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