eypandabear

From my current career: Ion Maiden (1st ion powered satellite) Adam (1, 2, X..., name of my Eve probes. Ba dum tsss.)

This is correct. More precisely, the relative amount of kinetic energy *imparted on the rocket* is higher. The chemical energy of the fuel is converted into kinetic energy, and this energy is distributed between the rocket and the exhaust. For example, let's take a rocket that is not moving relative to us. The rocket engine is fired for just a split second, resulting in a very small delta_v. The rocket gains the kinetic energy (1/2) m delta_v^2, neglecting the lost mass of the propellant, delta_m. The propellant gains the energy (1/2) delta_m w^2, where w is the exhaust velocity. Now let's do the same burn, but with the rocket already moving at v=v_0. The rocket gains (1/2) m [(v_0 + delta_v)^2 - v_0^2]. The propellant gains (1/2) delta_m [(v_0 - w)^2 - v_0^2] = (1/2) delta_m [w * (w - 2 v_0)]. But.. wait, why? Because, prior to the burn, the propellant was already moving together with the rocket. Because it is expelled backwards, it needs to first be decelerated to zero before it can be accelerated again in the direction of the thrust. Therefore the energy that it gets is less than it was in the case of v_0 = 0. You cannot really see from the above equations that this "missing" energy is exactly the same amount as that which the rocket gets more because I have neglected the transfer of mass, but it gives you an idea of what is happening. An interesting thing happens if the rocket's initial velocity v_0 is more than twice as high as the exhaust velocity w. In this case, the propellant energy gain becomes negative! The rocket actually gains additional energy from the fuel! This is because, seen from the outsider observer relative to which the rocket is moving, the fuel is now moving in the same direction as the rocket, but slowed down. Like I said, the above calculation is an approximation, but the gist is that a slow rocket has to put energy into the fuel to push it backwards, whereas a fast rocket steals stored kinetic energy from the fuel by pushing itself away from it (so to speak).

Hey guys, longtime lurker making an account here to contribute to this discussion. I believe there are two things in particular that confuse many people about the Oberth effect: The Oberth effect, like many things in physics, can be understood and explained in multiple equivalent ways. The Oberth effect is often confounded with gravity assists, which also tend to exploit the Oberth effect. I am not going to say anything here that hasn't been said before by others in this thread, I am just trying to distill the facts to help those who still struggle understand this concept. The important thing to see is that the Oberth effect is just the astronautical term for something that, on the face of it, has nothing to do with orbital mechanics. For any particle with mass m and velocity v, the non-relativistic kinetic energy can be given as E = (1/2) m v^2. As the particle is accelerated, the kinetic energy increases at a rate of dE/dv = mv = p, which is the momentum of the particle. Accelerating your car from 100 km/h to 120 km/h takes 22% more energy than from 80 to 100. The same is true for rockets. From a kinematic point of view, this is everything you need to know to understand the Oberth effect. Note that this has nothing to do with orbital mechanics, gravitational drag or what have you. Another way to look at it is that energy is a force F applied along a distance s. For a fixed burn time t and force (thrust) F, the distance s along which the force is applied is longer if the craft moves faster, which increases the energy. This is the exact same physical effect, just explained differently. Hermann Oberth famously recognised that this simple kinematic fact had implications for rocket-propelled spaceships (sci-fi in his day), hence the name. A spacecraft in an elliptical orbit moves fastest at periapsis, which means that the same delta-v applied at periapsis results in a higher increase in kinetic energy than if the burn had been performed at any other point. Kinetic energy at one point in the orbit corresponds to potential energy, i.e. altitude, at the opposite side, hence why burning at periapsis increases your apoapsis. This is also true vice versa, i.e. burning at apoapsis increases your periapsis. However, the potential energy increase in the first case is higher - this, in a nutshell, is the Oberth effect. At a more "microscopic" level, the higher kinetic energy can be described by the rocket exhaust obtaining less of the total energy, leaving more to the rocket. But this isn't necessary to understand the Oberth effect. All you need to know is that rocket engines apply velocity-independent thrust to the spacecraft.