Show that the four-momentum of the rocket''s exhaust

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Reference no: EM131098813

Photon-propelled rocket

A rocket of initial mass M0 starts from rest and propels itself forward along the x axis by emitting photons backward.

(a) Show that the four-momentum of the rocket's exhaust in the initial rest system can be written P = γMf v(-1, 0, 0, i), where Mf is the final mass of the rocket. (Note that this result is valid for the
exhaust as a whole even though the photons are Doppler-shifted.)

(b) Show that the final velocity of the rocket relative to the initial frame is

where μ = M0/Mf is the ratio of the rocket's initial mass to its final mass.

Reference no: EM131098813

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