The French physicist/mathematician Poincare proved in the late nineteenth century that under Newtonian mechanics no three or more body dynamical system was stable, there was always the possibility of the “butterfly effect”. A butterfly flapping its wings will perturb the earth's orbit in ways that will be magified trillions and trillions of times in 100 million years. The tiniest uncertainty in the current state of the bodies in the solar system means that predictions more than a few million years into future are fraught with uncertainty.
Sorry! I was so excited and relieved at this latest news that I responded to post #2 instead of post #1.
However, this has done nothing to relieve my ongoing anxiety over Apophis...and the governments capabilities to have any calculations correct, or, whether they would let us know the truth if the news for either 2029 or 2036 is bad.