Fathi Namouni

The effect of eccentricity and inclination on the motion near the Lagrangian points L4 and L5

We study the effect of eccentricity and inclination on small amplitude librations around the equilibrium points L4 and L5 in the circular restricted three-body problem. We show that the effective libration centres can be displaced appreciably from the equilateral configuration. The secular extrema of the eccentricity as a function of the argument of pericentre are shifted by ∼25 °

Resonance capture at arbitrary inclination

Resonance capture is studied numerically in the three-body problem for arbitrary inclinations. Massless particles are set to drift from outside the 1:5 resonance with a Jupiter-mass planet thereby encountering the web of the planets diverse mean motion resonances. Randomly constructed samples explore parameter space for inclinations from 0 to 180 deg with 5deg increments totalling nearly 6x10^5 numerical simulations. Thirty resonances internal and external to the planets location are monitored. We find that retrograde resonances are unexpectedly more efficient at capture than prograde resonances and that resonance order is not necessarily a good indicator of capture efficiency at arbitrary inclination. Capture probability drops significantly at moderate sample eccentricity for initial inclinations in the range [10deg,110deg]. Orbit inversion is possible for initially circular orbits with inclinations in the range [60deg,130deg]. Capture in the 1:1 coorbital resonance occurs with great likelihood at large retrograde inclinations. The planets orbital eccentricity, if larger than 0.1, reduces the capture probabilities through the action of the eccentric Kozai-Lidov mechanism. A capture asymmetry appears between inner and outer resonances as prograde orbits are preferentially trapped in inner resonances. The relative capture efficiency of retrograde resonance suggests that the dynamical lifetimes of Damocloids and Centaurs on retrograde orbits must be significantly larger than those on prograde orbits implying that the recently identified asteroids in retrograde resonance, 2006 BZ8, 2008 SO218, 2009 QY6 and 1999 LE31(Morais and Namouni, 2013, MNRAS 436, L30) may be among the oldest small bodies that wander between the outer giant planets.

Dynamical friction for accelerated motion in a gaseous medium

Dynamical friction arises from the interaction of a perturber and the gravitational wake it excites in the ambient medium. This interaction is usually derived assuming that the perturber has a constant velocity. In realistic situations, motion is accelerated as for instance by dynamical friction itself. Here, we study the effect of acceleration on the dynamical friction force. We characterize the density enhancement associated with a constantly accelerating perturber with rectilinear motion in an infinite homogeneous gaseous medium and show that dynamical friction is not a local force and that its amplitude may depend on the perturbers initial velocity. The force on an accelerating perturber is maximal between Mach 1 and Mach 2, where it is smaller than the corresponding uniform motion friction. In the limit where the perturbers size is much smaller than the distance needed to change the Mach number by unity through acceleration, a subsonic perturber feels a force similar to uniform motion friction only if its past history does not include supersonic episodes. Once an accelerating perturber reaches large supersonic speeds, accelerated motion friction is marginally stronger than uniform motion friction. The force on a decelerating supersonic perturber is weaker than uniform motion friction as the velocity decreases to a few times the sound speed. Dynamical friction on a decelerating subsonic perturber with an initial Mach number larger than 2 is much larger than uniform motion friction and tends to a finite value as the velocity vanishes in contrast to uniform motion friction.

The accelerated Kepler problem

The accelerated Kepler problem (AKP) is obtained by adding a constant acceleration to the classical two-body Kepler problem. This setting models the dynamics of a jet-sustaining accretion disk and its content of forming planets as the disk loses linear momentum through the asymmetric jet-counterjet system it powers. The dynamics of the accelerated Kepler problem is analyzed using physical as well as parabolic coordinates. The latter naturally separate the problem’s Hamiltonian into two unidimensional Hamiltonians. In particular, we identify the origin of the secular resonance in the AKP and determine analytically the radius of stability boundary of initially circular orbits that are of particular interest to the problem of radial migration in binary systems as well as to the truncation of accretion disks through stellar jet acceleration.

A numerical investigation of coorbital stability and libration in three dimensions

Motivated by the dynamics of resonance capture, we study numerically the coorbital resonance for inclination

Coorbital capture at arbitrary inclination

0\le I\le 180^\circ

Planetary science: Reckless orbiting in the Solar System

0≤I≤180∘ in the circular restricted three-body problem. We examine the similarities and differences between planar and three dimensional coorbital resonance capture and seek their origin in the stability of coorbital motion at arbitrary inclination. After we present stability maps of the planar prograde and retrograde coorbital resonances, we characterize the new coorbital modes in three dimensions. We see that retrograde mode I (R1) and mode II (R2) persist as we change the relative inclination, while retrograde mode III (R3) seems to exist only in the planar problem. A new coorbital mode (R4) appears in 3D which is a retrograde analogue to an horseshoe-orbit. The Kozai–Lidov resonance is active for retrograde orbits as well as prograde orbits and plays a key role in coorbital resonance capture. Stable coorbital modes exist at all inclinations, including retrograde and polar obits. This result confirms the robustness the coorbital resonance at large inclination and encourages the search for retrograde coorbital companions of the solar system’s planets.

On the Role of the Earth-Moon System in the Stability of the Inner Solar System

The classical disturbing function of the three-body problem is based on an expansion of the gravitational interaction in the vicinity of nearly coplanar orbits. Consequently, it is not suitable for the identification and study of resonances of the Centaurs and transneptunian objects on nearly polar orbits with the solar system planets. Here, we provide a series expansion algorithm of the gravitational interaction in the vicinity of polar orbits and produce explicitly the disturbing function to fourth order in eccentricity and inclination cosine. The properties of the polar series differ significantly from those of the classical disturbing function: the polar series can model any resonance as the expansion order is not related to the resonance order. The powers of eccentricity and inclination of the force amplitude of a