A blob of plasma in the jet of an active galaxy moves with constant velocity along…

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Relativity and Gravitation, Ch Minkowski spacetime, four-vectors and causal structure

Problem

A blob of plasma in the jet of an active galaxy moves with constant velocity

0.800c

along the

+x

axis of the observatory frame

S

, where

c = 2.998\times 10^{8}\ \mathrm{m\,s^{-1}}

. The blob's rest frame

S'

is in standard configuration with

S

. Gravity is ignored and the light travels in vacuum. ((a)) Find the rapidity

\psi

S'

relative to

S

. ((b)) Write the four-velocity

\mathbf{U}

of the blob in

S

, each component as a multiple of

c

, and evaluate

\mathbf{U}\cdot\mathbf{U}

. ((c)) The blob emits light of frequency

\nu_{\rm em} = 9.00\times 10^{14}\ \mathrm{Hz}

in its own rest frame and is moving directly away from the observatory along the line of sight. What frequency

\nu_{\rm rec}

is received in

S

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