# Rocket Equation from Newton’s 3rd Law, Force of Gravitation, and dp/dt [closed]

I am using the derivative of momentum (dp/dt) with Newton’s 3rd Law with the gravitational force of Earth.

$$F - F_{gravity} = \dfrac{\mathrm{d}p}{\mathrm{d}t} \\ F - \dfrac{G \, m_e \, m_r}{r^2} = v \, \dfrac{\mathrm{d}m}{\mathrm{d}t} + ma\\$$

$$F$$ = Force created by fuel (at time t)

$$G$$ = Gravitational Constant

$$m_e$$ = Mass of Earth

$$m_r$$ = Mass of rocket (at time t)

$$r$$ = Distance between Earth and rocket (at time $$t$$)

$$v$$ = Velocity of rocket relative to Earth (at time $$t$$)

$$dm/dt$$ = Instantaneous rate of change of mass of rocket (at time $$t$$)

$$m$$ = Also mass of rocket (at time $$t$$)

$$a$$ = Instantaneous acceleration of rocket (at time $$t$$, equal to $$dv/dt$$)

Is my equation correct for a standard rocket? Would dm/dt be negative as the rocket is losing mass over time?

• "Astronomy Stack Exchange uses MathJax to render LaTeX. You can use single dollar signs to delimit inline equations, and double dollars for blocks." See here for more information astronomy.stackexchange.com/editing-help: – SpaceBread Oct 24 '19 at 17:34
• Welcome to the Astronomy Stack Exchange! This question may fit well on the Space Exploration or Physics exchanges, it would be worth checking those to see if there's anything useful. – antispinwards Oct 24 '19 at 19:09
• I'm voting to close this question as off-topic because questions about the application of the Tsiolkovsky rocket equation to rockets is not about Astronomy as defined in the help center. – uhoh Jan 12 at 6:23