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A photon starship starts from rest and propels itself by emitting photons in the direction opposite to its motion until it reaches a speed v. Use energy momentum conservation law to show that the ratio of the initial rest mass, m, to it's final rest mass M is

m/M = sqrt[(1+v/c)/(1-v/c)].

I'm not sure how to approach it, i think my formulation is wrong. I've looked at:

(Eo/c,0)=(E1/c,p)+kE3/c(1,n) where Eo is the original energy of the space ship as measured in the initial frame, E1 the energy after and then E3 the energy of the photon. I've added a K to account for how many photons we need to get to a velocity v. However looking at this seems to give nothing. I've also used the identity E^2=E0^2+c^2p^2 to try and get something but it goes nowhere.

Essentially i know that in order to get the final rest mass i need to be in that frame and not the initial frame. I know from the initial frame the mass will be mgamma.

Overall i think my formulation is wrong and that my view of the situation is incorrect and so would like a push in the right direction.

Thanks.