PX155 - H4 - relativistic doppler effect - seeing vs observing

let $Δ t_{0}$ be the proper time interval between each pulse from a light source
in $S^{'} :$

Δ t^{'} = γ Δ t_{0}

\begin{aligned} Δ t_{u}^{'} & = γ Δ t_{0} - \frac{u}{c} γ Δ t_{0} \\ = γ Δ t_{0} (1 - \frac{u}{c}) \\ \frac{1}{f^{'}} & = \frac{γ}{f_{0}} (1 - \frac{u}{c}) \\ \frac{f^{'}}{f_{0}} & = \frac{1}{γ (1 - \frac{u}{c})} \end{aligned}

\frac{f^{'}}{f_{0}} = \frac{1}{γ (1 + \frac{u}{c})}

eg: a star, $S S 433$ , emits two jets of material at $0.26 c$ in opposite directions. at what $λ$ will light be received from the two jets?
- $λ_{0} = 656.2 n m$
- $γ = \frac{1}{\sqrt{1 - {0.26}^{2}}} = 1.0356$
- receding jet: $λ = γ (1 + \frac{u}{c}) = 856.3 n m \to$ red shifted
- approaching jet: $λ = γ (1 - \frac{u}{c}) = 502.9 n m \to$ blue shifted