"With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $\mathop A\limits^o$ is observed at 5896 $\mathop A\limits^o$ ?"

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Accepted Answer

"$f = {f_0}\sqrt {{{1 + \beta } \over {1 - \beta }}}$

$\beta = {v \over c}$

${f \over {{f_0}}} = \sqrt {{{1 + \beta } \over {1 - \beta }}}$

$${\left( {1 + {{\Delta f} \over {{f_0}}}} \right)^2} = (1 + \beta ){(1 - \beta )^{ - 1}}$$

$\beta$ is small compared to 1

$\left( {1 + {{2\Delta f} \over {{f_0}}}} \right) = (1 + 2\beta )$

$\beta = {{\Delta f} \over {{f_0}}} = {v \over c}$

$v = 6 \times {c \over {5890}} = 305.6$ km/s"

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $\mathop A\limits^o$ is observed at 5896 $\mathop A\limits^o$ ?

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With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $\mathop A\limits^o$ is observed at 5896 $\mathop A\limits^o$ ?

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