ADVANCED DYNAMICS — PHY 4241/5227 SOLUTIONS – SET 13

Problem 46: The equation for the redshift is

λ′ = λ \sqrt{\frac{1 + β}{1 − β}}
(\frac{λ′}{λ} )^{2} = \frac{1 + β}{1 − β}
(\frac{λ′}{λ} )^{2} − β (\frac{λ′}{λ} )^{2} = 1 + β
(\frac{λ′}{λ} )^{2} − 1 = β [1 + (\frac{λ′}{λ} )^{2}]
β = \frac{(λ′/λ)^{2} − 1}{(λ′/λ)^{2} + 1}

With λ′ = 729.2 and λ = 364.56 we find

β = \frac{v}{c} = 0.6 .