It all comes down to how Apophis passes the Earth on it’s next close passage (no real chance of impact associated with this one!) in 2029. If Apophis misses the Earth just right it could pass through an exceedingly narrow gravitation keyhole, which would alter the orbit of the asteroid just enough to make a possible impact in 2036. That said, it isn’t anything to get worked up about, the odds of the asteroid missing us are probably even better than what are being cited due to how incredibly hard it is to pin down the exact positions of the Earth and Apophis with enough accuracy to really predict the impact.
Now how can that be? I mean it is just gravity after all. It is true that just about any second year physics major in the country could take on the problem of the Sun and Apophis, and solve the system such that they could predict at all times where it would be in its orbit. It is also true that adding just a single additional body to that system (say Jupiter, or Earth) makes it such that no single person can exactly solve the resulting system! This “n-body” problem is at the heart of the very complex calculations needed to predict if an impact can take place. Since it can’t be worked out analytically, the orbits of asteroids in the solar system must be solved numerically, through simulating the orbits. Work out all the forces involved, let the solar system move for a very short period of time, work out the changed forces, evolve the system some more, and on and on. The resulting solution is only as good as the computer and code that is trying to solve it!
What type of accuracy is needed? A whole lot. It takes just 7 minutes for the Earth to travel a distance equal to its diameter. Every 7 minutes that go by Earth is in a completely new portion of space. One needs to find out if the asteroid shares that space within that 7 minute window. To complicate matters even more, to get that level of precision, much more than just point-particle Newtonian gravity must be taken into account. For example, the Sun isn’t a perfect sphere, and is slowly losing mass. The masses of the Planets and other asteroids are only known to a finite amount, and our own Milky Way Galaxy exerts a tidal force on the solar system. Largest of all the uncertainties is the way in which the asteroid itself absorbs and reradiates sunlight (the Yarkovsky effect). Depending on the thermal make-up of the asteroid and how it is spinning this force can significantly alter its orbit, even of fairly short time scales.
In short, it is really hard to nail down exactly where an asteroid will be at a particular time, which creates enough uncertainty to be unable to rule out an impact for objects like Apophis. As time goes on (and the projected time errors grow smaller) I fully expect the impact chance to continue to drop, although you’ll never see that on cover of the New York Times, as “Asteroid to miss the Earth – everything is fine” probably won’t move many copies.
Worse case, Apophis is only about 270 meters across, enough to cause some significant damage, but not any sort of Doomsday Scenario.
