I Oberth Maneuver Question

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otherwise we'd have a paradox where converting chemical energy into electricity and then a magnetic field would change the mass of the system at infinity which is impossible.
I'm confused on this point. This seems similar to the description of an oberth manuever, in which a craft derives extra kinetic energy at infinity from its propellant than would otherwise be possible, by burning its propellant while the propellant's kinetic energy is at a maximum with respect to a gravity well.

https://en.wikipedia.org/wiki/Oberth_effect
"At very high speeds the mechanical power imparted to the rocket can exceed the total power liberated in the combustion of the propellant; this may also seem to violate conservation of energy. But the propellants in a fast-moving rocket carry energy not only chemically, but also in their own kinetic energy, which at speeds above a few kilometres per second exceed the chemical component. When these propellants are burned, some of this kinetic energy is transferred to the rocket along with the chemical energy released by burning."
 
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jbriggs444

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I'm confused on this point. This seems similar to the description of an oberth manuever, in which a craft derives extra kinetic energy at infinity from its propellant than would otherwise be possible, by burning its propellant while the propellant's kinetic energy is at a maximum with respect to a gravity well.
You can account for the benefits in various ways.

If you are far outside any gravity well, consider the energy in the rocket fuel. It starts with high velocity and correspondingly high kinetic energy. When burned, it is exhausted at a lower velocity and low kinetic energy.

Or consider the work done by the rocket motor. For a fixed thrust, pushing against a high speed object produces more power than pushing against a low speed object.

Nothing changes much in a gravity well. In a free fall trajectory, the fuel has a constant total energy (chemical plus kinetic plus potential) no matter where you burn it. But if you burn it while it is moving faster, you siphon off more kinetic energy than if you burn it while it is moving more slowly.
 

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