Related papers: Relative Equilibria and Periodic Orbits in a Binar…
The rectilinear elliptic restricted Three Body Problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity $e'=1$, but the collision of the…
Space missions have discovered a large number of exoplanets evolving in (or close to) mean-motion resonances (MMRs) and resonant chains. Often, the published data exhibit very high uncertainties due to the observational limitations that…
In this work we study the orbital stability/instability in the energy space of a specific family of periodic wave solutions of the general $\phi^{4n}$-model for all $n\in\mathbb{N}$. This family of periodic solutions are orbiting around the…
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…
Stability of Hilda Asteroids in the solar system around the 3:2 resonance point is analyzed in terms of the Sun-Jupiter-asteroid elliptic restricted three-body problem. We show that the Hamiltonian of the system is well-approximated by a…
We show that under certain astrophysical conditions a binary system consisting of two compact objects can be stabilized against indefinite shrinking of orbits due to the emission of gravitational radiation. In this case, the lighter binary…
Asteroid body-fixed hovering problem using nonideal solar sail models in a compact form with controllable sail area is investigated in this paper. The nonlinear dynamic equations for the hovering problem are constructed for a spherically…
A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near asteroids are very…
Recent studies of accretion onto supermassive black hole binaries suggest that much, perhaps most, of the matter eventually accretes onto one hole or the other. If so, then for binaries whose inspiral from ~1 pc to 0.001 - 0.01 pc is driven…
Context. Binary asteroids are present in all populations of the Solar System, from near-Earth to trans-Neptunian regions. As is true for the small Solar System bodies (SSSBs), binary asteroids generally offer valuable insights into the…
We consider the Newtonian 5-body problem in the plane, where 4 bodies have the same mass m, which is small compared to the mass M of the remaining body. We consider the (normalized) relative equilibria in this system, and follow them to the…
Studying the orbital stability of multi-planet systems is essential to understand planet formation, estimate the stable time of an observed planetary system, and advance population synthesis models. Although previous studies have primarily…
We present the first dynamical solution of the triple asteroid system (45) Eugenia and its two moons Petit-Prince (Diameter~7 km) and S/2004 (45) 1 (Diameter~5 km). The two moons orbit at 1165 and 610 km from the primary, describing an…
In this paper, we extend the basic model of the restricted four-body problem introducing two bigger dominant primaries $m_1$ and $m_2$ as oblate spheroids when masses of the two primary bodies ($m_2$ and $m_3$) are equal. The aim of this…
Astrometric observations of resolved binaries provide estimates of orbital periods and will eventually lead to measurement of dynamical masses. Only a few very low mass star and brown dwarf masses have been measured to date, and the…
Since the discovery of the figure-8 orbit for the three-body problem [Moore 1993] a large number of periodic orbits of the n-body problem with equal masses and beautiful symmetries have been discovered. However, most of those that have…
Goal of the presented research is to construct simplified model of the core-halo structures in binary systems. Examples are provided by Thorne-Zytkov objects, hot Jupiters, protoplanets with large moons, red supergiants in binaries and…
The Stark problem is Kepler problem with an external constant acceleration. In this paper, we study the periodic orbits for Stark problem for both planar case and spatial case. We have conducted a detailed analysis of the invariant tori and…
The recent detection of the third planet in Kepler-47 has shown that binary stars can host several planets in circumbinary orbits. To understand the evolution of such systems we have performed two-dimensional hydrodynamic simulations of the…
The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on…