What can the KSP game actually teach about spaceflight and orbital mechanics, and what are its limitations?

I have seen at least several different users mention that they've found Kerbal Space Program helpful to understand issues of spaceflight and orbital mechanics.

According to Wikipedia:

While the game is not a perfect simulation of reality, it has been praised for its accurate orbital mechanics; all objects in the game except the celestial bodies are simulated using Newtonian dynamics. For instance, rocket thrust is applied to a vehicle's frame based on the placement of force-generating elements, and joints between parts have limited strength, allowing vehicles to be torn apart by excessive or misdirected forces.

The game simulates trajectories and orbits using patched conic approximation instead of a full n-body simulation; thus, it does not support Lagrange points, perturbations, Lissajous orbits, halo orbits or tidal forces. According to the developers, implementing full n-body physics would require the entire physics engine to be rewritten.

But that last bit is only because it was written with simplifying mathematical approximations in the first place, and just changing to 3-body Newtonian physics instead of patched conics would then allow "Lagrange points, perturbations, Lissajous orbits, (and) halo orbits..."; there would not be any need to invoke the extreme-sounding n-body limit. Within that framework, tidal forces would be straightforward to include as well.

disclaimer: KSP is a commercial product and I don't meant to advertise it by asking about it; personally I'd recommend starting with what you can get for free here in Stack Exchange, in books, on line, at various NASA, university, and private blog sites. But since it has been mentioned several times in this site I decide to learn more.

I am not sure if KSP teaches you any of the actual mathematics of spaceflight (e.g. equations) or if it just shows you what happens and gives you a false sense of "understanding" because after a while you start to know what's going to happen on the KSP screen, which is the whole idea behind getting better at a video game.

I'm interested in answers that explain (rather than just listing) how one can learn about spaceflight and orbital mechanics by paying money for and then playing this game. I am biased and highly skeptical that this game teaches you anything more than how to keep playing the game and posting comments here telling people to buy it; can you demonstrate otherwise?

• No, the accepted answer is still current. The accuracy limitation of the game are both technical (physics calculations is CPU intensive), and by gameplay design (we need simplifications to make the game playable; you don't have the time ressources of NASA to micro manage every space assets). – Antzi Aug 30 '17 at 4:58
• What's complicated is NOT the orbital mechanics as implemented into KSP, but more The drag, thrust, acceleration, bending, heating, and will my ship hold together equations. Most games tracks hundreds of items individually (O(n) complexity)) while KSP tracks hundreds of items in interaction within each other (O(n^2)) complexity – Antzi Aug 30 '17 at 5:27
• Different people have differing learning styles. In broad, one may learn by reading, listening, watching/observing, and doing. Think back to riding a bike, or tying your shoelaces. Reading doesn't really make it clear, but watching and doing are probably the optimal for many people. KSP lets those who learn by doing, do, and it has pretty explosions for when it "doesn't" – Criggie Aug 30 '17 at 7:44
• @uhoh KSP is mostly CPU intensive when it has to calculate the physics relating the flight in atmosphere, you only have a max physics warp factor of 4 in this area, but this may make the calculations too unstable, and cause problems relating to RUD (Rapid Unplanned Disassembly). Once you are in space, you can access a timewarp factor up to 100000, or even higher – Ferrybig Aug 30 '17 at 8:43
• @uhoh Another reason patched conic wins out is that it allows forward plotting. If travelling to an outer plant, you (most likely) want to make an escape burn from a low Kerbin orbit. The game allows you to position a planned maneuvre node and tweak its parameters, allowing you to plot an encounter with a distant moon hundreds of days in the future, and adjust that encounter in real time. Your future orbital path is shown an updates instantly as you make it, and this isn't possible with full n-body simulation. – Slow Dog Aug 30 '17 at 8:55

In my former job I was writing educational software.

In short, it's exactly what you described: we offered a paid version of what you could get for free by looking out on the internet, going to class, going to the library, ...

And yet, I'm still incredibly proud of it, knowing I made a difference.

What is the difference between well written software and a book?

It's all about pedagogy. Not only did our apps offer knowledge, they did so in a fun way. This is not about making the knowledge available, it's about making it desirable. With our apps, the kids not only learned (exactly the same content as they would've with books), but they actually wanted to!

