In the coordinate system of moving galaxy is emitted a wave. The coordinates of observer are chosen according to the rules described in chapter NEW MODEL OF EUCLIDEAN REALITY The trajectory of the observer is its time axis while the observer's space axes are the directions perpendicular to the trajectory of the observved galaxy  
The wave is propagating according to the rules described in chapterTHE SPEED OF LIGHT Finally the received wavelength is longer than the emitted. 

COMPUTATIONS OF THE RED SHIFT  

In the triangle ABC the following relationship must be satisfied (law of sines): From the triangle BDE results the relationship between angles: From the comparison of the angles at the vertexes of the triangle D and A results that Hence from the above we obtain 

Finally we obtain the following: And finally(we should remember that V=sinϕ): 