Respuesta :
Given:
The frequency emitted by the source, f_s=900 GHz
The observed frequency, f=820 GHz
To find:
The speed of the source and the direction of motion of the source.
Explanation:
The change in the frequency is given by,
[tex]\Delta f=f_s-f[/tex]On substituting the known values,
[tex]\begin{gathered} \Delta f=900\text{ GHz}-820\text{ GHz} \\ =80\text{ GHz} \end{gathered}[/tex]Thus the change in the frequency is positive. That is the frequency is decreasing. This is called a redshift and the star is moving away from the earth.
The speed of the source is given by the equation,
[tex]f=f_s\times\frac{c}{c+v}[/tex]Where c is the speed of light and v is the speed of the source.
On substituting the known values,
[tex]\begin{gathered} 820\times10^9=900\times10^9\times\frac{3\times10^8}{3\times10^8+v} \\ \implies v=\frac{900\times10^9\times3\times10^8}{820\times10^9}-3\times10^8 \\ =29.3\times10^6\text{ m/s} \end{gathered}[/tex]Final answer:
The velocity of the star is 29.3×10⁶ m/s
And the star is moving away from the earth.
