He mentions a 10% error in energy conservation, so not too great.
Probably he should have done research before he started, he would have found one of the several lecture notes that tell you how to integrate orbits. They tell you that symplectic methods are great for time reversible problems.
Or he would have found one of the public codes for integrating the solar system very far into the future.
Re:Some Notes on Orbital Mechanics
by tjradcliffe on Saturday February 07, 2015 @06:30PM
(#9015750)
Initial energy is conserved at the 10% level, which is not great.
I really didn't expect the RK4 thing to work at all, and once it was clear it kind of did decided to push on for fun.
Having said that, it is an adaptive RK scheme, and it seems to work pretty well, the article shows that the results match some reference data quite well, and it even captures some quite subtle effects, most notably the influence of the moon.