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Among the numerous discoveries resulting from the {\it Kepler} mission are a plethora of compact planetary systems that provide deep insights into planet formation theories. The architecture of such compact systems also produces unique…
We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and…
An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…
We discuss the existence and stability of circular orbits of a relativistic point particle moving in a central force field. The stability condition is somewhat more restrictive in Special Relativity. In the particular case of attractive…
In this paper, we explore the orbital stability of smooth solitary wave solutions to the modified Camassa-Holm equation with cubic nonlinearity. These solutions, which exist on a nonzero constant background $k$, are unique up to translation…
This paper deals with the application of the creep tide theory (Ferraz-Mello, CeMDA 116, 109, 2013) to the rotation of close-in satellites, Mercury, close-in exoplanets and their host stars. The solutions show two extreme cases: close-in…
The possibility of measuring the post-Newtonian gravitoelectric correction to the orbital period of a test particle freely orbiting a spherically symmetric mass in the Solar System is analyzed. It should be possible, in principle, to detect…
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…
Planets that orbit only one of the stars in stellar binary systems (i.e., circumstellar) are dynamically constrained to a limited range of orbital parameters and thus understanding conditions on their stability is of great importance in…
Multiple analytical and empirical stability criteria have been derived in the literature for two planet systems. But, the dependence of the stability limit on the initial mutual inclination between the inner and outer orbits is not well…
Dynamical studies of asteroid populations in retrograde orbits, that is with orbital inclinations greater than 90 degrees, are interesting because the origin of such orbits is still unexplained. Generally, the population of retrograde…
We calculate the precession of Keplerian orbits under the influence of arbitrary central-force perturbations. Our result is in the form of a one-dimensional integral that is straightforward to evaluate numerically. We demonstrate the…
The Kozai mechanism for exponentially exciting eccentricity of a Keplerian orbit by a distant perturber is extended to a general perturbing potential. In particular, the case of an axisymmetric potential is solved analytically. The analysis…
In this work we revisit the problem of the dynamical stability of hierarchical triple systems with applications to circumbinary planetary orbits. We carry out more than 3 10^8 numerical simulations of planets between the size of Mercury and…
We present three-dimensional atmospheric circulation models of a hypothetical "warm Jupiter" planet, for a range of possible obliquities from 0-90 degrees. We model a Jupiter-mass planet on a 10-day orbit around a Sun-like star, since this…
The planetary restricted three-body problem (RTBP) is considered. The primary mass M is much more than another masses mj, i=1..N, which revolve around M. The massless probe particle m moves on elliptic orbit, is perturbed by mj. It is well…
Multi-planetary systems are prevalent in our Galaxy. The long-term stability of such systems may be disrupted if a distant inclined companion excites the eccentricity and inclination of the inner planets via the eccentric Kozai-Lidov…
We present exact black hole solutions endowed with magnetic charge coming from exponential and logarithmic nonlinear electrodynamics (NLED). Classically, we analyze the null and timelike geodesics, all of which contain both the bound and…
We numerically and analytically work out the first-order post-Newtonian (1pN) orbital effects induced on the semimajor axis $a$, the eccentricity $e$, the inclination $I$, the longitude of the ascending node $\Omega$, the longitude of…
In this study, the potential locations of asteroidal small satellites (also called moonlets) with quasi-circular mutual orbit are analyzed. For the motion of the moonlets, only the solar gravity perturbation and the primary's 2nd…