The ISAS/JAXA Solar Power Sail mission, bound to explore the Jupiter trojans, will face many challenges during its journey. The landing manoeuvre is one of the most critical parts of any space mission that plans to investigate the surface of celestial bodies. Asteroids are mostly unknown bodies and in order to plan a successful landing on their surface, a great number of landing scenarios need to be taken into account. For the future mission to the Jupiter trojans, a study of the landing dynamics and their effects on the lander has to be done. A simple model of a lander has been created based on a design for the ISAS/JAXA Solar Power Sail mission, and the possible landing scenarios have been simulated. For this case, only the last part of the landing, which will be a free-fall has been taken into account. The lander is modelled as a rigid structure with a landing gear composed of four legs. The surface has been modelled as a flat plane with different inclinations and the possibility of including small obstacles or terrain roughness has been implemented. In the model, the lander is allowed 6 degrees of freedom. Several landing possibilities are tested with residual velocities and deviations in the starting point, and the stability of the lander is evaluated respect its geometry. Damping strategies have been considered to protect the instruments and reduce the impact, allowing for a safer landing. The effect of including crushable honeycomb dampers in the legs is also implemented, simulated and evaluated, by using a model of crushable honeycombs with different characteristics. In addition, the model includes also the position, direction and characteristics of the thrusters. Thus, it could be used to study other phases of the landing sequence where active control of the lander is needed, and evaluate the behaviour and response of different control-loop algorithms for attitude and position control of the lander.

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.