  Close encounters (CEs) between celestial objects may exert significant
influence on their orbits. The influence will be even enhanced when two groups
of celestial objects are confined in stable orbital configurations, e.g. in
adjacent mean motion resonances (MMRs). Plutinos and Neptune Trojans, trapped
in the 2:3 and 1:1 MMRs with Neptune respectively, are such examples.
%Meanwhile, many objects among these two groups have peculiar orbits, seemingly
as the vestige of CEs. As the first part of our investigation, this paper
provides a detailed description of CEs between Plutinos and Trojans and their
potential influences on the Trojans' orbits. Statistical analyses of CE data
from numerical simulations reveal the randomness lying in the CEs between the
two planetesimals. The closest positions of CEs distribute symmetrically inside
the given CE region and no particular bias is found between the positive and
negative effects on the orbital elements of Trojans. Based on the Gaussian
approximation on the distribution of the velocity orientation of Plutino, and
the integral derivatives of Gaussian perturbation equations, a theoretical
method is built to estimate the CE effects. To further verify the randomness of
CEs, a Monte Carlo approach is applied, and it generates distribution features
consistent with the numerical results. In summary, CEs brought by realistic
Plutinos exert impartial effects and tiny total influence on the orbital
elements of Trojans. However, driven by the random walk mechanism, tiny effects
may accumulate to a prominent variation given sufficient CEs, which will be
discussed in the accompanying paper.
