Evolution of Mercury-like orbits: A numerical study

Abstract

Abstract. 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 ν 1 and ν 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 ν 2 and ν 12 . We find retrograde and prograde hermeocentric orbits which are stable for durations in eccess of 4.5 Myr for initial semimajor axes <30 Mercury radii. Retrograde orbiters are stable for longer time scales than prograde. Collisions with Mercury occur for heliocentric objects, temporarily captured objects and for large hermeocentric orbits of both senses of motion. Gravitational scattering by Venus may constitute a possible route for transporting mercurian meteorites to Earth. We estimate the number of objects presently with orbits similar to that of Mercury and find that the current existence of such an object in the region has a low probability. We suggest an observational approach that would make the detection of hermeocentric objects larger than 1 km possible with a moderately sized telescope.

The Origin of Mercury

“…These results are consistent with those obtained by Gladman (2003) for slightly different initial conditions. Warrel et al (2003) found that hermeocentric and 1:1 Mercury mean motion resonance orbits can be stable for long time periods, but that ejecta with velocities only slightly greater than the escape velocity are likely to be reaccreted due to the necessity of successive close encounters with Mercury to achieve significant gravitational scattering. They did not, however, provide a numerical result.…”

Astrophysics in 2004

“…Mercury could have its own Trojan asteroids, though they would last only 20 kyr (Warell et al 2003) and does have its own magnetic field, for reasons that remain under discussion (Aharonson et al 2004, who have resurrected a fossil field). It used to have a chaotic relationship between its orbital and rotation periods, from which the 3 : 2 resonance was captured (Correia & Laskar 2004).…”

The Vulcanoid Asteroids: Past, Present and Future

“…From the foregoing, therefore, it may be argued that there are at least two good reasons why the solar system might have supported a primordial population of Vulcanoid asteroids -either as the result of direct planetesimal growth, or via the destruction of two or more closely-packed planets. To these scenarios we can additionally add the process of Hermian Trojan capture [23], as well as the inward evolution of cometary nuclei, near-Earth asteroids and assorted collisional ejecta from the outer solar system [24].…”

“…That the Vulcanoid zone is far from being a dynamically inactive region of the solar system is evidenced by the fact that both asteroids and cometary nuclei are regularly observed to pass through its borders in the modern era [23]. A search of the JPL Small-Body database, for example, reveals that at the present epoch there are 244 asteroids that cross the orbit of Mercury with perihelion distances located within the Vulcanoid zone.…”