  Revealing the mechanisms shaping the architecture of planetary systems is
crucial for our understanding of their formation and evolution. In this
context, it has been recently proposed that stellar clustering might be the key
in shaping the orbital architecture of exoplanets. The main goal of this work
is to explore the factors that shape the orbits of planets. We used a
homogeneous sample of relatively young FGK dwarf stars with RV detected planets
and tested the hypothesis that their association to phase space
(position-velocity) over-densities ('cluster' stars) and under-densities
('field' stars) impacts the orbital periods of planets. When controlling for
the host star properties, on a sample of 52 planets orbiting around 'cluster'
stars and 15 planets orbiting around 'field' star, we found no significant
difference in the period distribution of planets orbiting these two populations
of stars. By considering an extended sample of 73 planets orbiting around
'cluster' stars and 25 planets orbiting 'field' stars, a significant different
in the planetary period distributions emerged. However, the hosts associated to
stellar under-densities appeared to be significantly older than their 'cluster'
counterparts. This did not allow us to conclude whether the planetary
architecture is related to age, environment, or both. We further studied a
sample of planets orbiting 'cluster' stars to study the mechanism responsible
for the shaping of orbits of planets in similar environments. We could not
identify a parameter that can unambiguously be responsible for the orbital
architecture of massive planets, perhaps, indicating the complexity of the
issue. Conclusions. Increased number of planets in clusters and in over-density
environments will help to build large and unbiased samples which will then
allow to better understand the dominant processes shaping the orbits of
planets.
