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The maximum velocity $v$, observer time $t$, and traveler proper time $T$ calculated on the "Space travel calculator" site are identical to those on John Baez's relativistic rocket page, but the energy requirement and fuel mass calculations are botched. If you check the explanation notes provided, the energy requirement is calculated as \$e = 2mc^2(\gamma -...
I thought I would indicate how I see this problem. This question involves different ways of defining the payload and total mass of the rocket. The four momentum of a body in flat spacetime, such as a rocket, is $$P~=~(E,~{\bf p}).$$ The four-momentum has the spatial momentum and the energy. The energy the rocket before it starts to accelerates has the ...