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# sess21 - 21 Radiation from relativistically moving systems...

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21. Radiation from relativistically moving systems Reading: Shu, Vol.I, Ch. 16 and 17 21.1 Lorentz transformations Let us recapitulate the Lorentz transformations of special relativity. One frame of reference, K 0 , may move with velocity ~v = ~ βc relative to another system, K . For the coordinates parallel and perpendicular to the transformation direction the Lorentz transformations are x k = γ ± x 0 k + βct 0 ² x = x 0 (21 . 1) ct = γ ± βx 0 k + ct 0 ² (21 . 2) In astrophysics we often cannot measure where exactly a particle or an emitter is at a given time. If the length of the line-of-sight changes during a time interval dt , for example by relativistic motion of the emitter that is at rest in system K 0 , a distant observer at rest in system K would measure a time interval that is changed by retardation, i.e. the relocation of the emitter during the time of measurement. dt obs = (1 - β cos θ obs ) dt = γ (1 - β cos θ obs ) dt 0 = dt 0 D D = Dopplerfactor (21 . 3) where θ obs is the angle between the line-of-sight (the propagation direction of the radiation)

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sess21 - 21 Radiation from relativistically moving systems...

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