With what speed should a galaxy move outward with respect to earth...

f = {f}_{0}\sqrt{\dfrac{1 + \beta}{1 - \beta}}; \beta = \dfrac{v}{c}$</p><p>$\dfrac{f}{{f}_{0}}\sqrt{\dfrac{1 + \beta}{1 - \beta}}$</p><p>${\left(1 + \dfrac{\Deltaf}{{f}_{0}}\right)}^{2} = \left(1 + \beta\right) ( 1 - \beta{)}^{- 1}$</p><p>$\beta$is small compared to$1$</p><p>\left(1 + \dfrac{2\Deltaf}{{f}_{0}}\right) = \left(1 + 2\beta\right)$

$\beta = \dfrac{\Deltaf}{{f}_{0}} = \dfrac{v}{c}$

$v = 6 \times \dfrac{c}{5890} = 305 . 6km{sec}^{- 1}$