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Colloquially referred to as one of the hardest professions, rocket science is actually a common name for spacecraft/space-systems engineering. However, one can also generalize this to include all forms of rocketry, including rockets that are not capable of space travel.
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Derivation of Tsiolkovsky rocket equation
My textbook derives the rocket equation from conservation of momentum like so:
$$\begin{align}p_i&=p_f \tag{1}\\
mv&={(m-dm_g)}{(v+dv)}+dm_g(v-u)\\
mv&=mv+m\,dv-dm_g\,v-dm_g\,dv+dm_g\,v-dm_g\,u\\
m\, …
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Derivation of Tsiolkovsky rocket equation
I believe the textbook's instruction to disregard the $dm_g\,dv $ term is in error.
If we leave it in, and let $m_0$ denote the initial mass and $dm = -dm_g$ the change in mass, (1) reduces to
$$\ …