The speed and direction of objects moving through space is deterministic, but it is neither constant (obviously) nor completely predictable except in very special cases. In general the motion of systems of three or more bodies are chaotic, i.e. very small changes in initial conditions can result in very large changes in position and velocity in the future. Also, we can't measure positions and velocities with infinite precision. This has nothing to do with quantum mechanics, it's just that the data that comes out of our instruments has finite precision and so there will always be measurement errors. Finally, earth is a very small target, so figuring out whether something will hit it requires a lot of precision.

Also, quoting from the original article: "Often when new objects are first discovered, it takes several weeks of data to reduce the uncertainties and adequately predict their orbits years into the future."