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Close encounters (CEs) between celestial objects may exert significantinfluence on their orbits. The influence will be even enhanced when two groupsof celestial objects are confined in stable orbital configurations, e.g. inadjacent mean motion resonances (MMRs). Plutinos and Neptune Trojans, trappedin the 2:3 and 1:1 MMRs with Neptune respectively, are such examples.%Meanwhile, many objects among these two groups have peculiar orbits, seeminglyas the vestige of CEs. As the first part of our investigation, this paperprovides a detailed description of CEs between Plutinos and Trojans and theirpotential influences on the Trojans' orbits. Statistical analyses of CE datafrom numerical simulations reveal the randomness lying in the CEs between thetwo planetesimals. The closest positions of CEs distribute symmetrically insidethe given CE region and no particular bias is found between the positive andnegative effects on the orbital elements of Trojans. Based on the Gaussianapproximation on the distribution of the velocity orientation of Plutino, andthe integral derivatives of Gaussian perturbation equations, a theoreticalmethod is built to estimate the CE effects. To further verify the randomness ofCEs, a Monte Carlo approach is applied, and it generates distribution featuresconsistent with the numerical results. In summary, CEs brought by realisticPlutinos exert impartial effects and tiny total influence on the orbitalelements of Trojans. However, driven by the random walk mechanism, tiny effectsmay accumulate to a prominent variation given sufficient CEs, which will bediscussed in the accompanying paper.

On the close encounters between Plutinos and Neptune Trojans: I. Statistic analysis and theoretical estimations