Sure, maybe knowledge is enough of a motivation for you to learn about something, and thus you don't actually need this kind of software, but for many kids they need just a little bit more to get interested into learning, doing exercises, ...

Let me explain with some real life KSP examples:

• KSP can be used as a simulator.

Got an interesting idea about creating an orbital refueling station around the moon? Try it out and see the difference!

Want to try fuel saving by using a gravitational assist? Go ahead.

Sure you could take a sheet of paper and do the computations, but seeing it live on your screen, with the rocket and station you build and put in orbit yourself is a whole different thing.

• It's a driving force to make you research things you wouldn't have searched otherwise.

How to calculate if my ship has enough fuel to reach Saturn?
=> Learn about ISPs, rocket equation, ...

What is the optimal trajectory to go to orbit?
=> Learn about gravity drag, atmospheric drag, ...

This game builds up your interest in space. This is why they got a partnership with NASA and built a part of the game around it.

• It allows you to experience things

Some of the concepts of orbital mechanics are hard.

Sure you can read 10 times about why you need to decelerate in orbit to overtake another spaceship.

Sure you can learn that rendezvous is not aiming for where the other spaceship is, but where it will be.

• It makes you ponder engineering challenges

Are 3 landing legs better than 4?

Is my CG (center of gravity) too high? Is it aligned with my vector of thrust?

Should my aerodynamic surfaces go on the top or bottom?

Should I put this booster further apart to facilitate separation, or will the induced stability issues, pilot induced oscillation destroy/slow down my rocket?

KSP lets you experience all this, making it much easier to understand and internalise rather than just reading about it.

Let me conclude with a quote from a NASA engineer, about the failed rendezvous of Gemini 4:

There is a good explanation for what went wrong with rendezvous. The crew, like everyone else at MSC, "just didn't understand or reason out the orbital mechanics involved[...].

Yes that's right. Kids playing KSP now have a better understanding of orbital mechanics than NASA engineers and astronauts from 1965.

• Obligatory XKCD – DarkDust Aug 30 '17 at 12:49
• "Kids playing KSP now have a better understanding of orbital mechanics than NASA engineers and astronauts from 1965." This is probbly true, and absolutely amazing when you think about it. – Polygnome Aug 30 '17 at 20:45
• @uhoh Aldrins thesis about orbital rendezvous - which turned out to be an important cornerstone for NASA - is from 1963, just two years prior. So I think its at least probably that not everyone was familiar with it. I think they were knowledgeable about orbital mechanics, but the quote is about rendezvous - which can be very counter-intuitive. Aldrins thesis is about exactly that factor ;) I think its more that they didn't have the proper procedures, not that they couldn't figure it out in theory. They would probably have absolutely loved a simulator like KSP just to learn procedures ;) – Polygnome Aug 31 '17 at 15:24
• tl;dr version In the 60s NASA engineers could do ALL the math. But without the intuition of seeing how that math actually applies to real life, the math was useless to dock. KSP is phenomenal at providing this intuition. – Shane Sep 1 '17 at 19:58
• "It makes you ponder engineering challenges" Usually immediately before trying to land on the Mun. – Matt Lacey Sep 5 '17 at 0:33

In several press conferences, employees of NASA or private space firms have been asked if they played KSP, and some answered with "Yes".

NASA used patched conics to find candidate orbits for Apollo back in the days.

With that being said, KSP strikes the balance between accuracy and simplicity. Patched conics give a good idea how space works, without being so overly complicated that it's no longer fun to deal with. And that means it makes people learn stuff they otherwise wouldn't. The mantra "Space isn't high up, it's about going sideways fast" can be repeated thousands of times, and people won't get it. But when they actually try it out and see for themselves why it is how it is, they suddenly understand. When they fall back onto the planet after launching straight up, and then finally learn to pitch over and do a gravity turn to achieve orbit.

The fact that orbits are always influenced at the opposite side of the burn. That deceleration (retrograde burns) lowers the orbit and so forth. What radial burns do, what normal burns do, what inclination is and why it is important, how ascending and descending nodes work and why they are important, why rendezvous takes so long and what you need to do to actually make it. All those things are taught by KSP and make spaceflight accessible to people that otherwise wouldn't "get" it.

