Lagrange L4/L5 points and the origin of our Moon and Saturn's moons and rings

The current standard theory of the origin of the Moon is that the Earth was hit by a giant impactor the size of Mars causing ejection of debris from its mantle that coalesced to form the moon; but where did this Mars-sized impactor come from? Isotopic evidence suggests that it came from 1 AU radius in the solar nebula, and computer simulations are consistent with its approaching Earth on a zero-energy parabolic trajectory. How could such a large object form at 1 AU in a quiescent disk of planetesimals without having already collided with the Earth at an earlier epoch before having the chance to grow large? Belbruno and Gott propose that the giant impactor could have formed in a stable orbit from debris at the Earth's Lagrange point L(5) (or L(4)). It would grow quietly by accretion at L(5) (or L(4)), but eventually gravitational perturbations by other growing planetesimals would kick it out into a horseshoe orbit and finally into a chaotic creeping orbit, which Belbruno and Gott show would, with high probability, hit the Earth on a near zero-energy parabolic trajectory. We can see other examples of this phenomenon occurring in the solar system. Asteroid 2002AA29 is in a horseshoe orbit relative to the Earth that looks exactly like the horseshoe orbits that Belbruno and Gott found for objects that had been perturbed from L(4)/L(5). The regular moons of Saturn are made of ice and have the same albedo as the ring particles (ice chunks, plus some dust). We (J. R. Gott, R. Vanderbei, and E. Belbruno) propose that the regular icy moons of Saturn (out to the orbit of Titan), which are all in nearly circular orbits, formed out of a thin disk of planetesimals (ice chunks) rather like the rings of Saturn today only larger in extent. In such a situation formation of objects at L(4)/L(5) might be expected. Indeed, Saturn's moon Dione is accompanied by moons (Helene and Polydeuces) at both L(4) and L(5) Lagrange points, and Saturn's moon Tethys is also accompanied by moons (Telesto and Calypso) at both L(4) and L(5) Lagrange points. Epimetheus is in a horseshoe orbit relative to Janus that is exactly like the horseshoe orbit expected for an object that has been perturbed from a location at L(4)/L(5). We propose that the rings of Saturn visible today are all that remains of this original disk; they lie inside the Roche limit where tidal forces have simply prevented the formation of large moons by accretion. Further out, the icy particles have accumulated into icy moons. Objects in external solar systems on horseshoe orbits (like those of Epimetheus relative to Janus) could be detected by a slow sinusoidal variation with time of the calculated mass of a planet from radial velocity measurements.