Mathematical modeling of close encounters of Solar system small bodies with major planets and the Moon

We establish the choice of numerical integration method for the motion equations of solar system small bodies in moments of close encounters with major planets and the Moon. The performed research shows that the multi-step Adams–Moulton method with preliminary chosen smaller step and increased order of approximation is more preferable for these moments. The modeling of moments of encounters using the one-step Everhart method with variable step sufficiently increases the global time of numerical process and requires the following optimization of step change criterion.