The mathematical explanations on this page will teach you lots of stuff that will be useful when playing KSP, but the reverse is much less true.
Yes, KSP will help you build an intuition for orbital mechanics, but you can play it for years and never learn how to calculate something as simple as the length of an orbital period at a given altitude.
I find the intuition extremely helpful - without the intuition, it's hard to build a gut feeling for the interrelation and relative importance of the bits in the jargon soup for any given question - apijove vs ascending node, and so on.
What works best is therefore a combination of the two: I have often found myself digging into the math when I want to get something /really working/ in KSP. You start the game by trying to keep the burning end pointing down (and eventually sideways), but the Rocket Equation forces us learn about Hohmann Transfers if we want to get anywhere interesting. (And maybe even get back again.)
Notably, it's the /constraints/ that create the need to optimize, which push us from playing back to the math. The sibling commenter who doesn't like dealing with fuel misses the point: Caring about fuel pushes us to find the mathematical tools to solve our problems.
Compare to Outer Wilds, which has a really fun physics simulation - you can whip around planets like a madman - but there's no real constraints on fuel, and the solar system is small enough that speed isn't really a problem, either. No constraints means no one ever has to figure out a Hohmann transfer.
KSP drove me to learn those things. While attempting to reach further planets, I ended up researching specific impulse, calculating Δv, relating altitude to speed to orbital period, and so on. I even downloaded a program that calculated optimal launch windows.
So yes, none of this was in the game per se, but I wouldn't have done any of it if it wasn't for the game. The median person has exactly zero use for orbital mechanics, and KSP is about as close as it gets to a practical application unless you work at a space agency.
Seriously, understanding dynamics and other basic physics in depth never hurt anyone, while real use of orbital calculations is much rarer than playing games, writing SF and so on.
Sort of. KSP teaches you rocket building and how precious fuel is. You need to invest a lot of time to get to the stage where you transfer between planets. You also can't just pick up the resident star, give it a whack, and see what happens to the solar system (because it's all two-body mechanics).
That's what I wanted to learn about: orbital mechanics, but as a game. I could not find anything online so I built it myself. The UX is bad, I've been meaning to improve it but you know how it goes. Apologies in advance if the interface is beyond comprehension: it's not you, it's me.
Use arrow keys to control the space craft that looks oddly similar to the letter "A". You're orbiting Earth (denoted with E) and there is also the international space station roaming around, as well as the moon if you scroll to zoom out.
Try getting near the ISS or even the moon! It's tricky if you're doing this for the first time.
For me, this really helped to get a feel for orbital mechanics. I never played KSP more than a few minutes on a friend's PC, but based on Juno:NewOrigins (simplerockets2) being rather similar, I don't really enjoy the engine building aspect or the aspect of constantly being out of fuel. It's more realistic obviously, but spacecraft design wasn't my goal. I wanted to understand how things in orbits affect each other and this lets you do that.
You can also take control of the earth in the "bodies" menu. Set engine thrust to some giganewtons or whatever and fly the earth to a new place :). Or try some of the scenarios in the menu. Also note the simulation speed on the top left, otherwise getting to e.g. the moon takes a while.
Nice website! Dunno if you're the owner but I'd add "obvious" to your list of words to scan. Nothing's more frustrating than when the author says "and obviously [not obvious thing]"
Actually this reminds me of a funny story about a math professor. He's teaching a class and is going through a proof and skips part of it, saying "I'll skip this part because it's trivial." A student comes up after class and asks about the trivial part. He tries to explain it for a few minutes, and can't quite get it, and the student has to go to her next class, so they agree to revisit the issue next class.
The next day the professor tells the student "I stayed up all night working on this and can confirm that it is indeed trivial"
Then how about: One common way to learn orbital mechanics is playing ksp. For this you need to [buy a computer] [purchase and install the game] and [do the tutorial]. For maximum enjoyment it is recommended to watch [Scott Manley's playthroughs on YouTube] between sessions to deepen your understanding.
