Oberth effect

Part of a series on
Astrodynamics
Orbital mechanics
Orbital elements Apsis Argument of periapsis Eccentricity Inclination Mean anomaly Orbital nodes Semi-major axis True anomaly
Types of two-body orbits by eccentricity Circular orbit Elliptic orbit Transfer orbit (Hohmann transfer orbit Bi-elliptic transfer orbit) Parabolic orbit Hyperbolic orbit Radial orbit Decaying orbit
Equations Dynamical friction Escape velocity Kepler's equation Kepler's laws of planetary motion Orbital period Orbital velocity Surface gravity Specific orbital energy Vis-viva equation
Celestial mechanics
Gravitational influences Barycenter Hill sphere Perturbations Sphere of influence
N-body orbits Lagrangian points (Halo orbits) Lissajous orbits Lyapunov orbits
Engineering and efficiency
Preflight engineering Mass ratio Payload fraction Propellant mass fraction Tsiolkovsky rocket equation
Efficiency measures Gravity assist Oberth effect
Propulsive maneuvers Orbital maneuver Orbit insertion
v t e

In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then uses its engines to further accelerate as it is falling, thereby achieving additional speed.^[1] The resulting maneuver is a more efficient way to gain kinetic energy than applying the same impulse outside of a gravitational well. The gain in efficiency is explained by the Oberth effect, wherein the use of a reaction engine at higher speeds generates a greater change in mechanical energy than its use at lower speeds. In practical terms, this means that the most energy-efficient method for a spacecraft to burn its fuel is at the lowest possible orbital periapsis, when its orbital velocity (and so, its kinetic energy) is greatest.^[1] In some cases, it is even worth spending fuel on slowing the spacecraft into a gravity well to take advantage of the efficiencies of the Oberth effect.^[1] The maneuver and effect are named after the person who first described them in 1927, Hermann Oberth, a Transylvanian Saxon physicist and a founder of modern rocketry.^[2]

Because the vehicle remains near periapsis only for a short time, for the Oberth maneuver to be most effective the vehicle must be able to generate as much impulse as possible in the shortest possible time. As a result the Oberth maneuver is much more useful for high-thrust rocket engines like liquid-propellant rockets, and less useful for low-thrust reaction engines such as ion drives, which take a long time to gain speed. Low thrust rockets can use the Oberth effect by splitting a long departure burn into several short burns near the periapsis. The Oberth effect also can be used to understand the behavior of multi-stage rockets: the upper stage can generate much more usable kinetic energy than the total chemical energy of the propellants it carries.^[2]

In terms of the energies involved, the Oberth effect is more effective at higher speeds because at high speed the propellant has significant kinetic energy in addition to its chemical potential energy.^[2]: 204 At higher speed the vehicle is able to employ the greater change (reduction) in kinetic energy of the propellant (as it is exhausted backward and hence at reduced speed and hence reduced kinetic energy) to generate a greater increase in kinetic energy of the vehicle.^[2]: 204