Ever since their discovery, the Trojans have raised many questions among astrophysicists. In 1989 it was found that there were more L4 than L5 Trojans and the current L4:L5 ratio value is estimated to be 1.6. However, this asymmetry could not be explained by Jupiter’s current orb
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Ever since their discovery, the Trojans have raised many questions among astrophysicists. In 1989 it was found that there were more L4 than L5 Trojans and the current L4:L5 ratio value is estimated to be 1.6. However, this asymmetry could not be explained by Jupiter’s current orbit and must therefore have arisen during the early development of the Solar System. It was suggested that an outward migration as described by the Nice model could cause the asymmetry. To investigate this, we extended a recent research by modelling an outward migration of Jupiter on the actual Trojans and their symmetric copies. In this manner, we had a broad initial Trojan distribution, which allowed us to investigate several effects of initial values like the Trojan inclinations and maximum angular deviations from the Lagrange point. The simulations used a recently found midpoint Yoshida integrator, which allowed fourth order symplectic simulations for our non-separable Hamiltonian problem. From the simulations it followed that the ratio could only be explained if the Trojans initially had large angular deviations from the Lagrange point, which is possible if they later lost energy due to for example mutual collisions. Also the small initial inclinations as predicted for the early Trojans would in general have risen due to the migration, but it could not explain the the inclinations up to 40 degrees for today Trojans, implying that the increase in inclination must have been caused by other reasons. We found that not only the total migration distance and duration are important, but also the function that describes the evolution of Jupiter’s semi-major axis and the eccentricity of Jupiter’s orbit. For further research we suggest to use data sets on those quantities from simulations with the Nice model, to investigate these related problems together. We believe that our model and code is of great advantage for such a research, because of its optimisations and it allows to implement the data on the distance and eccentricity directly into the model without having to alter the equations of motion.