Li-Yong Zhou

Apsidal corotation in mean motion resonance: the 55 Cancri system as an example

The inner two planets around 55 Cancri were found to be trapped in a 3 : 1 mean motion resonance (MMR). In this paper, we study the dynamics of this extrasolar planetary system. Our numerical investigation confirms the existence of the 3 : 1 resonance and implies a complex orbital motion. Different stable motion types, with and without apsidal corotation, are found. Owing to the high eccentricities in this system, we apply a semi-analytical method based on a new expansion of the Hamiltonian of the planar three-body problem in the discussion. We analyse the occurrence of apsidal corotation in this MMR and its influence on the stability of the system.

The origin of the high-inclination Neptune Trojan 2005 TN53

Aims. We explore the formation and evolution of the highly inclined orbit of Neptune Trojan 2005 TN 53 . Methods. With numerical simulations, we investigated a possible mechanism for the origin of the high-inclination Neptune Trojans as captured into the Trojan-type orbits by an initially eccentric Neptune during its eccentricity damping and rapid inward migration, then migrating to the present locations locked in Neptunes 1:1 mean motion resonance. Results. Two 2005 TN 53 -type Trojans out of our 2000 test particles were produced with inclinations above 20°, moving on tadpole orbits librating around Neptunes leading Lagrange point.

Evidence for Lévy Random Walks in the Evolution of Comets from the Oort Cloud

With a simple map model, derived within the framework of the planar circular restricted three-body problem (SunuuJupiteruucomet), we study the dynamical evolution of near-parabolic comets under the perturbation of Jupiter. The commonly adopted random walk assumption about the energy evolution of the comets is examined. Numerical results show that for the comets on Jupiter-crossing orbits, due to the large energy changes with Jupiter per passage, the statistical evolution of the cometary energy follows a Lévy random walk, thus statistically the final energy parameter that a comet reaches is linked to the number of passages by a power law Kf ∼ nf. The mechanism that generates the Lévy random walk is explained in this model.

Evolution of Jovian planets in a self-gravitating planetesimal disk

Aims. We explore the orbital evolution of the four Jovian planets embedded in a self-gravitating planetesimal disk, along with the simultaneous accretion of small bodies by proto-Uranus and proto-Neptune. Methods. We adopt the code NBODY4 running on the GRAPE-type special-purpose computer for numerically simulating the primordial evolution of the outer Solar System, where the total gravitational forces due to the Sun, the four Jovian planets, and the massive planetesimals are all taken into account. Results. There is no significant accretion of proto-Uranus and proto-Neptune during their migration stage, only on the order of 0.1 Earth mass. The self-gravitating disk can provide a new replenishment of planetesimals outside a few AU beyond Neptune into the scattering zone, resulting in larger radial displacement of Neptune than in the non-self-gravitating disk. The present location of Neptune requires an original planetesimal disk outer edge at ∼35 AU. The distribution of the surviving planetesimals is very similar to the observed Kuiper belt.

The Role of Hyperbolic Invariant Sets in Stickiness Effects

With the standard map model, we study the stickiness effect of invariant tori, particularly the role of hyperbolic sets in this effect. The diffusion of orbits originated from the neighborhoods of hyperbolic points, periodic islands and torus is studied. We find that they possess similar diffusion rules, but the diffusion of orbits originated from the neighborhood of a torus is faster than that originated near a hyperbolic set. The numerical results show that an orbit in the neighborhood of a torus spends most of time around hyperbolic invariant sets. We also calculate the areas of islands with different periods. The decay of areas with the periods obeys a power law, and the absolute values of the exponents increase monotonously with the perturbation parameter. According to the results obtained, we conclude that the stickiness effect of tori is caused mainly by the hyperbolic invariant sets near the tori, and the diffusion speed becomes larger when orbits diffuse away from the torus.

Phase space transport in a map of asteroid motion

Abstract We have studied the chaotic transport in a nonlinear model directly applicable to asteroid motion. An exponential and an algebraic diffusion law are observed in different regions of the phase space. We have also investigated the effects of small perturbations and found they can not only accelerate but also decelerate the transport.

Structure of the phase space near Lagrange's triangular equilibrium points

Abstract We have constructed a mapping for the planar circular restricted three-body problem and used it to study the structure and stability of the phase space near the Lagrangian triangular points of libration. It is found that when the mass ratio of the primaries μ