Apophis asteroid 2029 and gravitational keyhole?

You can, you know, write your own computer code to integrate the trajectories of hypothetical asteroids that make close ped by Earth. You could even include the gravitational influence of the moon and the other planets, in addition to that of the sun and Earth. Then just keep incrementing time (by short steps) and updating the information about the asteroid's velocity, position, and gravitational acceleration. It's an easy code to write. My excuse for not writing it (yet again) is lack of motivation: I'm in the middle of reading "Forty Thousand in Gehenna" by C.J. Cherryh.