Momentum Conservation

• $$\begin{array}{rl}-mv& =-(M-\Delta m)(v+\Delta v)+\Delta m(-v+u_e)\\ & =-M\Delta v+\Delta m{u}_e\\ ⟹M\Delta v& =\Delta m{u}_e\\ M\frac{\Delta v}{\Delta t}& =\frac{\Delta m}{\Delta t}{u}_e\\ M\frac{dv}{dt}& =\dot{m}{u}_e\end{array}$$

IMPORTANT

Thrust Equation

• $Ma=F=\dot{m}{u}_e$

IMPORTANT

Rocket Equation

• $\Delta v=u_e\log \left((\right)\frac{M_1}{M_2})$