Derivation of The Relativistic Explanation
A relativistic jet coming out of the center of an AGN is moving along AB with a velocity v. We are observing the jet from the point O. At time a light ray leaves the jet from point A and another ray leaves at time from point B. Observer at O receives the rays at time and respectively.
- , where
Apparent transverse velocity along CB,
- , where
If (i.e. when velocity of jet is close to the velocity of light) then despite the fact that . And of course means apparent transverse velocity along CB, the only velocity on sky that we can measure, is larger than the velocity of light in vacuum, i.e. the motion is apparently superluminal.
Read more about this topic: Superluminal Motion
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