The fact that Trojan asteroids have been on stable orbits for such a long time hints at one of the main problems in explaining their origins. Once an object is in a Trojan orbit, it is hard to escape, but similarly, it is also difficult to get into a Trojan orbit in the first place. However, if Jupiter and Saturn were once on different orbits than they currently are, then mutual dynamical interactions could have “opened” up the Trojan orbits of Jupiter, allowing asteroids to both enter and leave the region.
The Nice model, named after the city in France where the model was originally developed, describes a possible early evolution of the Solar System and explains many of the observed properties of the Solar System that we see today. It postulates that when the giant planets first formed they were closer to the Sun then the present day orbits would place them. The planets interacted with each other and with the surrounding small bodies and eventually underwent an instability, in which Neptune, Uranus and Saturn moved outwards and Jupiter moved inwards a little bit (it is even possible that there was an additional Neptune-like planet that was ejected from the Solar System!)
During this instability, many outer Solar System asteroids were scattered between the planets, and some of them would have been trapped in the Trojan population of all of the giant planets. Because Jupiter is the biggest planet, the stable region around its Lagrange points) are the largest, so it trapped the most of these outer Solar System asteroids.
During this capture process, asteroids from throughout the giant planet forming region would have been trapped on Trojan orbits, thus possibly explaining why the Trojan asteroids show such a large diversity in color and (by implication) composition. Lucy will learn much more about the composition of these diverse objects and allow us to test these ideas.