Related papers: Variations in orbital elements of planets
The existence and bifurcation of homoclinic orbits in planar piecewise linear homogeneous systems with two regions separated by a discontinuity boundary are investigated in this paper. In addition, existence of periodic orbits and stability…
Thousands of confirmed and candidate exoplanets have been identified in recent years. Consequently, theoretical research on the formation and dynamical evolution of planetary systems has seen a boost, and the processes of planet-planet…
In a previous paper we introduced examples of Hamiltonian mappings with phase space structures resembling circle packings. It was shown that a vast number of periodic orbits can be found using special properties. We now use this information…
Understanding the consequences of the gravitational interaction between a star and a planet is fundamental to the study of exoplanets. The solution of the two-body problem shows that the planet moves in an elliptical path around the star…
We investigated the underlying architecture of planetary systems by deriving the distribution of planet multiplicity (number of planets) and the distribution of orbital inclinations based on the sample of planet candidates discovered by the…
It is shown herein that planets with eccentric orbits are more likely to transit than circularly orbiting planets with the same semimajor axis by a factor of (1-e^2)^{-1}. If the orbital parameters of discovered transiting planets are…
Explicit formulas for {\sl orbital carriers} of periods $4$, $5$, and $6$ are reported for discrete-time quadratic dynamics. A systematic investigation of {\sl orbital inheritance} for periods as high as $k\leq 12$ is also reported.…
The oscillations of the test particles on circular orbits in field of super-extremal charged central object are researched. The formulae for oscillation frequencies are obtained in cases of circular orbits perturbations caused by small…
We broaden the investigation of the dynamical properties of tidally perturbed, rotating star clusters by relaxing the traditional assumptions of coplanarity, alignment, and synchronicity between the internal and orbital angular velocity…
Exoplanets are often found with short periods or high eccentricities, and multiple-planet systems are often in resonance. They require dynamical theories that describe more extreme motions than those of the relatively placid planetary…
Graph maps that are homotopic to the identity and that permute the vertices are studied. Given a periodic point for such a map, a {\em rotation element} is defined in terms of the fundamental group. A number of results are proved about the…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
The orbital parameters of extra-solar planets have a significant impact on the probability that the planet will transit the host star. This was recently demonstrated by the transit detection of HD 17156b whose favourable eccentricity and…
We study the classical 120-degree and related orbital models. These are the classical limits of quantum models which describe the interactions among orbitals of transition-metal compounds. We demonstrate that at low temperatures these…
The motion of a classical spinning test particle in the field of a weak plane gravitational wave is studied. It is found that the characteristic dimensions of the particle's orbit is sensitive to the ratio of the spin to the mass of the…
The excitation of the axial quasi-normal modes of a relativistic star by scattered particles is studied by evolving the time dependent perturbation equations. This work is the first step towards the understanding of more complicated…
This chapter reviews the most recent advancements on the topic of terrestrial and giant planet interiors, including Solar System and extrasolar objects. Starting from an observed mass-radius diagram for known planets in the Universe, we…
The scattering determinant for the scattering of waves from several obstacles is considered in the case of elastic solids with voids. The multi-scattering determinant displays contributions from periodic ray-splitting orbits. A discussion…
It is argued that apart from the well known dependence of the Am phenomenon on the mass, age (effective temperature, gravity) and rotation there is also a complex dependence on the orbital parameters in binary systems. This is why the…
There are several physical processes that mediate the interaction between an exoplanet and its host star, with the four main ones being due to magnetic, particle (stellar outflow), radiative and tidal interactions. These interactions can be…