There's little chaos. Something in orbit can be projected out for a long time with little error based on just a few observations, so even things not sending data back we can track fairly trivially. If something is in orbit it stays in mostly the same orbit unless it hits something else.

(There are very small changes based on gravity depending on how dense the area below it is, but that effect is fairly small and probably accounted for in simulations to some degree. Low orbits will also have some atmospheric effects too. They will all also have small changes based on solar radiation as well, but this is really minor.)