I suppose this gives us some idea of resonant orbits – or why we are not being constantly bombarded by objects and debris from elsewhere in the solar system. The theory here is that it involves Fibonacci numbers. At http://tallbloke.wordpress.com/2014/01/22/why-phi-earths-secret-neighbours/ … is a post by somebody calling himself Oldbrew. Perhaps he is a real ale enthusiast but the subject has nothing to do with beer and all to do with a couple of Apollo asteroids – two of several dozen. They cross the orbit of the Earth regularly and have semi major axes greater than that of the Earth, by perihelion distance less than Earth's aphelion distance. They are orbiting the Earth in a synodic relationship. Toro completes 5 orbits of the Sun evry 8 Earth years and 5 Sisyphus orbits take 13 earth years/orbits.
Toro's orbit, as the alert may have noticed, is virtually identical to that of the Venus-Earth synodic period (Venus orbits Earth 13 times every 8 years). The Venus-Toro synodic period is almost exactly one year (365 as opposed to 365.2492 days). Toro also crosses the orbit of Mars and is in a 20:17 orbital relationship with that planet. The orbital periods involve Fibonacci numbers – so it is alleged.
The author makes the point there is a class of Earth grazing objects – see the link at http://en.wikipedia.org/wiki/Earth-grazing_fireball