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Relative Velocity

The relative velocity is the velocity of an object or observer in the rest frame of another object or observer. If it is constant


In the Newtonian limit where the Galilean transformation is approximately:



This holds true and is identical with the vector difference between the velocities A and B as evaluated in terms of a single coordinate system:

v_AB= v_B- v_A

Due to Einstein’s Special Relativity, this does not hold true in general. The expression “the velocity of A relative to B” is shorthand for “the velocity of A in the coordinate system where B is always at rest.

To obtain vAB from vA and vB in an arbitrary reerence frame, the Lorentz transformation is necessary. If vA and vB are collinear, the formula is:

v_AB= (v_B- v_A)/(1- (v_A v_B)/c^2 )

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