EXexDM69·May 7, 2017
> But honestly I am certain that it is something in particular and not something mysterious about conservation of energy/momentum which i have not come across yet, because there is no formula in that gravity simulation which should be able to destroy momentum
It's a well established fact that numerical integration methods either gain or lose energy (in particular, the Runge-Kutta family is known to lose energy over time). For celestial mechanics simulations, a special class of numerical integration methods called "symplectic integrators" are used and their purpose is to conserve energy and angular momentum.
> but if you do any adjustments to correct it, that is a kind of fudge not based in true physics.
When you are numerically integrating differential equations that model physical phenomena, you're not doing "true physics" but an approxi
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mation thereof.
And an approximation that makes Earth drift 70 km per year or Saturn's moons drift out of orbit in a few hundred years is a very bad approximation by scientific standards.
The methods used for celestial mechanics calculations need to be precise over thousands to millions of years. And the way they work is to "fudge" with the numerical methods to preserve energy and angular momentum. It's a much better approximation of "true physics" than your toy simulation.
Your assumption that the issues are due to floating point errors is incorrect. 64 bit double precision is millimeter accurate to the orbit of Neptune. That's good enough for scientific applications.
If you're interested in this, you could take a look at this scientific grade N-body simulator and the methods it uses:
https://github.com/hannorein/rebound