Related papers: Planetary Orbital Equations in Externally-Perturbe…
We study the stability of circular orbits of the electromagnetic two-body problem in an electromagnetic setting that includes retarded and advanced interactions. We give a method to derive the equations of tangent dynamics about circular…
Motivated by the large number of compact extrasolar planetary systems discovered by the Kepler Mission, this paper considers perturbations due to possible additional outer planets. The discovered compact systems sometimes contain multiple…
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…
We present a semi-analytical correction to the seminal solution for the secular motion of a planet's orbit under gravitational influence of an external perturber derived by Heppenheimer (1978). A comparison between analytical predictions…
(Abridged) In planetary systems with two or more giant planets, dynamical instabilities can lead to collisions or ejections through strong planet--planet scattering. Previous studies for simple initial configurations with two equal-mass…
Tidally distorted rotating stars and gaseous planets are subject to a well-known linear fluid instability -- the elliptical instability. It has been proposed that this instability might drive enough energy dissipation to solve the…
Transiting planets are generally close enough to their host stars that tides may govern their orbital and thermal evolution of these planets. We present calculations of the tidal evolution of recently discovered transiting planets and…
In this paper we consider a Vlasov or collisionless Boltzmann equation describing the dynamics of planetary rings. We propose a simple physical model, where the particles of the rings move under the gravitational Newtonian potential of two…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
Gravitational systems in astrophysics often comprise a body -- the primary -- that far outweights the others, and which is taken as the centre of the reference frame. A fictitious acceleration, also known as the indirect term, must…
We analytically compute the orbital effects induced on the motion of a spinning particle geodesically traveling around a central rotating body by the general relativistic two-body spin-spin and spin-orbit interactions. We use the weak-field…
As a planet orbits, it causes periodic modulations in the light curve of its host star. Due to the combined effects of the planet raising tides on the host star, relativistic beaming of the starlight, and reflection of light off the…
The competition between the torques induced by solid and thermal tides drives the rotational dynamics of Venus-like planets and super-Earths orbiting in the habitable zone of low-mass stars. The tidal responses of the atmosphere and…
We analyze in this paper the existence of the "out-of-plane" equilibrium points in the restricted three-body problem with oblateness. From the series expansion of the potential function of an oblate asteroid, we show analytically all…
This chapter concerns the long-term dynamical evolution of planetary systems from both theoretical and observational perspectives. We begin by discussing the planet-planet interactions that take place within our own Solar System. We then…
Mutually misaligned circumbinary planets may form in a warped or broken gas disc or from later planet-planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large…
We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric…
This work introduces a new set of orbital elements to fully represent the zonal harmonics problem around an oblate celestial body. This new set of orbital elements allows to obtain a complete linear system for the unperturbed problem and,…
The problem of the two-body gravitational interaction has been solved numerically based on the classical mechanics principles. One of the bodies is a deformable three-axis ellipsoid (central body) and the other is a material point…
Nearly half of the exoplanets found within binary star systems reside in very wide binaries with average stellar separations beyond 1,000 AU (1 AU being the Earth-Sun distance), yet the influence of such distant binary companions on…