The Strange Physics Behind the Oberth Effect

I have a tiny spring-powered rocket here that can remotely launch this ball. So, here's the question: which launch gives the rocket more kinetic energy? Firing it while it's standing still or already moving? We all know that motion is relative. Moving at a constant velocity should be the same as not moving at all. But, does that still hold true for rockets? Because this little spring launcher stores only about 300 mJ of energy. But, somehow by launching it while it's already moving, I managed to get over 400 mJ of kinetic energy increase from it. That should be impossible. Nobody tell ElectroBOOM about this because it sure feels like I just created free energy. But, what we're seeing here is actually a real physics effect called the Oberth effect, one of the most powerful effects in all of space travel. — In this video, I'm going to show you how this works and where this free energy actually comes from. But, before we continue, I want to thank the sponsor for this video, Outskill. Have you noticed how Claude is suddenly everywhere right now? And naturally, everyone online keeps saying you need to learn AI. — But, almost nobody actually teaches you how to use these tools in a practical way. That's why Outskill is hosting what they call the world's first Claude-a-thon, happening live this weekend from 10:00 a. m. to 7:00 p. m. Eastern time. It's a two-day deep dive into Claude and more than 10 other AI tools. — And right now, they're giving away 1,000 free seats for a limited time. More than 10 million people worldwide have already attended their trainings, and they're rated 4. 9 out of five on Trustpilot. During the workshop, you'll learn how to do deep research with Claude, build your own dashboards and artifacts, create presentations with AI, connect tools together to automate workflows, and build custom GPTs and agents, — and even generate videos and visuals with AI. They even show you things like setting up Claude connectors to automate tasks like job searches and other repetitive work. And if you sign up now, you'll also get bonuses like 50 secret Claude codes to make Claude way more powerful. And you'll also get an AI prompt library and a personalized AI toolkit builder completely free. The training is also mentored by leaders from companies like Microsoft, Google, Amazon, and Nvidia. So, if you want to check it out, use the link in the description or scan the QR code on screen and join the WhatsApp community before the free seats run out. And thanks again to Outskill for sponsoring this video. Now, let's get back to our experiment. Now, in order to demonstrate this effect, I needed a very controlled rocket where we can carefully account for the energy input and make repeatable launches. So, instead of using a chemical rocket, I built a spring-loaded rocket. This is a ball launcher with a spring inside it. When I press the ball in it, it compresses the spring. Then, I can remotely trigger the release using this actuator right here. Now, based on the exit velocity of the ball, I measured that the spring stores about 300 mJ of mechanical energy. So, this is basically a tiny rocket with a known amount of stored energy, with the ball being its exhaust. To make it move like a rocket in space, I mounted it on this long swing here. Near the bottom of the swing, the motion is almost perfectly linear and has very little acceleration over a short time interval. So, it approximates a frictionless motion in space. Now, first, let's launch it from rest and see what it looks like. When I launch it, the rocket ends up moving about 0. 4 m/s. Now, here's something very important about rockets you have to understand. They should gain the same change in velocity no matter how fast they're already moving. So, whether the rocket's standing still or already flying through space, launching the ball should still increase the rocket's speed by the same amount. So, let's test if that's true. If I first get the rocket moving about 2. 5 m/s and then launch the ball, sure enough, the rocket still gains about 0. 4 m/s and ends up moving around 2. 9 m/s. So, everything checks out so far. The rocket got the same change in velocity both times, but now things get weird. Let's calculate the kinetic energy gained by the rocket in both cases. In the first launch, the rocket went from 0 to 0. 4 m/s. That corresponds to a gain of only about 31 mJ of kinetic energy. But in the second launch, the rocket went from 2. 5 to 2. 9 m/s. That corresponds to a gain of about 425 mJ of kinetic energy. That's a huge increase. Now, at this point, you might think that this is easy to explain with the kinetic energy equation. Kinetic energy equals 1/2 * the mass * velocity squared. So, as velocity increases linearly, kinetic energy increases much faster. But that explanation actually doesn't solve the mystery. It explains why the numbers come out larger, but it doesn't explain where the extra energy actually comes from. Remember, this rocket only stored about 300 mJ of energy in the spring. So, how did the moving rocket gain 425 mJ of kinetic energy? Well, to answer that, we need to account for the entire system. Up to this point, we've completely ignored the ball. The ball is moving

