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A powered flyby, or Oberth maneuver, describes a maneuver in which a rocket falls into a gravitational well, and then accelerates when its fall reaches maximum speed. The resulting maneuver is actually a more efficient way to gain kinetic energy than applying the same impulse outside of a gravitational well.
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Oberth Effect in Solar Sails: Where does the extra energy comes from?
When two spacecrafts moving at different speeds are accelerated by solar sails, with everything else being equal, the $\Delta V$ is the same for them (or, rather, almost the same for non-relativistic …