The Mun (the equivalent to the Moon in KSP) is in an equatorial orbit to make it easier for new players to get there (no launch window, no inclination change), but those things can be used to get to the second, much smaller moon, Minmus.

The concept of Hohmann transfers, bi-elliptical transfers and other transfers is explained. The difference between fuel-efficiency and time efficiency can be learned by KSP. Ejection angles and launch windows for interplanetary missions can be learned with KSP. Gravity assists work, and can be very useful. That's a concept a lot of people struggle with, but in KSP you can try it out and see how that works.

Re-entry heating exists and matters somewhat, depending on the settings. You learn that you should neither plow too fast too deep into the atmosphere neither too low so that you skip it. The concept of re-entry is hard to grasp for some people, but with KSP, you can easily see why it works how it works and what's important about it.

The rocket equation, and especially the tyranny of the rocket equation, is important in KSP. You learn good engineering techniques. You learn that you can't bring what you want, that rockets grow exponentially. The concept of staging and why it is important comes naturally with KSP. Some basic aerodynamics — how CoM and CoL work, how drag affects the path of your rocket — are explained.

What Isp is and does is explained. That Isp at sea level and Isp in vacuum are different things and are important is explained. That you can steer a rocket with gimbaling engines, reaction wheels or RCS is explained, and that some of those are better in some situations then others (RCS for ascent? Not the best idea!).

In short: KSP teaches a lot, while using physics and orbital mechanics that are not so overly complicated that it gets too frustrating. It stays in the area that most people can still grasp.

And for those who want the extra challenge, the game can be modded. N-Body physics are provided by a mod called "Principia", and the star system can be transformed to the Real Solar System by the mod of the same name (RSS). Historic engines and other parts are provided by the mod called "Realism Overhaul" (RO). Signal delay is provided by RemoteTech, life support by one of the various LS mods (Kerbalism, USI-LS etc).

So apart from the base experience that already teaches lots of the concepts of spaceflight (I forgot about heating and radiators in my list above) while maintaining accessible and approachable (if you don't want to learn too much, trial and error will get you somewhat far), the modding community has created a lot of mods that bring even more important concepts to the player (FAR has a more realistic aerodynamic simulation, for example).

And the game lets you deal with it how you want. Don't want to learn about launch azimuth? Fine, don't. The parts have enough delta-v so that you can be sloppy sometimes. Want to learn? Good! You can learn about it, and then apply what you have learned and see it actually work. See your orbit end up exactly what you wanted (or not). The community has created lots of maths tools and helpers for that as well.

Finally, Squad (the developer) already has/had a deal with NASA. NASA helped them make some parts, the so called "NASA parts" that are still in the game today (I believe they were originally for the "Asteroid day" official mod, but are now in the base game).

So yeah, it's not a 100% accurate simulator. But its close enough to teach the concepts, and simple enough so that its accessible for a very wide audience. In that regard, I think it offers a great example for how educational games should work in the future. Because it's actually fun to play and makes stuff easy to understand.

Some random things I haven't mentioned: Aerodynamics (Rudder, Elevons, Trim, placement of wings, CoM, CoL and concept of lift for planes), how an FDAI (called Navball in KSP) works, reference frames (the FDAI has "surface" mode [rotating reference frame of the body] and "orbital" reference frame [non-rotating frame of the body], as well as "target" frame [frame centered around the own vessel]), connectivity of antennas and signal strength (inverse square law), solar power output (again, inverse square law, you learn why solar panels don't work well for outer planets), you learn about the pendulum rocket fallacy and a lot more things.

