Related papers: Relative Equilibria and Periodic Orbits in a Binar…
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 report the discovery of 24 spectroscopic binary companions to giant stars. We fully constrain the orbital solution for 6 of these systems. We cannot unambiguously derive the orbital elements for the remaining stars because the phase…
Asteroid families are formed as the result of collisions. Large fragments are ejected with speeds of the order of the escape velocity from the parent body. After the family formation, the fragments' orbits evolve in the space of proper…
We report on the orbital architectures of Kepler systems having multiple planet candidates identified in the analysis of data from the first six quarters of Kepler data and reported by Batalha et al. (2013). These data show 899 transiting…
Castor is a system of six stars in which the two brighter objects, Castor A and B, revolve around each other every $\sim$450 yr and are both short-period spectroscopic binaries. They are attended by the more distant Castor C, which is also…
At the Lagrange relative equilibrium of the three-body problem, for all values of the masses, the elliptic eigenvalues associated with vertical eigenvectors give rise to spatial quasi-periodic orbits, which become periodic in a rotating…
This study investigates the different novel forms of the dynamical equations of a particle orbiting a rotating asteroid and the effective potential, the Jacobi integral, etc. on different manifolds. Nine new forms of the dynamical equations…
By introducing simple topological constraints and applying a binary decomposition method, we show the existence of a set of prograde double-double orbits for any rotation angle $\theta \in (0, \pi/7]$ in the equal-mass four-body problem. A…
We investigate the orbital stability of a tilted circumbinary planetary system with three giant planets. The planets are spaced by a constant number ($\Delta$) of mutual Hill radii in the range $\Delta=3.4-12.0$ such that the period ratio…
We have numerically explored the stable planetary geometry for the multiple systems involved in a 2:1 mean motion resonance, and herein we mainly study the HD 82943 system by employing two sets of the orbital parameters (Mayor et al. 2004;…
A considerable number of astrometric binaries whose positions on the sky do not obey the standard model of mean position, parallax and linear proper motion, were observed by the Hipparcos satellite. Some of them remain non-discovered, and…
We prove the existence of periodic orbits of the two fixed centers problem bifurcating from the Kepler problem. We provide the analytical expressions of these periodic orbits when the mass parameter of the system is sufficiently small.
We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and…
Current observations indicate that the planet formation process often produces multiple planet systems with nearly circular orbits, regular spacing, a narrow range of inclination angles, and similar planetary masses of order $m_{\rm…
Families of asteroids generated by the collisional fragmentation of a common parent body have been identified using clustering methods of asteroids in their proper orbital element space. An alternative method has been developed in order to…
HR 8799 is currently the only multiple-planet system that has been detected with direct imaging, with four giant planets orbiting at large separations from this young late A star. Orbital motion provides insight into the stability, and…
We investigate the equilibrium points and orbits around asteroid 1333 Cevenola by considering the full gravitational potential caused by the 3D irregular shape. The gravitational potential and effective potential of asteroid 1333 Cevenola…
Given two positive real numbers $M$ and $m$ and an integer $n>2$, it is well known that we can find a family of solutions of the $(n+1)$-body problem where the body with mass $M$ stays put at the origin and the other $n$ bodies, all with…
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry…
A number of irregular moons of the Jovian planets have recently been discovered. Most adequate way of their origin is capture, but detailed mechanism is unknown. A few possibilities are discussed: collisions, gas drag, tidal destruction of…