How fast and in what direction must galaxy a be moving 17 an absorption line found at 500 nm for a stationary galaxy 1s shifted to 400 nm for a? (b) how fast and in what direction is galaxy b moving if it shows the same line shifted to 550 nm ?

v = 0.22 c and wavelength is decrease so galaxy A is move away from stationary galaxy

v = 0.095 c and wavelength is increase so galaxy B come toward stationary galaxy

Explanation:

Given data

found = 500 nm

shifted A = 400 nm

shifted B = 550 nm

to find out

How fast and in what direction is galaxy

solution

we use here formula  that is

(λ) shifted = √(1-β / 1+β)  (λ)found

1-β / 1+β =  (4/5)²         1

1-β / 1+β =  16 / 25

β = 0.22

v/c = 0.22

v = 0.22 c

here wavelength is decrease so galaxy A is move away from stationary galaxy

and

here according to equation 1

and we use shifted 550 nm

so

1-β / 1+β =  (5.5/5)²

1-β / 1+β =  30.25 / 25

β = 0.095

so  v/c = 0.095

v = 0.095 c

here wavelength is increase so galaxy B come toward stationary galaxy

0.19 m/s and 0.45 m/s