= Relativistic rocket equation
{title2=$m\gamma^2\,dv+u\,dm=0$}
For collinear motion without external forces, a rocket ejecting material backwards at constant speed $u$ in its instantaneous rest frame obeys $m\gamma^2\,dv+u\,dm=0$. Here $m$ is the rocket's <rest mass>, including stored <internal energy>, and $\gamma$ is its <Lorentz factor> in the chosen <inertial frame>. The equation follows from <momentum conservation>, <conservation of relativistic energy>, and the <relativistic velocity-addition formula>; expelled rest mass is not simply the decrease in rocket rest mass.
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