Re: The problem of relativistic synchronisation

Le 05/09/2024 à 14:24, "Paul.B.Andersen" a écrit :

It should be:
  Vapp = v⋅sin(μ)/(1 - (v/c)⋅cos(μ))

This equation is correct, but it is not the equation of the apparent speed.
The apparent speed is given as follows, if we take the angle µ, formed by the direction of the mobile and the projection of the sight.
Vapp= v/(1+cosµ.v/c) Your equation, my dear Paul, and which is this one: Vapp(perp)=sinµ.v/(1+cosµ.v/c) and which is the perpendicular projection of the apparent speed, is not the apparent speed, but its transverse projection on the background of the sky.
This projection, which is not really an apparent speed, but the apparent transverse speed of the apparent speed, can, as you say, and the phenomenon may seem surprising, be faster than c.
It is indeed strange, but logical if we know the RR well, that the transverse projection of an apparent speed can be greater than this same purely transverse speed.
This is a particular relativistic effect indeed.
I simply ask you not to confuse apparent transverse velocity (Vapp=v), and transverse projection of an apparent velocity (Vapp" = sinµ.Vapp = sinµ.v/(1+cosµ.v/c)
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 R.H.
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