Semi-analytical near-Earth objects propagation: the orbit history of (35107) 1991 VH and (175706) 1996 FG3

The propagation of small bodies in the Solar system is driven by the combination of planetary encounters that cause abrupt changes in their orbits and secular long-term perturbations. We propose a propagation strategy that combines both of these effects into a single framework for long-term, rapid propagation of small bodies in the inner Solar System. The analytical secular perturbation of Jupiter is interrupted to numerically solve planetary encounters, which last a small fraction of the simulation time. The proposed propagation method is compared to numerical integrations in the Solar system, effectively capturing properties of the numerical solutions in a fraction of the computational time. We study the orbital history of the Janus mission targets: (35107) 1991 VH and (175706) 1996 FG3, obtaining a stochastic representation of their long-term dynamics and frequencies of very close encounters. Over the last million years the probability of a strongly perturbing flyby is found to be small.