On accuracy and computing power:

Being a game, the simulation has a hard realtime requirement. Patched conics are not only far easier to understand for a wide audience, but they are also much faster. Patched conics have an analytical solution. That means it's cheap to calculate positions. Furthermore, finding closest approach / intercepts is cheap, which is needed for maneuver planning. The added benefit is that it makes finding a rendezvous something accessible for a wide audience. It's not fun to try to find a close approach for two vessels when you need a simulator to make that decision. The base concepts apply whether you use patched conics or not. A more realistic model does not add much educational value, but a lot of frustrations for players — who mostly have no background whatsoever in orbital mechanics. Furthermore, the game needs to be able to simulate literally hundreds of vessels at the same time — something that is only possible with patched conics in real time. The aforementioned mod for n-body physics quickly breaks down after collisions of vessels that generate lots of debris. Furthermore, it doesn't matter whether a vessel is in atmosphere or not from a physics point of view. The physics engine still needs to simulate all parts and all joints between all parts to figure out how the vessel behaves, especially under thrust. Those hard realtime requirements put a hard cap on what you can realistically achieve on the average home computer. Again, it's a game, it needs quick results, it's not an academic simulation. It's close enough to teach the concepts. It doesn't claim to have 100% scientific accuracy.

To the point raised in other comments, that it uses "17th century maths". Sure it does. But so do a lot of people. You don't start teaching people physics by jumping into quantum mechanics. You don't even start with GR/SR. You start with classical, Newtonian physics. Those are still around, and still valid as ever, and still have their applications. Just because we nowadays know that they aren't accurate on certain scales doesn't mean those physics are useless. Again, KSP has to strike a balance between accuracy and simplicity. Be accurate enough to actually use the real concepts of spaceflight, while being simple enough to appeal to a wide audience.

Have you ever been at a planetarium? When they show the orbits of planets in the solar system, they use patched conics. Because that's enough to give people an idea how that stuff works, without being too over-the-top. Have you ever looked at orbits plotted in a Jacobian frame? Those look extremely confusing, while arguably being more "accurate".

• +n! This is a really well thought out and extensive answer, much more than I expected. Thank you very much for taking the time to think this through and explain it! – uhoh Aug 30 '17 at 9:19
• Before I started playing KSP this would've all been gibberish. – Mazura Aug 30 '17 at 9:45
• @uhoh The longer i think about it, the more things come to my mind that KSP explains that I haven't listed here, but I had to make a cut somewhere. – Polygnome Aug 30 '17 at 9:50
• One other thing you can learn from KSP: the pendulum rocket fallacy: gaming.stackexchange.com/questions/220705/… – Ross Ridge Sep 1 '17 at 2:37
• I never understood why rockets start their ascent so slowly until I played KSP. I knew but didn't understand. Same with inclination, you don't realise how big a bastard it is to change inclination until you actually watch your fuel gauge going down towards zero and still being 20 degrees away from your target plane. And with the RO mod a whole new world opens up with ullage, interstage problems, non-restartable engines and the general lack of throttleability. – biziclop Sep 3 '17 at 15:00

In a sense, you're correct; KSP does not teach you any of the math involved in orbital dynamics. But it gives you an incredibly good intuitive sense of how they work. For example, one of the first things you learn is just how much fuel you need to get to orbit. You quickly have to come to grips with the tyranny of the rocket equation if you want to get anywhere at all.

Once you've gotten above the atmosphere, the next thing you learn is where the appropriate burn points are. You need to burn at apogee to raise your perigee. Then, you burn at perigee to circularize your orbit.

After you're in orbit, you then have to tackle all sorts of things, like changing orbital inclination, docking, and gravity assists to other planets.

So no, it doesn't provide you with equations and how to solve them. And yes, the physics engine is off (but can you blame them? It would be quite a task to program a full n-body simulation for a simple video game).

But ask yourself: what does the average person want? Do they want to learn all of the mathematics behind spaceflight? No, they usually don't. And if they do, they don't turn to KSP. But thanks to KSP, people who play it are more familiar with how spacecraft orbits work. It presents something normally complex and out-of-reach in an entertaining and intuitive way. And in the end, KSP isn't meant to teach a student how to calculate whether or not a rocket will crash. It's a game, meant for entertainment. The fact that it also helps you develop an intuitive sense of orbital mechanics is a bonus.

