相关论文: Satellite dynamics on the Laplace surface

We study the shape stability of disks moving in an external Laplacian field in two dimensions. The problem is motivated by the motion of ionization fronts in streamer-type electric breakdown. It is mathematically equivalent to the motion of…

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,…

We study the dynamics of $N$ point vortices on a rotating sphere. The Hamiltonian system becomes infinite dimensional due to the non-uniform background vorticity coming from the Coriolis force. We prove that a relative equilibrium formed of…

Recent discoveries of several transiting planets with clearly non-zero eccentricities and some large inclinations started changing the simple picture of close-in planets having circular and well-aligned orbits. Two major scenarios to form…

Satellite tracking involves sending electromagnetic signals to Earth. Both the orbit of the spacecraft and the electromagnetic signals themselves are affected by the curvature of spacetime. The arrival time of the pulses is compared to the…

The origin of the high inclination of Uranus' spin-axis (Uranus' obliquity) is one of the great unanswered questions about the Solar system. Giant planets are believed to form with nearly zero obliquity, and it has been shown that the…

The insolation a planet receives from its parent star is the main driver of the climate and depends on the planet's orbital configuration. Planets with non-zero obliquity and eccentricity experience seasonal insolation variations. As a…

Planetary satellites are an integral part of the heirarchy of planetary systems. Here we make two predictions concerning their formation. First, primordial satellites, which have an array of distinguishing characteristics, form only around…

Let $-\Delta_{\cal S}$ be the Laplace operator in ${\cal S} \subset \mathbb{R}^3$ on a waveguide shaped surfaces, i.e., ${\cal S}$ is built by translating a closed curve in a constant direction along an unbounded spatial curve. Under the…

The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…

The semiclassical orbitals of a relativistic electron on a rotating sphere threaded by an intense magnetic dipole field are examined. Several physically distinct regimes emerge, depending on the relative sizes of the mass, total energy,…

We numerically investigate the orbital dynamics of a two-dimensional galactic model, emphasizing the influence of stable and unstable manifolds on the evolution of orbits. In our analysis we use evaluations of the system's Lagrangian…

The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on…

Observations of the spatial distribution and kinematics of young stars in the Galactic centre can be interpreted as showing that the stars occupy one, or possibly two, discs of radii ~0.05-0.5 pc. The most prominent (`clockwise') disc…

The long-term dynamics of the geostationary Earth orbits (GEO) is revisited through the application of canonical perturbation theory. We consider a Hamiltonian model accounting for all major perturbations: geopotential at order and degree…

Sufficiently massive growing giant planets have circumplanetary disks, and the capture of solid bodies by the disks would likely influence the growth of the planets and formation of satellite systems around them. In addition to dust…

Context. The 98{\deg}-obliquity of Uranus is commonly attributed to giant impacts that occurred at the end of the planetary formation. This picture, however, is not devoid of weaknesses. Aims. On a billion-year timescale, the tidal…

When a planetary tidal disk -like Saturn's rings- spreads beyond the Roche radius (inside which planetary tides prevent aggregation), satellites form and migrate away. Here, we show that most regular satellites in the solar system probably…

We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…

The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an…