RECESSION OF GALAXIES - The red shift

We learn about the increase of the galaxies' velocities on basis of the observations of increase of the wavelengths which are emitted by the galaxies. If the velocity of the galaxy is higher then the received wavelength is longer. This phenomena is named "the red shift"
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):


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