[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 Transylvanian Saxon physicist and a founder of modern rocketry Hermann Oberth, who first described them in 1927.
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.
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]: 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.
The work results in a change in kinetic energy Differentiating with respect to time, we obtain or where
Thus it can be readily seen that the rate of gain of specific energy of every part of the rocket is proportional to speed and, given this, the equation can be integrated (numerically or otherwise) to calculate the overall increase in specific energy of the rocket.
Integrating the above energy equation is often unnecessary if the burn duration is short.
) by When the vehicle has left the gravity well, it is traveling at a speed For the case where the added impulse Δv is small compared to escape velocity, the 1 can be ignored, and the effective Δv of the impulsive burn can be seen to be multiplied by a factor of simply and one gets Similar effects happen in closed and hyperbolic orbits.
If the vehicle travels at velocity v at the start of a burn that changes the velocity by Δv, then the change in specific orbital energy (SOE) due to the new orbit is Once the spacecraft is far from the planet again, the SOE is entirely kinetic, since gravitational potential energy approaches zero.
The effect becomes more pronounced the closer to the central body, or more generally, the deeper in the gravitational field potential in which the burn occurs, since the velocity is higher there.
So if a spacecraft is on a parabolic flyby of Jupiter with a periapsis velocity of 50 km/s and performs a 5 km/s burn, it turns out that the final velocity change at great distance is 22.9 km/s, giving a multiplication of the burn by 4.58 times.
[2]: 204 Contrast this to the situation of static firing, where the speed of the engine is fixed at zero.
[5] The Oberth effect can therefore partly make up for what is extremely low efficiency early in the rocket's flight when it is moving only slowly.