The Nonlinear Library LW - An Actually Intuitive Explanation of the Oberth Effect by Isaac King
Jan 12, 2024
10:34
Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: An Actually Intuitive Explanation of the Oberth Effect, published by Isaac King on January 12, 2024 on LessWrong.
This is a linkpost for An Actually Intuitive Explanation of the Oberth Effect.
Like anyone with a passing interest in
Kerbal Space Program physics and spaceflight, I eventually came across the Oberth Effect. It's a very important effect, crucial to designing efficient trajectories for any rocket ship. And yet, I couldn't understand it.
Wikipedia's explanation focuses on how kinetic energy is proportional to the square of the speed, and therefore more energy is gained from a change in speed at a higher speed. I'm sure this is true, but it's not particularly helpful; simply memorizing formulae is not what leads to understanding of a phenomenon. You have to know what the numbers mean, how they correspond to the actual atoms moving around in the real universe.
This explanation was particularly galling as it seemed to violate relativity; how could a rocket's behavior change depending on its speed? What does that even mean; its speed relative to what? Whether a rocket is traveling at 1 m/s or 10000000 m/s relative to the Earth, the people on board the rocket should observe the exact same behavior when they fire their engine, right?
So I turned to the internet; Stack Overflow, Quora, Reddit, random physicists' blogs. But they all had the same problem. Every single resource I could find would "explain" the effect with a bunch of math, either focusing on the quadratic nature of kinetic energy, or some even more confusing derivation in terms of work.
A few at least tried to link the math up to the real world. Accelerating the rocket stores kinetic energy in the propellant, and this energy is then "reclaimed" when it's burned, leading to more energy coming out of the propellant at higher speeds. But this seemed unphysical; kinetic energy is not a property of the propellant itself, it depends on the reference frame of the observer! So this explanation still didn't provide me with an intuition for why it worked this way, and still seemed to violate relativity.
It took me years to find someone who could explain it to me in better terms.
Asymmetric gravitational effects
Say your spacecraft starts 1 AU away from a planet, on an inertial trajectory that will bring it close to the planet but not hit it. It takes a year to reach periapsis going faster and faster the whole way. Then it takes another year to reach 1 AU again, slowing down the whole time.
Two things to note here: The coordinate acceleration experienced by the spacecraft (relative to the planet) is higher the closer it gets, because that's where gravity is strongest. Way out at 1AU, the gravitational field is very weak, and there's barely any effect on the ship. Secondly, note that the trajectory is symmetric, because orbital mechanics is time-reversible. That's how we know that if it takes 1 year to fall in it will also take 1 year to get back out, and you'll be traveling at the same speed as you were at the beginning.
Now imagine that you burn prograde at periapsis. Now you'll be traveling faster as you leave than you were as you came in. This means that gravity has less time to act on you on the way out than it did on the way in. Of course the gravitational field extends all the way out to 1 AU, but if we take just a subregion of it, like the region within which the acceleration is at least 1 m/s2, you'll spend less time subject to that level of acceleration.
So the Oberth effect is just a consequence of you maximizing the amount of time gravity works on you in the desired direction, and minimizing it in the other direction. (And of course you'd get the inverse effect if you burned retrograde; a more efficient way to slow down.)
This has nothing to do with propellant. Maybe instead of thrusters, there's a gi...
This is a linkpost for An Actually Intuitive Explanation of the Oberth Effect.
Like anyone with a passing interest in
Kerbal Space Program physics and spaceflight, I eventually came across the Oberth Effect. It's a very important effect, crucial to designing efficient trajectories for any rocket ship. And yet, I couldn't understand it.
Wikipedia's explanation focuses on how kinetic energy is proportional to the square of the speed, and therefore more energy is gained from a change in speed at a higher speed. I'm sure this is true, but it's not particularly helpful; simply memorizing formulae is not what leads to understanding of a phenomenon. You have to know what the numbers mean, how they correspond to the actual atoms moving around in the real universe.
This explanation was particularly galling as it seemed to violate relativity; how could a rocket's behavior change depending on its speed? What does that even mean; its speed relative to what? Whether a rocket is traveling at 1 m/s or 10000000 m/s relative to the Earth, the people on board the rocket should observe the exact same behavior when they fire their engine, right?
So I turned to the internet; Stack Overflow, Quora, Reddit, random physicists' blogs. But they all had the same problem. Every single resource I could find would "explain" the effect with a bunch of math, either focusing on the quadratic nature of kinetic energy, or some even more confusing derivation in terms of work.
A few at least tried to link the math up to the real world. Accelerating the rocket stores kinetic energy in the propellant, and this energy is then "reclaimed" when it's burned, leading to more energy coming out of the propellant at higher speeds. But this seemed unphysical; kinetic energy is not a property of the propellant itself, it depends on the reference frame of the observer! So this explanation still didn't provide me with an intuition for why it worked this way, and still seemed to violate relativity.
It took me years to find someone who could explain it to me in better terms.
Asymmetric gravitational effects
Say your spacecraft starts 1 AU away from a planet, on an inertial trajectory that will bring it close to the planet but not hit it. It takes a year to reach periapsis going faster and faster the whole way. Then it takes another year to reach 1 AU again, slowing down the whole time.
Two things to note here: The coordinate acceleration experienced by the spacecraft (relative to the planet) is higher the closer it gets, because that's where gravity is strongest. Way out at 1AU, the gravitational field is very weak, and there's barely any effect on the ship. Secondly, note that the trajectory is symmetric, because orbital mechanics is time-reversible. That's how we know that if it takes 1 year to fall in it will also take 1 year to get back out, and you'll be traveling at the same speed as you were at the beginning.
Now imagine that you burn prograde at periapsis. Now you'll be traveling faster as you leave than you were as you came in. This means that gravity has less time to act on you on the way out than it did on the way in. Of course the gravitational field extends all the way out to 1 AU, but if we take just a subregion of it, like the region within which the acceleration is at least 1 m/s2, you'll spend less time subject to that level of acceleration.
So the Oberth effect is just a consequence of you maximizing the amount of time gravity works on you in the desired direction, and minimizing it in the other direction. (And of course you'd get the inverse effect if you burned retrograde; a more efficient way to slow down.)
This has nothing to do with propellant. Maybe instead of thrusters, there's a gi...