Review of the dynamics in the Kirkwood gaps

Abstract

The study of mean motion resonance dynamics was motivated by the search for an explanation for the puzzling problem of the Kirkwood gaps. The most important contributions in this field within the last 32 years are reviewed here. At the beginning of that period, which coi'ncides with the first long-term numerical investigations of resonant motion, different hypotheses (collisional, gravitational, statistical and cosmological) to explain the origin of the gaps were still competing with each other. At present, a general theory, based on gravitational mechanisms only, is capable of explaining in a uniform way all the Kirkwood gaps except the 2/1 one. Indeed, in the 4/1, 3/1, 5/2 and 7/3 mean motion commensurabilities, the overlap of secular resonances leads to almost overall chaos where asteroids undergo large and wild variations in their orbital elements. Such asteroids, if not thrown directly into the Sun, are sooner or later subject to strong close encounters with the largest inner planets, the typical time scale of the whole process being of the order of a few million years. Unfortunately, this mechanism is not capable of explaining the 2/1 gap where the strong chaos produced by the overlapping secular resonances does not attain orbits with moderate eccentricity, of low inclination and with low to moderate amplitude of libration. In the light of the most recent studies, it appears that the 2/1 gap is the global consequence of slow diffusive processes. At present, the origin of these processes remains under study.

Orbital and temporal distributions of meteorites originating in the asteroid belt

“…The 3:l resonance is located at 2.5 AU. Wisdom (1985) showed that the resonance pushes all particles to Mars-crossing, and some to Earth-crossing orbits; later work (see Moons, 1997 for a review) showed that the resonance can pump particle eccentricities nearly to unity. Even at e = I , particles in the resonance do not quite cross the orbit of Jupiter; and in any case, the resonance protects them from Jovian close encounters.…”

Potential Jupiter-Family comet contamination of the main asteroid belt

“…Despite this lack of close planetary encounters to explain this particle's evolution onto a main-belt-like orbit, we note that besides having the largest T J,s of the eight particles, placing it very close to the ostensible boundary between asteroids and comets at the outset of the integrations, it begins (and ends) very close to the strongly chaotic 2:1 MMR with Jupiter, known for being capable of causing large fluctuations in eccentricities (cf. Murray, 1986;Moons, 1997;Nesvorný & Ferraz-Mello, 1997), and may also be subject to secular resonances (cf. Williams & Faulkner, 1981) and threebody MMRs (cf.…”

Mean Motion Resonances at High Eccentricities: The 2:1 and the 3:2 Interior Resonances

“…Planetary mean motion resonances may also exist in exoplanetary systems (Marcy et al 2001;Lee & Peale 2002;Fabrycky et al 2014;Petigura et al 2015;Nelson et al 2016;Mills et al 2016). Furthermore, unstable mean motion resonances are also of great significance; for example, the Kirkwood Gaps in the asteroid belt are linked to the unstable and chaotic MMRs with Jupiter (Moons 1996), and the stability of our planetary system itself is intimately related to the role of MMRs (Murray & Holman 1999) The phase space structure near MMRs is quite complex, and there is a considerable literature on their mathematical analysis. The planetary three body problem, with m 1 m 2 , m 3 , is the usual starting point of such studies.…”