too, and it also has kinetic energy. So, let's track the energy of the ball as well. In the standing still rocket case, the ball goes from 0 to 3. 5 m/s. That corresponds to a gain of about 276 mJ of kinetic energy. Now things make sense again. So, the rocket gained 31 mJ, and the ball gained 276 mJ. Together, that adds up to about 307 mJ, which is almost exactly what you'd expect from the energy stored in the spring. So, no energy was magically created. Some of the spring energy went into moving the rocket, and some ball. But now let's look at the moving rocket case. We already showed that the rocket gained about 425 mJ of kinetic energy. But now let's track the ball. Before the launch, the ball was already moving along with the rocket 2. 5 m/s. After launch, the ball slowed down to only about 1 m/s. That means that the ball actually lost kinetic energy. In fact, the ball lost about 112 mJ of kinetic energy. So, I've been throwing a lot of numbers around, but let's take a step back and see how this all comes together. If I make a bar chart of the total energy available in the system when the rocket was standing still, then we see that before the launch, all the energy was stored in the spring. But then after the launch, the energy was divided between the ball and the rocket. You can see that only 10% of the energy went to the rocket, the rest went to the ball. But now let's look at the same bar graph, but for when the rocket was moving. You can see that before it launched, we have the energy of the moving rocket in gray here, but we have stored energy in the kinetic energy of the ball and stored energy in the spring. Then after the launch, you can see that we gained all the energy from the spring and also almost all of the kinetic energy of the ball. So, we had a 30% increase in kinetic energy of the rocket when it was moving compared to only 10% increase when it was still. Now, I don't think you understand how useful this is. There's no limit to the energy increase we get from this. So, the change in velocity for a given rocket burn is fixed. That means that if you want more energy, you just need to be moving faster. And the faster you're moving, the more energy you get out of it. Move 10 times faster and you get 10 times more energy for a given rocket burn. And this becomes incredibly important in space. Because in space, it's not necessarily your speed that matters most, it's your total energy. Your total energy is split between kinetic energy from how fast you're moving and gravitational potential energy from how far away you are from a planet or star. So, if you want to gain the most total energy possible, you don't want to fire your rockets when you're moving slowly far away from the planet. You want to fire them when you're moving the fastest. In an orbit, this point is called the periapsis. I can show what I mean in this Kerbal Space Program software. If I do a rocket burn near periapsis, watch how the orbit changes very quickly. And I can easily keep my rocket on until my orbit has enough energy to escape the planet. But if I do the same burn at the slowest point of the orbit, then my orbit doesn't change nearly as much when I burn the rockets, — meaning I can't get as far away from the planet using the same amount of rocket fuel. The same thing also works in reverse. If you want to slow down as much as possible, you also want to fire your rockets when you're moving the fastest at periapsis. That gives you the largest decrease in energy for the same amount of fuel. Now, the Oberth effect may even be one of the keys to eventually traveling to other stars. — Imagine starting far away from the Sun. Out there, the spacecraft and its fuel have enormous gravitational potential energy because of their distance from the Sun. — If we fall toward the Sun, that gravitational potential energy gets converted into kinetic energy, causing us to move incredibly fast near the Sun. Then, if we fire our rockets while moving at those extreme speeds, the Oberth effect allows the same rocket burn to produce an enormous increase in energy. So, on a large scale, you can picture the Oberth effect as using gravity to build up huge amounts of kinetic energy, then transferring more of that energy to the spacecraft while leaving the exhaust moving slower and deeper in the Sun's gravity well. And thanks for watching another episode of The Action Lab. I hope you learned something. If you haven't subscribed to my channel yet, remember to hit that subscribe button, and we'll see you next time.