On the origin of chaotic behavior in the 21 Kirkwood gap

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.

supporting

confidence: 87%

“…The third paper was by Henrard and Caranicolas (1990) and concems the 3/1 case. Lemaitre and Henrard (1990).…”

mentioning

confidence: 99%

Review of the dynamics in the Kirkwood gaps

Moons

1997

“…In fact, dynamical system with two degrees of freedom is replete of secondary resonances between the main frequencies of the problem. The appearance of these secondary resonances depends on the region of phase space and the fixed parameters (Lichtenberg and Lieberman 1983;Lemaitre and Henrard 1990), and their importance in the dynamics of systems of satellites is discussed in several papers (Tittemore and Wisdom 1990;Malhotra and Dermott 1990;Champenois and Vienne 1999).…”

Section: Secondary Resonancesmentioning

confidence: 98%

Dynamics of two satellites in the 2/1 Mean–Motion resonance: application to the case of Enceladus and Dione

Callegari

Yokoyama

2007

The dynamics of a pair of satellites similar to Enceladus-Dione is investigated with a two-degrees-of-freedom model written in the domain of the planar general three-body problem. Using surfaces of section and spectral analysis methods, we study the phase space of the system in terms of several parameters, including the most recent data. A detailed study of the main possible regimes of motion is presented, and in particular we show that, besides the two separated resonances, the phase space is replete of secondary resonances.

“…9a. A similar phenomenon was largely discussed by Lemaltre and Henrard (1990) studying the 2/1 mean motion resonance. We will come back to this problem in a further paper, while discussing the dynamics in the v5 resonance.…”

Section: An Estimation Of the Quadratic Term In The Massesmentioning

confidence: 88%

Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location

Morbidelli

Henrard

1991

In this paper a theoretical perturbation approach to the problem of the dynamics in secular resonance is exposed. This approach avoids any expansion of the main term of the Hamiltonian (linear term in the masses) with respect to the eccentricity or the inclination of the asteroid, in order to achieve results valid for any value of these variables. Moreover suitable action-angle variables are introduced to take properly into account the dynamics related to the motion of the argument of perihelion of the asteroid, which is relevant at high inclination. A class of secular resonances wider than that usually considered is found. An explicit computation of the location of the main secular resonances, estimating also the contribution of the quadratic term in the masses by means of classical series expansion, is reported in the last sections. The accuracy of computations obtained by series expansion is discussed in the paper.