The Jupiter Trojan asteroids are minor bodies that orbit 60 degrees before and 60 degrees behind Jupiter. Because these orbits are stable over the lifetime of the Solar System, the properties of these objects may inform us about the conditions under which the Solar System formed. We present BVRI photometry for 110 of the intrinsically brightest and presumably largest members of the L4 and L5 Jupiter Trojans. We use a new principal color component derived by Chatelain et al. (2016) that is indicative of taxonomic types relevant to the Jupiter Trojan asteroids. We find that 83% of the largest Jupiter Trojans are consistent with a D-type classification, while 17% show shallower slopes more consistent with X-type and C-type classifications. We show the L4 and L5 populations to be taxonomically indistinguishable at large sizes, as well as include findings about certain objects that have resulted from these data. Specifically, multi-filter light curves for twelve objects show signs of V-I color variation in as many as two thirds of these objects, and our richest datasets allow for the determination of phase curves and shapes for some asteroids including a new shape model and pole solution for (1173) Anchises. Our goal is to use this study to shed light on these fascinating objects and to place the Trojans in context in the larger Solar System.

Jupiter Trojan asteroid dynamics have been studied for a long time but it is only within the last decades that the known population has become large enough to make other studies meaningful. In four articles I have been scratching the surface of the unknown Trojan knowledge space. Paper I presents photometric observations confirming a larger variety in surface redness for the smaller Trojans compared to the larger ones, in line with the groups in the outer main asteroid belt. However, the largest Trojans are significantly redder compared to the largest Cybele and Hilda asteroids. Paper II is an investigation of the Trojan discovery completeness. The analysis shows that all Trojans down to a limiting absolute magnitude of H=11.5 mag have been discovered. Missing Trojans in the almost discovery-completed section should have inclinations above the mean of the same group. The faintest Trojans are discovery biased due to orbit orientations similar to the Milky Way. Paper III is a general review of dynamical and physical properties of the discovery-completed sample of Jupiter Trojans found in Paper II. The two Trojan swarms are often treated as being equal, but are different in a number of details. Two known facts are that the L5 swarm is less rich, while the L4 swarm has a larger fraction of low inclination Trojans. Trojans are in general red objects but the mean redness is higher for Trojans which have not collided compared to Trojans in families. Paper IIII is an investigation of Trojan collisions, family detection and evolution. Collision circumstances were mapped using numerical simulations and recorded Trojan close approaches. Synthetic families were created and evolved numerically. The result suggests that the HCM family detection technique can find Trojan families even in a densely populated parameter space. However, interlopers cannot be avoided at any level but their contribution should be less than 30%. Synthetic families can be identified with backwards orbital integrations for times up to a Gyr-scale. However, there are discrepancies between real Trojan families and my synthetic families.