Question

If a spectral line from a distant star is measured to have a wavelength of 497.14nm, but is normally at 497.22nm how fast (speed, not velocity) with respect to the Earth is the star moving in m/s?

Answer 1

Measured wavelength is,

$\Delta$$\lambda$ + $\lambda$ = 497.14 nm

Normal wavelength $\lambda$ = 497.22 nm

$\Delta$$\lambda$ = 497.22 - 497.14 = 0.08 nm

z = v / c

(-0.08 / 497.22) = (v / 3*10^8)

v = -48268 m/s

Speed of star  with respect to the Earth =  -48268 m/s