Rockets are momentum engines. A certain amount of fuel adds a certain amount of momentum to the spacecraft. Momentum is just a simple Mass * Velocity so if your spacecraft remains roughly the same mass then a certain change in momentum is really a change in velocity
But orbits are defined by the energy that a spacecraft has, and energy is Mass * Velocity^2 so a certain change in momentum/velocity has a different effect on the energy of the spacecraft depending on how fast its going
Burning a rocket engine when the spacecraft is traveling quickly ends up adding a lot more energy to the spacecraft for the same fuel as you would get by burning the engine when traveling slowly. The Oberth Effect is the process of making a close approach to a planet so its gravity pulls the spacecraft in and gets it going wayyyy faster briefly and then burning the engine to make use of the significantly higher speed to get more energy from its fuel so it can change its orbit with less fuel. The downside is that it requires the course to actually pass near planets so it can make a journey significantly longer while allowing it to be done with way less fuel
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