The transverse Doppler effect is the nominal redshift or blueshift predicted by special relativity that occurs when the emitter and receiver are at the point of closest approach. Light emitted at this instant will be redshifted. Light received at this instant will be blueshifted.
Assuming the objects are not accelerated, light emitted when the objects are closest together will be received some time later, at reception the amount of redshift will be
Light received when the objects are closest together was emitted some time earlier, at reception the amount of blueshift is
Classical theory does not make a specific prediction for either of these two cases, as the shift depends on the motions relative to the medium.
The transverse Doppler effect is a consequence of the relativistic Doppler effect.
In the frame of the receiver, θ0 represents the angle between the direction of the emitter at emission, and the observed direction of the light at reception. In the case when θ0 = π/2, the light was emitted at the moment of closest approach, and one obtains the transverse redshift
The transverse Doppler effect is one of the main novel predictions of the special theory. As Einstein put it in 1907: according to special relativity the moving object's emitted frequency is reduced by the Lorentz factor, so that – in addition to the classical Doppler effect – the received frequency is reduced by the same factor.
Read more about this topic: Relativistic Doppler Effect
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