• Don't think about this like a scientist. These people are game designers. Doing the calculations is only a small piece of the whole thing. Besides the physics engine, you also need the graphics, the text, the design, etc. They chose to cut a small corner on the physics engine so that they could incorporate everything else while staying within budget and on schedule. – Phiteros Aug 30 '17 at 4:40
• @uhoh It's that you have n^2 interactions between bodies (okay, really n^2+nm where n are planets and m are rockets), however what really breaks it is timewarping. Patched conics lets them speed up time to 10000000x normal rate or something ridiculous like that, because they can directly calculate an object's position at any future point in its orbit. – user253751 Aug 30 '17 at 6:03
• @uhoh No, it can exactly calculate the position of a body in a Keplerian orbit. Now real life bodies wouldn't be in Keplerian orbits. But in the game all objects are in Keplerian orbits. and therefore the calculation is exact for all objects in the game. And this is actually more accurate than numerical integration which accumulates errors. – user253751 Aug 30 '17 at 6:12
• @uhoh: The main problem with real orbits is that you'd need constant station-keeping. If you develop a fleet of fifty different spacecrafts, satellites and probes, it would soon become unmaintainable, because instead of a dozen employees for maintaining one satellite, you're only one to maintain the whole fleet. With keplerian orbits you can place a satellite in orbit and forget about it. This is a conscious gameplay mechanics choice; a sacrifice of realism to increase playability, just like radius of Kerbin. For your "you should not" - You should not make a game tedious and annoying. – SF. Aug 30 '17 at 8:45
• @OrangeDog: And not just for the current craft position, but for a lot of these ahead in time, as drawing the trajectories (actual and planned, post-maneuver) is an absolutely essential element of the gameplay, replacing all the manual calculations you'd need to perform. – SF. Aug 30 '17 at 10:21

The other 4 answers here do a wonderful job of articulating what I love about KSP, but I'd like to point out one more thing from my perspective as a game designer who has logged over 600 hours in the game.

While much of the game is simplistic relative to the real world, it is accurate enough to be intuitive why things failed. Rocket flipped over during launch? Gotta adjust aerodynamics or try a different launch profile. Got partway to my destination and ran out of fuel? Maybe I should look into more efficient engines or miniaturizing my rocket. Trying to get back to Kerbin from one of its moons, but you're low on fuel? Better make sure to exit the moon's orbit the opposite direction as its motion. Made it back to Kerbin but all my Kerbalnauts died from hitting the side of the mountain? Add more parachutes. KSP is more than the orbital dynamics, it is engineering with rapid iterations on design. Obviously guess-and-check development doesn't work for NASA, but with access to a "Revert to launch" and "Revert to vehicle assembly" buttons always available to you (unless you turn them off or a mod does it for you), learning why things don't work and how to fix them is much easier than just crunching numbers.

The ability to try, fail, attempt to fix the problem and try again in rapid cycles is part of what makes KSP a great learning tool. Once you've been in the game enough, you build a good intuition for how it works in real life, and the mods mentioned in Polygnome's answer can add in those extra levels of realism if you want to up the challenge. While the vanilla game hides most of the numbers from you (total delta V, current ISP, distance above the ground rather than distance above sea level), there are mods that make those accessible too. I personally can't play without Kerbal Engineer showing me some of those. Same goes for launch windows, eyeballing when to do a planetary transfer is hard, but using Kerbal Alarm Clock to calculate it down to the second helps a lot too.

In summary, KSP does a great job of making some of the challenges NASA faces very intuitive, and the ability to iterate rapidly on plane and spacecraft designs makes learning them fun and engaging. If you are the type that wants to dig into the math, optimizing every part of the mission, free mods are easily available to give you that option. If you want it to be much closer to realism, that can be done easily. Other mods give you new solar systems to explore, so you never run out of challenges.

And as an example, here is a YouTube video from a very skilled KSP player explaining how the Oberth Effect and gravity assists are useful to optimize your fuel consumption. Note that this video is old and things have improved greatly since then. Even with the game's simplified understanding of orbital mechanics, they still matter.

You concentrate on the unrealistic points which have to be present in the game and ignore strong realistic points. The Kerbal Space Program is not a perfect spacecraft simulator however it successfully teaches the basics. Most importantly even if it doesn't full N-body simulation it's perfectly capable of simulating Kepler's orbits that give you good first approximation for many spacecraft missions.

Because other answers already emphasized many strong points let me put a personal perspective. Because of my background as a physicist and general interest in the space exploration I knew all the equations and had all the knowledge required long before playing KSP. However when I tried to perform a docking between two vessels it took me one hour of constant trajectory corrections because even with all this knowledge I did a lot of really stupid stuff. Which exactly what was happenning during the first real docking missions. The reason is that even when you have the knowledge without experience your mind doesn't apply it the right way. This is what games like KSP are very good in - they give you very nice intuition about basic orbital mechanics.

