  Trojans are defined as objects that share the orbit of a planet at the stable
Lagrangian points $L_4$ and $L_5$. In the Solar System, these bodies show a
broad size distribution ranging from micrometer($\mu$m) to centimeter(cm)
particles (Trojan dust) and up to kilometer (km) rocks (Trojan asteroids). It
has also been theorized that earth-like Trojans may be formed in extra-solar
systems. The Trojan formation mechanism is still under debate, especially
theories involving the effects of dissipative forces from a viscous gaseous
environment. We perform hydro-simulations to follow the evolution of a
protoplanetary disk with an embedded 1--10 Jupiter-mass planet. On top of the
gaseous disk, we set a distribution of $\mu$m--cm dust particles interacting
with the gas. This allows us to follow dust dynamics as solids get trapped
around the Lagrangian points of the planet. We show that large vortices
generated at the Lagrangian points are responsible for dust accumulation, where
the leading Lagrangian point $L_4$ traps a larger amount of submillimeter
(submm) particles than the trailing $L_5$, which traps mostly mm--cm particles.
However, the total bulk mass, with typical values of $\sim M_{\rm moon}$, is
more significant in $L_5$ than in $L_4$, in contrast to what is observed in the
current Solar System a few gigayears later. Furthermore, the migration of the
planet does not seem to affect the reported asymmetry between $L_4$ and $L_5$.
The main initial mass reservoir for Trojan dust lies in the same co-orbital
path of the planet, while dust migrating from the outer region (due to drag)
contributes very little to its final mass, imposing strong mass constraints for
the in situ formation scenario of Trojan planets.
