What speed (in km/s) should a galaxy move wit | vedclass

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Question

(A) The Doppler effect for light is given by the formula $\frac{\Delta \lambda}{\lambda} = \frac{v}{c}$,where $v$ is the radial velocity of the source

Vedclass · Accepted Answer

$306$

Vedclass · Answer

(A) The Doppler effect for light is given by the formula $\frac{\Delta \lambda}{\lambda} = \frac{v}{c}$,where $v$ is the radial velocity of the source relative to the observer,$\lambda$ is the original wavelength,and $\Delta \lambda$ is the shift in wavelength.Given: $\lambda = 589.0 \; nm$,$\Delta \lambda = 589.6 - 589.0 = 0.6 \; nm$,and $c = 3 	imes 10^8 \; m/s$.Substituting the values into the formula:$v = c 	imes \frac{\Delta \lambda}{\lambda} = (3 	imes 10^8 \; m/s) 	imes \left( \frac{0.6 \; nm}{589.0 \; nm} ight)$.$v = 3 	imes 10^8 	imes 0.00101867 \; m/s \approx 3.056 	imes 10^5 \; m/s$.Converting to $km/s$: $v \approx 305.6 \; km/s \approx 306 \; km/s$.Since the wavelength has increased (redshift),the galaxy is moving away from us.

What speed (in $km/s$) should a galaxy move with respect to us so that the sodium line at $589.0 \;nm$ is observed at $589.6 \;nm$?

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