• I don't know the strong points because I haven't tried it. So I've asked here and encouraged people to talk about the strong points. Thanks for your input! – uhoh Aug 30 '17 at 15:35

I'd like to first address this part:

But that last bit is only because it was written with simplifying mathematical approximations in the first place, and just changing to 3-body Newtonioan physics instead of patched conics would then allow "Lagrange points, perturbations, Lissajous orbits, (and) halo orbits..."; there would not be any need to invoke the extreme-sounding n-body limit. Within that framework, tidal forces would be straightforward to include as well.

n-body isn't essentially different from 3-body. If you have a 2-body problem, You can immediately calculate the configuration for any future moment in time. But 3-body and above is chaotic, which means that you have to do step-by-step integration, and the further into the future you go, the more precise the calculations have to be to remain accurate. This means smaller time steps and custom-precision numerics - and it means the computational effort is not linear in the time elapsed (as would be the case for step-by-step integration of a non-chaotic system), it is theoretically exponential. Compared to 2-body which is logarithmic (I would want to say constant since you just plug in a formula, but just representing the time elapsed is logarithmic in it).

This means that you will not be able to timewarp x1000000 as you can currently do in the game, and you can't visually see the entire orbit. This means that to have 3-body you don't just need to rewrite the engine, you would have to rethink what is possible in the game and how the UI and UX works.

Not to say that it cannot be done - since nobody will be die if the calculations are a bit off, you can do approximations to make the computation tractable - but it is something best left for a completely new installment of the game. On top of that, while the effects you get from 3-body are nice, there's a ton to explore that does not involve them.

On to more general considerations. I think that pretty much anything you can learn from KSP, you can learn by studying from books and using less-gamified simulators. But what makes KSP unique is the visceral, emotional feedback you get. Doing calculations on paper is one thing. But getting an audiovisual show, with rockets burning, air ebbing, and the blue marble shrinking, for a rocket that you designed, is quite another.

It's also quite different to have game-centric goals and objectives that you have a stake in succeeding to accomplish. Suppose you're trying to complete a simple mission, getting a ship to orbit. You design a ship and, if you're inclined, you do some calculations and estimate that it can succeed. It probably won't be very accurate since there are a lot of factors to take into account, which are time consuming at best. So you do a rough estimate and test it out in practice. And so you find yourself flying at suborbital speeds, with a bit of fuel left that should take you to orbit. You hope it will be sufficient, and as you watch your speed going up and your fuel supply dwindling, you think "come on come on come on...", and then either rejoice at your success or mope about your failure, knowing that at the very least you'll have to redo the whole thing again. Of course, the same goes for more complicated missions where it's even harder to plan everything in advance.

I think this kind of visceral feedback is important, as it makes the learning much more vivid and memorable, and allows you to have some fun in the process.

Another feature of KSP is that you have a lot of flexibility in how you choose to plan ahead. You can ignore all formulas and computations entirely and just wing it, making use of the game's visual aids as needed. But then you will probably not be very efficient.

Or you can do only very rudimentary calculations when the situation calls for it.

Or you can make very sophisticated calculations and planning, requiring good understanding of rocket dynamics and orbital mechanics, complete with your custom-made simulations that you go through before trying out anything in the actual game.

There are also many plugins you can use which either provide additional aids, or give you data you can use in your calculations.

Myself, I had a launch simulator I used in earlier versions of the game to maximize the potential of my designs. But in recent versions they have modified the aerodynamics model to be more realistic but also much, much more complicated. It would take me a lot of effort to rewrite the simulator accordingly to give me actionable information, so for now I've just dropped it and let the game simulate everything for me.

As for the kind of things you can specifically learn about, these include things such as launches (complete with staging, TWR, air resistance and gravity turns), reentries (slowing down to reentry trajectory, dealing with heat, braking using parachutes or rockets depending on atmosphere, and landing in one piece at the location you wanted), orbital maneuvers (including reaching the specific orbit you want and delta-v economy), orbital rendezvous (with celestial bodies or misplaced crew members), and gravitational slingshots.

