KSP Explained: Part 1 – “Slingshot Orbits”

In my “How KSP made me smarter” post, I talked about “Slingshot Orbits”, also known as gravity assists. For those who haven’t played KSP, or just want to know why these happen, In it’s simplest terms a gravity assist is when a spacecraft uses the gravity of a planet or moon to increase it’s own velocity. They are a relatively simple mechanic to put into practice once you understand how they work, but the hard part is being able to get your head around the fact that you’ll have to picture where something is going instead of where it was going.

To put this into context, one of the main space projects that has used gravity assists was the Voyager missions that NASA launched in the ’70s. Voyager 2 used many gravity assists from different planets to slingshot itself out beyond our solar system. If you wanted to do this in KSP, you’d either need some cheat codes/bugged parts, or a hell of a lot of fuel and time. Using this mechanic you can get spacecraft a lot further than the delta-v that they can produce, would get you. It all revolves around the fact that orbiting is actually just falling* (each of these asterisks is a topic I’ll later cover). To orbit, you have to be travelling fast enough for you to be falling towards a planet, but miss it entirely. If you were to be travelling towards a planet’s sphere of influence*, no matter what speed you are travelling at, at the same distance from the planet, you will feel the same gravitational pull. This means that there is a certain velocity a craft will have where it will enter the planet’s SoI, but continue on an escape trajectory back out of the SoI.

What gravity assists count on, is using that gravitational pull to increase the velocity of a craft.

Here’s where it starts to get a bit maths-y. If we start in two dimensions with a planet moving to the left from our view point. If a spacecraft is travelling in the complete opposite direction to the planet, but is narrowly avoiding crashing into the planet.

Let’s call the speed of travel for the spacecraft V, and the speed of travel for the planet U. The planet will move at a constant of U whether the spacecraft is in it’s sphere of influence or not. Until it reaches the planets SoI, the craft moves at a constant of V. When the spacecraft flies close to the planet on it’s trajectory, it will be travelling at the speed V+U in relation to the planet, which is still travelling at U. By the time the spacecraft has escaped the orbit of the planet, it is still travelling at the speed V+U but also is now travelling in the complete opposite direction to how it was before, in that it is now travelling in the same direction as the planet. This means that we will now see the spacecraft travelling at the speed U+(U+V), or 2U+V.

Obviously this is an over simplified way of explaining the problem, but it does give us a reason as to why gravitational assists work. It also means that we can explain how inverting the process will slow us down, rather than speed us up.

If the space craft was travelling in the same direction as the planet, when it began to orbit it would decrease in speed, as the spacecraft would be travelling at V-U. This also carries over to when the spacecraft has left the orbit of the planet, as it’s speed will be V-2U.

You can use gravity assists to either speed up or slow down your velocity, but no matter which you choose, for it to work you will end up travelling in another direction to how you were before the assist. Keep this in mind.

Okay, lesson over.