Evolution of Mercury-like orbits: A numerical study

The orbital evolution of ~$30\,000$ objects has been studied numerically for time scales of up to 11 Myr in order to investigate the dynamical importance of Mercury on objects with orbits similar to the planet's, as well as the existence of stable hermeocentric orbits. We find that Mercury, despite its small mass, exhibits a strong dynamical influence on objects with heliocentric Mercury-like orbits. The orbits of such objects may become temporarily and repeatedly Trojan-like for durations exceeding 20 kyr, exhibiting horseshoe orbits in the 1:1 resonance with periods of around 60 years. Objects with Mercury-like orbits may evolve dynamically to Venus crossers on time scales of 50–100 kyr by successive close encounters with Mercury which quasi-instantaneously increase the semimajor axis and cause subsequent capture in strong secular resonances, which force the eccentricity to high values. Initially, all particles were located in the $\nu_1$ and $\nu_{11}$ resonances which strongly affect their dynamical evolution. Only objects for which the semimajor axis and eccentricity were significantly increased due to close encounters with Mercury escaped these resonances. The effects on the orbital elements of close approaches within the Hill radius of Mercury are generally minor and their values are then unlikely to change significantly. The largest changes to the orbital elements at such events occur for Hill sphere traverse times of 2 days, when a, e and i may change by as much as 0.07 AU, 0.13 and 3.5°. However, secular resonances are generally considerably more efficient in affecting the orbital elements, particularly $\nu_2$ and $\nu_{12}$. We find retrograde and prograde hermeocentric orbits which are stable for durations in eccess of 4.5 Myr for initial semimajor axes