The resonant dynamical evolution of small body orbits among giant planets

Abstract

Abstract.Mean motion resonances (MMRs) can lead either to chaotic or regular motion. We report on a numerical experiment showing that even in one of the most chaotic regions of the Solar System -the region of the giant planets, there are numerous bands where MMRs can stabilize orbits of small bodies in a time span comparable to their lifetimes. Two types of temporary stabilization were observed: short period (∼10 4 years) when a body was in a MMR with only one planet and long period (over 10 5 years) when a body is located in overlapping MMRs with two or three planets. The experiment showed that the Main Belt region can be enriched by cometary material in its pre-active state due to temporary resonant interactions between small bodies and giant planets.

Potential Jupiter-Family comet contamination of the main asteroid belt

“…Rubincam, 1995) or cometary outgassing (cf. Marsden et al, 1973;Yeomans et al, 2004), or mutual gravitational interactions among asteroids (e.g., Novaković et al, 2015), our results show that considering only the major planets and the Sun, purely gravitational dynamical pathways exist in our solar system via which objects with comet-like orbits (with T J,s < 3) can evolve onto main-belt-like, and even MBC-like, orbits (with T J values of > 3.05), apparently via the influence of MMRs with Jupiter and gravitational interactions with terrestrial planets, consistent with the findings of Gabryszewski & W lodarczyk (2003). Secular perturbations may also contribute to the dynamical evolution of these objects (e.g., Knežević et al, 1991;Morbidelli & Henrard, 1991;Bailey & Emel'yanenko, 1996;Michtchenko et al, 2010;Machuca & Carruba, 2012), though we did not explicitly consider them in this work.…”

“…Figure 3). Finally, we note that essentially all of these particles have a f values placing them extremely close to a major, or at least moderate-order (i.e., low-integer), MMR ( Table 2), suggesting that these resonances may be responsible for helping to temporarily trap these objects in the main belt during the integration period, presumably by providing protection against close encounters with Jupiter (e.g., Gladman et al, 1997;Malyshkin & Tremaine, 1999;Gabryszewski & W lodarczyk, 2003;Pittich et al, 2004;Brož et al, 2005;Carvano et al, 2008;Fernández et al, 2014).…”

“…Values of e (and therefore q and Q) and i, how- ever, are seen to change dramatically for most particles, though the timescales of these changes varies from particle to particle. Notably, we see that while the semimajor axes of most of these highlighted particles appear to be strongly associated with the nearby MMRs listed in Table 2 over at least some portion of the integrations, some exhibit irregular fluctuations (e.g., particles C, D, and G) or small consistent offsets from the suspected associated MMR (e.g., particles E, F, and H), suggesting that some of these particles are additionally influenced by other nearby and possibly overlapping two-and three-body MMRs (where overlapping MMRs can actually impart additional short-term stability in certain cases; Gabryszewski & W lodarczyk, 2003), or other secular effects. For reference, we show more detailed plots (Figures 10 and 11) of each particle's evolution in 100 yr intervals over the final ∼50 000 years of our integrations (over which most of these particles have attained consistently main-belt-like orbits) of a, e, i, the longitude of perihelion, , and the relevant resonant angle, θ (corresponding to the suspected associated MMR for each particle listed in Table 2), where θ is given by θ = (p + q)λ J − pλ − q (4)…”