Oberth Effect Calculator

The Oberth effect states that a rocket burn performed at high velocity produces far more kinetic energy per unit of propellant than the same burn at low velocity. This is because kinetic energy is proportional to v squared: adding DV at speed v changes KE by (1/2)m((v+DV)^2 - v^2) = m(v*DV + DV^2/2). The extra energy v*DV scales with the existing speed, so burning at periapsis of a hyperbolic trajectory near a massive body is far more efficient than burning in deep space. It is the core reason gravity assists with burns are so powerful for outer-planet missions.

At periapsis: v_p = sqrt(v_inf_in^2 + v_esc^2), where v_inf_in is the incoming hyperbolic excess speed and v_esc = sqrt(2*mu/r_p) is the local escape speed. After burning DV: v_after = v_p + DV. Outgoing excess: v_inf_out = sqrt(v_after^2 - v_esc^2). Oberth gain = v_inf_out - v_inf_in - DV. The gain is always positive when v_esc > 0, and increases with higher v_esc (lower periapsis) and higher v_p.

A pure gravity assist (unpowered) deflects the spacecraft velocity in the planet's rest frame but conserves the hyperbolic excess speed magnitude. The spacecraft gains heliocentric kinetic energy only because the planet imparts momentum through its gravitational field. A powered flyby (Oberth maneuver) adds a propellant burn at periapsis: the high local speed amplifies the energy yield of the burn, adding extra kinetic energy on top of the pure gravity assist. Real outer-planet missions (like Cassini to Saturn) combine both effects.

Jupiter has the strongest gravitational field of any planet: mu = 1.267e17 m^3/s^2, radius 71,492 km. The escape velocity at a close periapsis of 50,000 km altitude is about 45.7 km/s. A 0.5 km/s burn at that periapsis produces about 2.9 km/s of extra outgoing excess velocity compared to firing the same burn in deep space. The Sun is even stronger (v_esc at 1 AU = 42.1 km/s) but is inaccessible without first decelerating from Earth orbit.

The energy multiplier is DKE_Oberth / DKE_rest = (2v*DV + DV^2) / DV^2 = 1 + 2v/DV. For an ISS-orbit burn (v = 7.66 km/s) with DV = 0.5 km/s: multiplier = 1 + 2*7.66/0.5 = 31.6. This means the burn is 31.6 times more energetically effective than firing the same engine at rest. At very high orbital speeds (e.g., solar escape trajectory near perihelion), multipliers above 100 are achievable.

Yes. Firing retrograde (against the direction of travel) at periapsis is equally amplified. A retrograde burn at periapsis removes more kinetic energy per unit propellant than the same burn far from the body. This technique is used for orbit capture: arriving at Jupiter or Saturn on a hyperbolic trajectory and firing retrograde at periapsis costs far less delta-v than capturing into orbit from a large apoapsis. Cassini used a Saturn orbit insertion burn of about 0.63 km/s at periapsis instead of the several km/s that would be needed from far away.

Hyperbolic excess velocity v_inf is the speed a spacecraft has when it is infinitely far from a body: v_inf = sqrt(v^2 - v_esc^2) for any v greater than escape speed. For a spacecraft arriving from deep space with v_inf_in, the Oberth maneuver converts a burn DV at periapsis into an outgoing v_inf_out = sqrt((sqrt(v_inf_in^2 + v_esc^2) + DV)^2 - v_esc^2), which is always greater than v_inf_in + DV when v_esc > 0. The Oberth gain quantifies this extra velocity.

Lower periapsis means higher escape velocity and higher periapsis speed, which amplifies the Oberth effect. For Earth with a 0 km altitude (surface, theoretical): v_esc = 11.18 km/s. At 200 km altitude: v_esc = 11.02 km/s. At 2000 km altitude: v_esc = 9.96 km/s. Every 100 km increase in periapsis altitude reduces v_esc by about 0.05 to 0.09 km/s and reduces the Oberth gain accordingly. For inner solar system flybys, keeping periapsis as low as planetary protection and trajectory constraints allow maximises the Oberth benefit.

A solar Oberth maneuver is a proposed deep-space propulsion concept: send a spacecraft on a highly elliptical trajectory with perihelion very close to the Sun (0.1 to 0.3 AU), then fire a large burn at perihelion where solar escape velocity is 100 to 200 km/s. The Oberth amplification at that speed makes even modest burns equivalent to enormous velocity changes in deep space. Studies suggest a nuclear thermal burn of 2 to 4 km/s at 3 solar radii perihelion could accelerate a probe to 20 AU/year, reaching interstellar distances in decades rather than centuries.

The Oberth effect is universal: it applies to any mass. The kinetic energy gained per unit mass is DKE/m = v*DV + DV^2/2, independent of the spacecraft mass. A heavier spacecraft gains proportionally more total kinetic energy from the same DV because KE = (1/2)*m*v^2. However, propellant mass for the burn scales with spacecraft mass (via the rocket equation), so the efficiency benefit per kilogram of propellant is what matters practically, and that is always 1 + 2v/DV times better than firing the same Isp engine at rest.

Use the Powered Flyby mode: select the central body (e.g. Jupiter for outer-planet missions), enter the periapsis altitude (minimum safe distance above the planet), the incoming excess velocity from your trajectory, and the planned burn delta-V. The calculator shows the outgoing excess velocity and the Oberth gain compared to firing the same burn in deep space. Use the Energy Gain mode to quickly estimate how much more energetically effective a given burn is at your current orbital speed versus firing from rest, using just orbital velocity and burn DV as inputs.

Virtually all deep-space missions exploit the Oberth effect implicitly. Earth departure burns for Mars missions are fired at perigee (lowest point) of the parking orbit to maximise the benefit. Cassini's Saturn orbit insertion burn was fired at periapsis to minimise the delta-v needed for capture. The New Horizons mission used a Jupiter gravity assist in 2007 to add heliocentric speed via the gravitational Oberth mechanism. The Parker Solar Probe uses repeated Venus gravity assists to lower its solar perihelion, eventually achieving the highest perihelion speed ever recorded and exploiting the solar Oberth effect passively.

A gravity assist uses the relative motion between a planet and the spacecraft to change the spacecraft's heliocentric speed without any propellant burn. The Oberth effect is about making a propellant burn more efficient by performing it at high speed near a massive body. They can be combined: a spacecraft arrives on a flyby trajectory (gaining heliocentric speed from the gravity assist), then fires its engine at periapsis (gaining extra speed from the Oberth effect on top of the gravity assist). The two effects multiply: a powered Jupiter flyby can add 3 to 5 km/s of heliocentric speed beyond what either mechanism alone provides.