As mentioned earlier, the audiovisual feedback and gamified objectives make all these things quite different from learning them on paper.

All in all, I don't know if I would recommend paying for the game just to learn more about orbital mechanics. But if you want to enjoy the game itself while learning along the way, it's definitely worth trying out.

Also, a case can be made that you can learn a lot by just watching videos of others playing the game and doing all kinds of stuff, there's plenty of that. And it will give you a better idea of what to expect from the game and whether you are interested in experiencing it yourself.

Disclaimer: I am not in any way affiliated with the makers of the game, and I do not receive any sort of compensation for convincing people to buy it. I play it, I enjoy it, and I believe that by doing so I have gained a better understanding of, and just as importantly, appreciation for, orbital mechanics.

By way of example, I have recently taken an interest in the topic of non-rocket launches. You can't do any of that in KSP, but thinking intelligently about these things requires a good understanding of concepts like TWR, Isp, delta-v requirements for touching space and for reaching LEO and GEO, etc. These things wouldn't have made as much sense to me if I hadn't had experience playing KSP.

• Very well written and considered answer; thank you! I appreciate your addressing patched conics vs numerical integration, and you point out something important; to obtain a fixed final accuracy after long time periods for n>2, the computation increases something like exponentially. However I have a hunch that because of the same chaotic effects, the difference between a patched conic (PC) sequential two-body solution and the correct solution might also diverge with time, in some cases also exponentially. So it might be said that PC is fundamentally already exponentially wrong. – uhoh Sep 3 '17 at 3:27
• Long term I hope to run patched conics and numerical integration side-by-side and try to extract computation times. Since the computation power of personal electronic devices is increasing exponentially, it's possible that time warping a three or four-body problem by a million is still attainable in a few seconds to an accuracy better than the fundamental errors introduced by using patched conics. That kind of discussion would need a benchmark and an new question. Thanks again for the well-written and thought-out answer! – uhoh Sep 3 '17 at 3:32
• 1. Sure, glad you enjoyed the answer. 2. Correct, patched conics can ultimately be quite wrong, but they are consistent. If the game displays my trajectory, and then I timewarp to a time in the future, I will be at the exact spot originally predicted. With chaotic numerical integration, I can end up somewhere quite different, depending on how the calculation was done. That's important game-wise. 3. Exponential growth in computing power is mostly parallel. I believe the calculations needed here are sequential, so it's not obvious we'll see that much of an improvement. – Meni Rosenfeld Sep 3 '17 at 10:36
• All good points! Thank you for taking the time to elaborate. Now you really have me thinking. You are right, it is going to be pretty difficult for ODE solvers to take full advantage of parallelized calculations. When I say my laptop has a gigaflop, that's for array multiplication, and even if I used the best complied ODE solver I probably won't see that kind of speed. This is really interesting to think about! :-) – uhoh Sep 3 '17 at 11:18
• @uhoh Parallelism will be helpful, because you will have to calculate the future positions of many things which won't be interacting with each other - the game ignores collisions (and other things) while timewarping, and only planets exert gravity. I'm still left with the impression you're considering the calculation of a single object, though, possibly not aware that the game tracks the position of hundreds (or thousands) of player objects. Most of those are "debris" - discarded fuel tanks, fairings, etc - but some will be satellites and space stations important to the player. – Slow Dog Sep 4 '17 at 8:05

KSP teaches an intuitive understanding of orbital mechanics in a way that reading text books, watching videos or any other non-interactive method of learning fails to achieve. By displaying a real-time prediction of future orbits as manoeuvres are planned and executed, it instils a visual representation of orbital changes that can be used to to reason about arbitrary situations while not even playing the game.

As an example, I posed a question about orbital rendezvous to someone who supposedly knew about spaceflight, but he was unable to answer sensibly, whereas any moderately experienced KSP player would know what to do. In the same way NASA knew about the mathematics of orbital rendezvous but had to build simulators to teach astronauts how to it, KSP makes orbital mechanics a matter of practical application rather than a theoretical knowledge.

• SE is about good questions and good answers, not shooting down other users' ships! :-) Here is a new KSP question for you; go for it! – uhoh Sep 1 '17 at 0:30