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The literature on relativistic beaming / doppler beaming is scarce, so I hope the community can shed some "light" on this topic. I want to derive a formula for the phenomenon known as relativistic light aberration.

Suppose, in the rest frame of the star, $S^{\prime}$, moving at speed ${v}$, that light is being emitted at an angle ${ \theta^{\prime} } $ relative to the vector from the observer to the source at the time when the light is emitted. Due to the aberration effect, the angles at which the photons will be emitted in $S^{\prime}$ will differ from those observed by someone moving relative to the star in S. This is given by: $$\cos(\theta) =\frac{\cos(\theta^{\prime})-\beta}{1-\beta\cos(\theta^{\prime})}$$

Photons from the source which reach the observer are tilted towards the direction of the source's motion (relative to the observer). Relativistic beaming is when light radiates isotropically.

Now, I am not asking anyone for a full derivation but just a hint or the right direction to start. I will update this question with my derivation afterwards, I just need to know how to being. Thanks! (PS: This is NOT a homework question, it's a question for research purposes)

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  • $\begingroup$ There is a very good introductory article with historical context at: mathpages.com/rr/s2-05/2-05.htm. You will have to decide for yourself how much of a hint to take from it! $\endgroup$
    – m4r35n357
    Commented Jul 19, 2019 at 17:17

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