At its minimum speed (Speed=0, Accuracy=15), Gravitorium checks gravitational forces and alters the position of bodies once a second (of simulated time). The results in most circumstances are accurate for quite reasonable periods of time (a hundred years of simuated time or so).
However, at maximum speed (Speed=max, Accuracy=0), Gravitorium only updates position once every few hours, and the accuracy is so low that planets may well drift completely out of their orbits in a matter of days of simulated time.
In general, accuracy will be lowest when bodies are undergoing a high degree of acceleration (or when their orbits have a high degree of curvature), because they can move a considerable distance in between the times Gravitorium rechecks the acceleration.
The way Gravitorium works is like assuming that curved orbits are made up of lots of little straight lines. When the actual path of the object isn't curved very much, you can afford to simulate this path by only readjusting (drawing another straight line) every so often, and you'll get quite a close match. But when a body is in a close orbit around a large mass, its path is very strongly curved, and to get close to the correct path, you need to draw lots of very short straight lines very often.
That's why you need to slow Gravitorium down to the minimum if you need to accurately simulate bodies which are undergoing high amounts of acceleration.
However, when all is said and done, Gravitorium is just a simulation, mostly for fun. If you want to see things happening quickly, feel free to bump up the speed a bit and see what happens. In most circumstances you'll get a good enough sense of the likely behaviour of the system even at quite high speeds, though you wouldn't want to pilot a spaceship on the basis of its results.
This is a Newtonian simulator, based on the laws of motion and gravitation worked out by Sir Isaac Newton in the 1700s. It doesn't take into account relativistic effects as discovered by Albert Einstein in the 1910s. Mostly, this doesn't matter much, but where bodies are undergoing high acceleration, relativistic effects do make a difference. In our own Solar System, for example, the perihelion of Mercury changes somewhat more because of these effects than Newtonian physics can explain. Sorry, but Gravitorium doesn't aspire to that kind of accuracy.