The rubber sheet runs into problems when you try to introduce high inclination orbits, or non-inspiralling (or at least very very slowly inspiralling) nearly ci

The rubber sheet runs into problems when you try to introduce high inclination orbits, or non-inspiralling (or at least very very slowly inspiralling) nearly circular orbits. It also doesn't do well when the mass-to-mass ratios of the objects on the sheet are small. It also doesn't do well when you want the masses to spin. (How many of the large bodies in our solar system have nearly zero spin angular momentum? And the difference between perihelion and aphelion for Venus and Neptune are small, and there doesn't seem to be any danger of them inspiralling sunwards in the next several thousand of their respective solar orbits.)