Answer:
The speed of galaxy relative to the earth is [tex]3.9 \times 10^{6}[/tex] [tex]\frac{m}{s}[/tex]
Explanation:
Given :
Observed frequency [tex]f_{obs} = 1.013 f[/tex]
Actual frequency [tex]f_{act} = f[/tex]
For finding the speed of galaxy relative to the earth.
From the doppler effect of light,
[tex]f_{obs} = \frac{c+v}{c} f _{act}[/tex]
Where [tex]c = 3 \times 10^{8} \frac{m}{s}[/tex], [tex]v=[/tex] relative speed
[tex]1.013 f= \frac{c+v}{c} f[/tex]
[tex]0.013c = v[/tex]
[tex]v = 0.013 \times 3 \times 10^{8}[/tex]
[tex]v = 3.9 \times 10^{6} \frac{m}{s}[/tex]
Therefore, the speed of galaxy relative to the earth is [tex]3.9 \times 10^{6}[/tex] [tex]\frac{m}{s}[/tex]
