Related papers: The Kepler Problem: Orbit Cones and Cylinders
Most extrasolar planets currently known were discovered by means of an indirect method that measures the stellar wobble caused by the planet. We previously studied a triple system composed of a star and a nearby binary on circular coplanar…
For a given triangle $\triangle ABC$, we define two sequences of points on line $BC$ and provide their generalizations to real functions such that centers of circumscribed circles around $A$ and adjacent points in subsequences generate a…
The radial component of the motion of compact binary systems composed of neutron stars and/or black holes on eccentric orbit is integrated. We consider all type of perturbations that emerge up to second post-Newtonian order. These…
Stars and planets are the fundamental objects of the Universe. Their formation processes, though related, may differ in important ways. Stars almost certainly form from gravitational collapse and probably have formed this way since the…
A decomposition of the angular momentum of the classical electromagnetic field into orbital and spin components that is manifestly gauge invariant and general has been obtained. This is done by decomposing the electric field into its…
We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m+4$ points in general position on the weighted projective plane…
We analyze the observed distribution of the orbital eccentricity and period of binary radio pulsars in globular clusters using computational tools to simulate binary-single star interactions. Globular clusters have different groups of…
We investigate the orbital dynamics of circumbinary planetary systems with two planets around a circular or eccentric orbit binary. The orbits of the two planet are initially circular and coplanar to each other, but misaligned with respect…
Galactic microlensing has the capability to determine the position angle of the detected planets in a sky reference frame. By a broad enough statistics, it is possible to investigate possible anisotropies in the distribution of the orbital…
Stringy and disklike sources of the rotating compact astrophysical objects are considered on the base of the Kerr geometry. It is argued that analyticity of the Kerr solutions may result the appearance of singular strings, which may be the…
The analysis performed as well as extensive numerical simulations have revealed the possibility of the generation of homoclinic orbits as a result of homoclinic bifurcation in a porous pellet. A method has been proposed for the development…
The interaction between a planet located in the inner region of a disc and the warped outer region is studied. We consider the stage of evolution after the planet has cleared-out a gap, so that the planetary orbit evolves only under the…
We consider Hamiltonian functions of classical type, namely even and convex with respect to the generalized momenta. A brake orbit is a periodic solution of Hamilton's equations such that the generalized momenta are zero on two different…
The recent discovery of free-floating planets and their theoretical interpretation as celestial bodies, either condensed independently or ejected from parent stars in tight clusters, introduced an intriguing possibility. Namely, that some…
The motion of a particle with a spin in spherical harmonic oscillator potential with spin-orbit interaction is studied. We have focus our attention on spatial motion of wave packets, giving a description complementary to motion of spin…
When a planet passes in front of a starspot during a transit of its host star, it causes a small upward blip in the light curve. Modelling the transit with the starspot allows the size, brightness and position of the spot to be measured. If…
Let $\Aa_t$ be the directed quiver of type $\Aa$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank conditions to define the…
We develop an analytic model for transit timing variations produced by orbital conjunctions between gravitationally interacting planets. If the planetary orbits have tight orbital spacing, which is a common case among the Kepler planets,…
In this paper, a surface geometric constraint approach is used in designing the orbits of a solar sail. We solve the solar sail equation of motion by obtaining a generalized Laplace-Runge-Lenz (LRL) vector with the assumption that the cone…
Prior to the 1990s, speculations about the occurrence of planets around other stars were based only on planet formation theory, observations of circumstellar disks, and the knowledge that at least one seemingly ordinary star had managed to…