In space you can't turn like a plane because there is no air resistance. The only way to turn is either to reverse all your momentum, or to slingshot around a gravity well.

Do any games use this mechanic? I imagine an easy implementation: Flip to show current speed, allowing for 2 speeds, plus a third speed that must be lost at end of turn by entering orbit. Movepoints are used to adjust velocity and direction (it costs 0 move points to maintain velocity and direction). Turn when you move adjacent to a planet, or enter orbit to slow completely and turn any amount.

The result is hopefully that you plot strike routes which involve slingshotting around planets with various defenses, out-turn enemies rather than outrunning them, and worry more when your flight plan needs to be altered, since you might fall out of the solar system

The most original game that implements newtonian mechanics and keplerian orbits (via conic sections) is Orbiter http://orbit.medphys.ucl.ac.uk/​,​ but it is rather on the simulator side.​ There is a spin-off of it, Kerbal Space Program, which is more on the “build a rocket and fly places if you don't explode” side, but newtonian physics. Especially the atmopsheric flight is not as well implemented as in Orbiter. All of them are based on trivial 2-body-calculations, 1 main mass and a flying contraption with 0 mass, which makes the calculation numerically solvable. I have read about a few guys who tried to implement the 3 body problem in a game environment (which would allow for Lagrange points and real sling shots e.g. of a rocket in an earth-moon-system), but this apparently has not been brought to an end.

Try orbital encounter and docking in one of the mentioned games, if you haven't done so. Having played both I must say that warfare would probably be really boring. It is not that you just shoot at something. In order to get an encounter, e.g. for a missile shot at an enemy, you either have to wait until you're in a the right position for a maneuver (to equalize inclination or accelerate for an encounter), or launch it directly into the desired orbit, both of which can take time (hours to years, depending on orbital parameters) or even be impossible (not enough maneuvering capacity). I could imagine that “Guys, in 6 months we're at the right phase angle to launch a missile into the right inclination to hit the enemy 13 months later” isn't exactly thrilling. The enemy would of course know that and would also know that a minuscule change to its own orbit ahead of time would make the attack a sure miss. Or you have fancy ray weaponry, but then it might not be worth to put that much effort in all that physics …

KSP has some mods for npoint if want to go to that degrees. https://github.com/mockingbirdnest/Principia​

But even unmodded KSP I think shows that space combat with today's potential technology would not be that interesting for a game. Probably mostly missiles, lasers, maybe some sort of railguns, but at vast distances.

With or without mods, try getting a rendezvous quickly quickly then flying around it in a fighter like way. Look at how little delta-V the target could use to avoid the intercept.

Now if some unlimited fuel drive was possible to avoid the delta-V limitations you can avoid some of that, probably mods to try it. I suspect getting a rendezvous with a suitably small relative speed to do something interesting will still be very difficult, especially if the target tries to evade it.

EDIT: I believe Elite: Dangerous claims to use Newtonian physics, but only for “normal space”/non-cruise. Which I think artificially limits the speed to something like 500m/s (relative to the “area”) to force things to stay at close distances. Super-cruise doesn't use Newtonian physics at all, making it easy for players to reach a point of interest, and be magically set to a speed relative to the area.

I think the older elite games were more complete, but can't recall the details.

It woul really be cool to implement these things, but we'd need a bunch of math gurus for all the integrals and differentials and whatnot.

KSP and Orbiter put planets and moons “on rails”, meaning they just stubbornly follow an orbital path. A ship can only be in 1 sphere of influence (soi), and it just abruptly tranistions between them. It is allways on some sort of conic section path, elliptical in a closed, parabolical at escape velocity or hyperbolical above escape v, with respect to the current soi's central mass. So that simplyfies things, but won't help to calculate the mutual influence of two bodies, e.g. earth and moon, on a ship between them.

Is there a book about the math necessary for integration of forces and amounts over time ? I mean something in between the introductions into game physics and a 4 semester course ? Euler, Runge-Kutta, stability issues, maybe algorithmic approach ?

Am not a math guy or computer science guy by original trade, but genuinely interested …

@lorenzogatti : that reminds me of Wooden Ships & Iron Men :-)

Green_Baron said:
Is there a book about the math necessary for integration of forces and amounts over time ?

Sorry I know the asked price is astronomical but still: Numerical Methods for Engineers

And in the context: Orbital Mechanics