Related papers: The Kepler Problem: Orbit Cones and Cylinders

A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables…

We consider the 4-body problem in spaces of constant curvature and study the existence of spherical and hyperbolic rectangular solutions, i.e. equiangular quadrilateral motions on spheres and hyperbolic spheres. We focus on relative…

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…

Planetary systems have their origin in the gravitational collapse of a cloud of gas and dust. Through a process of accretion, is formed a massive star and a disk of planetesimals orbiting the star. Using a formalism analogous to quantum…

Spirals in protoplanetary discs have been used to locate the potential planet in discs. Since only the spiral shape from a circularly orbiting perturber is known, most previous works assume that the planet is in a circular orbit. We develop…

Here we provide an overview of what is known, and what is not known, about an interesting dynamical system known as the Kepler-Heisenberg problem. The main idea is to pose a version of the classical Kepler problem of planetary motion, but…

This chapter of the book Planetary Ring Systems addresses the origin of planetary rings, one of the least understood processes related to planet formation and evolution. Whereas rings seem ubiquitous around giant planets, their great…

One can formulate the classical Kepler problem on the Heisenberg group, the simplest sub-Riemannian manifold. We take the sub-Riemannian Hamiltonian as our kinetic energy, and our potential is the fundamental solution to the Heisenberg…

We study circular orbits that are tilted with respect to the equatorial plane around a Kerr black hole. We write the equations for the parameters of a tilted circular orbit in terms of the orbit's radius and the Carter constant, or…

I describe models for the formation of planetary systems surrounding the remnants of stellar mergers and collisions. I focus primarily on models for the viscous evolution of disks suitable for the formation of the planets surrounding the…

We recommend an intensive effort to survey and understand the obliquity distribution of small close-in extrasolar planets over the coming decade. The orbital obliquities of exoplanets--i.e., the relative orientation between the planetary…

Orbits of known extrasolar planets that are located outside the tidal circularization regions of their parent stars are often substantially eccentric. By contrast, planetary orbits in our Solar System are approximately circular, reflecting…

Study of the classical motion of two identical particles on a plane subject to non-Coulomb potentials in a constant magnetic field presented in polar coordinates. With the rigorous analysis of the potentials and the constants of motion, we…

We investigate, by means of numerical simulations, the possibility of forming counter-rotating old stellar components by major mergers between an elliptical and a spiral galaxy. We show that counter-rotation can appear both in dissipative…

The formation, structure and evolution of protoplanetary discs is considered. The formation of giant planets within the environment of these models is also discussed.

This is a paper about triangle cubics and conics in classical geometry with elements of projective geometry. In recent years, N.J. Wildberger has actively dealt with this topic using an algebraic perspective. Triangle conics were also…

Formulas about the side lengths, diagonal lengths or radius of the circumcircle of a cyclic polygon in Euclidean geometry, hyperbolic geometry or spherical geometry can be unified.

Planet formation is often considered in the context of one circumstellar disk around one star. Yet stellar binary systems are ubiquitous, and thus a substantial fraction of all potential planets must form and evolve in more complex,…

The herein presented analytical framework fully describes the motion of coplanar systems consisting of a stellar binary and a planet orbiting both stars on orbital as well as secular timescales. Perturbations of the Runge-Lenz vector are…