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- Using Newton’s 3rd Law, gravitational force, and derivative of momentum to model a rocket going into space while losing mass.

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

F - [Force of gravity on rocket] = dp/dt

F - (G * m_e * m_r / r2 ) = v * dm/dt + 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? Is v relative to the Earth or the expelled gases and why?

F - [Force of gravity on rocket] = dp/dt

F - (G * m_e * m_r / r2 ) = v * dm/dt + 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? Is v relative to the Earth or the expelled gases and why?