The Oberth effect is the phenomenon where a rocket engine produces more useful work when fired at high speeds, particularly near a gravitational body.The idea was first clearly described by Hermann Oberth in his 1923 book, although hints also appeared in Tsiolkovsky's work. The law works due to the nonlinear dependence of kinetic energy on speed. Imagine you push a cart. If it is barely moving, your push adds almost no energy to it — most of the energy turns into heat in your shoes. If the cart is racing, you push off the ground, transferring momentum while remaining nearly in place, and almost all the work turns into its acceleration. In space, the planet's gravitational field plays the role of the ground, and the rocket exhaust provides the 'push.' The faster the rocket relative to the planet, the greater the percentage of fuel energy converted into motion.
Hermann Oberth, one of the pioneers of astronautics, formulated the effect in 1923 in his work 'The Rocket into Interplanetary Space.' He showed that it is most advantageous to fire the engine at the moment of maximum speed relative to the center of attraction, which later became a standard technique in celestial mechanics. Oberth's ideas were developed by Konstantin Tsiolkovsky and Robert Goddard, but the clear energetic justification was given by Oberth. Later, in the space age, the effect began to be actively used for maneuvers near giant planets, especially in the Voyager and Cassini programs.
The Oberth effect is fundamental to Hohmann transfers and powered gravity assists. For example, to leave low Earth orbit and head to the Moon, it is advantageous to fire an impulse at perigee. The reverse situation: braking to enter orbit around another planet is most efficient at the pericenter of the approach hyperbola. Limits of applicability: the effect is noticeable when the exhaust velocity is comparable to the current orbital velocity, and it is negligible for low-speed vehicles like atmospheric drones.
Orbital maneuvers of spacecraft: firing the engine at pericenter (the point closest to the planet) yields the maximum energy gain, saving fuel when reaching high orbits and interplanetary transfers.
Oberth first proposed using an 'orbital refueling system' — refueling at high speed, which could allow reaching high velocities without enormous single-use rockets.
