I'm currently trying to understand how the Rocket Equation works.
I've gotten this far:
mv = (m+Δm)(v+Δv) − Δm(v−ve) Left side is the momentum of the rocket+fuel BEFORE, and right side is the momentum of the entire system AFTER the fuel has been expelled out the back.
After this, the brackets are removed causing the equation to become this:
mv = mv + Δmv + Δmv + ΔmΔv - Δmv + Δmve
ΔmΔv is ignored due to it being too small, and when we clean up the equation, it becomes:
mΔv = -Δmve
Now, what is mΔv in the equation? I can see that -Δmve is "momentum of the expelled fuel", since -Δm is the mass of the expelled fuel (still a positive number) and ve is the velocity of the fuel being expelled.
If we just calculate it, mΔv is [original mass]*[change in velocity for rocket]. That.. doesn't really result to anything important, does it?
So, the question summed up is: Is mΔv an important part that I should understand, or should I simply skip over that as-is and start integrating?
I'm sure this must have a simple answer, but I can't wrap my head round it! Right after this is integration. I'd like to go forward but can't, because I can't understand this one bit! Can someone help? :)