Watched the Apollo 11 famous footage of the launch and the camera perspective was from the ground focused on the ascending rocket. When it came time for staging and dropping the first stage, we can clearly see cutoff of rocket motors, separation and ignition of the second stage.
One thing that puzzled me always was the first stage as it falls away is seen trailing vapor, residue from its shut off engines. This reasonably has to be residual unburned oxidizer/propellant. its enough of a plume to be visible even 30+ seconds later it is still leaking away as the second stage carries the rocket further away and away.
Im asking bc every ounce, every bit of weight is calculated for and certainly fuel is no exception. Why lug the fuel up there just to shut the engines off presumably early and not burn it. Any reason for this inefficiency?
EDIT: Including link to video. [https://www.youtube.com/watch?v=dhTvadtW2dc](https://www.youtube.com/watch?v=dhTvadtW2dc) Begin watching at time 36:38
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To add to the great answers that have already been given: you want the rocket engine to shut down in a controlled manner. [SpaceX’s third ever launch is an example](https://en.wikipedia.org/wiki/Falcon_1#Third_flight) of this going wrong: the first stage shut down, and the first and second stages separated normally. But before the second stage’s engine ignited, some remaining fuel in the first stage engine evaporated, this was enough to push the first stage slightly forward into the second stage and damage it.
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