Tadashi Yokoyama

On the orbits of the outer satellites of Jupiter

In this work we study the basic aspects concerning the stability of the outer satellites of Jupiter. Including the eects of the four giant planets and the Sun we study a large grid of initial conditions. Some important regions where satellites cannot survive are found. Basically these regions are due to Kozai and other resonances. We give an analytical explanation for the libration of the pericenters

Effects of the planetary migration on some primordial satellites of the outer planets - I. Uranus’ case

J. Another dierent center is also found. The period and amplitude of these librations are quite sensitive to initial conditions, so that precise observational data are needed for Pasiphae and Sinope. The eect of Jupiters mass variation is briefly presented. This eect can be responsible for satellite capture and also for locking

Effect of Jupiter's mass growth on satellite capture The prograde case

J in temporary libration.

Possible effects of secular resonances in Phobos and Triton

The Nice model of the dynamical instability and migration of the giant planets can explain many properties of the present solar system, and can be used to constrain its early architecture. In the jumping-Jupiter version of the Nice model, required from the terrestrial planet constraint and dynamical structure of the asteroid belt, Jupiter has encounters with an ice giant. Here, we study the survival of the Galilean satellites in the jumping-Jupiter model. This is an important concern because the ice-giant encounters, if deep enough, could dynamically perturb the orbits of the Galilean satellites and lead to implausible results. We performed numerical integrations where we tracked the effect of planetary encounters on the Galilean moons. We considered three instability cases from Nesvorný & Morbidelli that differed in the number and distribution of encounters. We found that in one case, where the number of close encounters was relatively small, the Galilean satellite orbits were not significantly affected. In the other two, the orbital eccentricities of all moons were excited by encounters, Callistos semimajor axis changed, and, in a large fraction of trials, the Laplace resonance of the inner three moons was disrupted. The subsequent evolution by tides damps eccentricities and can recapture the moons in the Laplace resonance. A more important constraint is represented by the orbital inclinations of the moons, which can be excited during the encounters and not appreciably damped by tides. We find that one instability case taken from Nesvorný & Morbidelli clearly does not meet this constraint. This shows how the regular satellites of Jupiter can be used to set limits on the properties of encounters in the jumping-Jupiter model, and help us to better understand how the early solar system evolved.

Application of Wisdom's perturbative method for 5 : 2 and 7 : 3 resonances

Context. During the first hundred million years after the formation of our solar system, the four giant planets are believed to have migrated significantly (by up ≈20 AU). The current scenario and dynamics of the satellites of these planets must be the result of both the initial conditions of their formation and this early extensive migrational episode. Aims. We examine the effects of the migration on the primordial satellites of Uranus. Methods. We use the Nice model to generate templates for the evolution of the four giant planets and record the time history of these planets and important close encounters. The satellites are then added to Uranus and these objects are integrated according to the dynamics stored in the templates. Results. We show that Oberon is the outermost regular satellite of Uranus that is able to resist the close encounters during the extensive migrational episode. Some theories predict that Uranus’ satellites can form out to a 57 RU distance from the planet, but we show that even those at ≈27 RU from the planet cannot support the instabilities that appeared during migration. Close objects, such as the current regular satellites of Uranus, can survive quite stably and we are able to place some constraints on the masses of the

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

Abstract The dynamics of some fictitious satellites of Venus and Mars are studied considering only solar perturbation and the oblateness of the planet, as disturbing forces. Several numerical integrations of the averaged system, taking different values of the obliquity of ecliptic (e), show the existence of strong chaotic motion, provided that the semi major axis is near a critical value. As a consequence, large increase of eccentricities occur and the satellites may collide with the planet or cross possible internal orbits. Even starting from almost circular and equatorial orbits, most satellites can easily reach prohibitive values. The extension of the chaotic zone depends clearly on the value of e, so that, previous regular regions may become chaotic, provided e increases sufficiently.

Expansion of the disturbing function for high eccentricity and large amplitude of libration

We study the effects of Jupiter mass growth in order to permanently capture prograde satellites. Adopting the restricted three-body problem, Sun-Jupiter-Particle, we performed numerical simulations backward in time while considering the decrease in Jupiter’s mass. We considered the particle’s initial conditions to be prograde, at pericenter, in the region 100R ≤ a ≤ 400R and 0 ≤ e ≤ 0.5. The results give Jupiter’s mass at the moment when the particle escapes from the planet. Such values give an indication of the conditions that are necessary for capture. An analysis of these results shows that prograde satellite capture is more complex than a retrograde one. It occurs in a two-step process. First, when the particles get inside about 0.85RHill (Hills’ radius), they become weakly bound to Jupiter. Then, they keep migrating toward the planet with a strong decrease in eccentricity, while the planet is growing. The radial oscillation of the particles reduces significantly when they reach a radial distance that is less than about 0.45RHill from the planet. Three-dimensional simulations for the known prograde satellites of Jupiter were performed. The results indicate that Leda, Himalia, Lysithea, and Elara could have been permanently captured when Jupiter had between 50% and 60% of its present mass.

Some aspects of the dynamics of fictitious Earth's satellites

Abstract Due to the tides, the orbits of Phobos and Triton are contracting. While their semi major axes are decreasing, several possibilities of secular resonances involving node, argument of the pericenter and mean motion of the Sun will take place. In the case of Mars, if the obliquity ( e ), during the passage through some resonances, is not so small, very significant variations of the inclination will appear. In one case, capture is almost certain provided that e ⩾20°. For Triton there are also similar situations, but capture seems to be not possible, mainly because in S 1 state, Tritons orbit is sufficiently inclined (far) with respect to the Neptunes equator. Following Chyba et al. (Astron. Astrophys. 219 (1989) 123), a simplified equation that gives the evolution of the inclination versus the semi major axis, is derived. The time needed for Triton crash onto Neptune is longer than that one obtained by these authors, but the main difference is due to the new data used here. In general, even in the case of non-capture passages, some significant jumps in inclination and in eccentricities are possible.