
8.26 *10^14 Hz * ( 1.00353 )
= 8.289*10^14 Hz