Related papers: The Kepler map in the three-body problem
A large variety of periodic tables of the chemical elements have been proposed. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. The periodic table…
We outline an approach yielding proper motions with higher precision than exists in present catalogs for a sample of stars in the Kepler field. To increase proper motion precision we combine first moment centroids of Kepler pixel data from…
The four-spacecraft formation is essential for measurements of various physical fields. The use of this formation on substantially elliptical heliocentric Kepler orbits allows measuring gradients of gravitation field in Solar system. The…
A significant fraction of Kepler systems are closely-packed, largely coplanar and circular. We study the stability of a 6-planet system, Kepler-11, to gain insights on the dynamics and formation history of such systems. Using a technique…
Exact results are derived, specifically the perihelion shift and the Kepler orbit, for a bound test particle in the Schwarzschild metric with cosmological constant $\Lambda=0$. A series expansion, of $\Delta\phi = 2(2(1-2M/p(3-e))^{-1/2}…
A brief excursion into the three-body problem in quantum mechanics is presented for graduate students or researchers in nuclear physics. Starting from single-particle coordinates, the three-body Schr\"{o}dinger equation is systematically…
The energy, the $p$-energy ($p\in\mathbb{R}$ with $p\geq 2$) and the extrinsic $k$-energy ($k\in\mathbb{N}$) for maps between Riemannian manifolds are central objects in the geometric calculus of variations. The equator map from the unit…
The Melnikov method is applied to a class of generalized Ziegler pendulums. We find an analytical form for the separatrix of the system in terms of Jacobian elliptic integrals, holding for a large class of initial conditions and parameters.…
In this paper we consider the circular restricted three body problem which models the motion of a masless body under the influence of the Newtionan gravitational force caused by two other bodies, the primaries, which move along cicular…
We describe two exotic systems of classical mechanics: the McIntosh-Cisneros-Zwanziger ('MICZ') Kepler system, of motion of a charged particle in the presence of a modified dyon; and Gibbons and Manton's description of the slow motion of…
The Kepler problem is a physical problem about two bodies which attract each other by a force proportional to the inverse square of the distance. The MICZ-Kepler problems are its natural cousins and have been previously generalized from…
In the three dimensional flat space any classical Hamiltonian, which has five functionally independent integrals of motion, including the Hamiltonian, is characterized as superintegrable. Kalnins, Kress and Miller have proved that, in the…
Exploiting the symmetry of the regular icosahedron, Peter Doyle and Curt McMullen constructed a solution to the quintic equation. Their algorithm relied on the dynamics of a certain icosahedral equivariant map for which the icosahedron's…
Analyzing the available photometry from the Kepler satellite and other databases, we performed detailed light curve modeling of 10 eclipsing binary systems that were found to exhibit a periodic modulation of their orbital periods. All of…
The formation and disappearance of spiral arms are studied by focusing on jammed Keplerian gas in a coupled map lattice (CML) with a minimal set of procedures for simulating diverse patterns in astronomical objects. The CML shows that a…
The quantum principle of relativity (QPR) puts forward an ambitious idea: extend special relativity with a formally superluminal branch of Lorentz-type maps, and treat the resulting consistency constraints as hints about why quantum theory…
Einstein used 4-dimensional space time geometry to explain gravity. However, in 1962, Baierlein, Sharp and Wheeler proposed a Jacobi type timeless Lagrangian based on the 3-dimensional geometry of space to reproduce the same physics. In…
We present a comprehensive study of phase curves and secondary eclipses in the Kepler data set using all data from 16 quarters that were available in 2013-2014. Our sample consists of 20 confirmed planets with R_p > 4 R_e ,P < 10d, V_mag <…
Kepler is a space telescope that searches Sun-like stars for planets. Its major goal is to determine {\eta}_Earth, the fraction of Sunlike stars that have planets like Earth. When a planet 'transits' or moves in front of a star, Kepler can…
The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy $E$, the axial component of the angular momentum, $L_{z}$, and Carter's constant $Q$. These parameters are obtained by…