Related papers: Stable Periodic Orbits for Spacecrafts around Mino…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
Outer satellites of the planets have distant, eccentric orbits that can be highly inclined or even retrograde relative to the equatorial planes of their planets. These irregular orbits cannot have formed by circumplanetary accretion and are…
The existence, radii and radial stability of the equatorial and non-equatorial (particularly, the polar) spherical orbits are discussed for particles with different conserved energy. The radii of these orbits generally are solutions of a…
An analytical approximation to periodic orbits in the circular restricted three-body problem is provided. The formulation given in this work is based in calculations known from classical mechanics, but with the addition of the necessary…
This work investigates experimentally and numerically the dynamics of rigid particles settling under gravity in a highly viscous fluid. We demonstrate that certain shapes: cones, crescent moons, arrowheads, and open flat rings reorient and…
The NEA 2001 SN263 is the target of the ASTER MISSION - First Brazilian Deep Space Mission. Araujo et al. (2012), characterized the stable regions around the components of the triple system for the planar and prograde cases. Knowing that…
The recently discovered planetary system in the binary GamCep was studied concerning its dynamical evolution. We confirm that the orbital parameters found by the observers are in a stable configuration. The primary aim of this study was to…
We study stability of a circular orbit of a spinning test particle in a Kerr spacetime. We find that some of the circular orbits become unstable in the direction perpendicular to the equatorial plane, although the orbits are still stable in…
A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the…
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…
The study of circular orbits offers profound insights into the structure of spacetime around black holes. While the topological properties of these orbits are well-established for neutral particles, the influence of electric…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
We consider the motion of massive and massless particles in a five-dimensional spacetime with a compactified extra-dimensional space where a black hole is localized, i.e., a caged black hole spacetime. We show the existence of circular…
We present our investigations of the physical and dynamical properties of selected Earth co-orbital asteroids. The photometric optical light curves as well as rotation periods and pole solutions for a sample of four Earth co-orbital…
We present a procedure for determination of positions and orbital elements, and associated uncertainties, of outer Solar System planets. The orbit-fitting procedure is greatly streamlined compared to traditional methods because acceleration…
We study almost periodic orbits of quantum systems and prove that for periodic time-dependent Hamiltonians an orbit is almost periodic if, and only if, it is precompact. In the case of quasiperiodic time-dependence we present an example of…
Off-equatorial circular orbits with constant latitudes (halo orbits) of electrically charged particles exist near compact objects. In the previous paper, we discussed this kind of motion and demonstrated the existence of minima of the…
We consider the Ostrovsky and short pulse models in a symmetric spatial interval, subject to periodic boundary conditions. For the Ostrovsky case, we revisit the classical periodic traveling waves and for the short pulse model, we…
We provide a constructive method designed in order to control the stability of a given periodic orbit of a general completely integrable system. The method consists of a specific type of perturbation, such that the resulting perturbed…
Asteroid (514107) Kaepaokaawela is the first example of an object in the 1/1 mean motion resonance with Jupiter with retrograde motion around the Sun. Its orbit was shown to be stable over the age of the Solar System which implies that it…