Related papers: The Kepler Problem: Orbit Cones and Cylinders
The stellar spin orientation relative to the orbital planes of multiplanet systems are becoming accessible to observations. Here, we analyze and classify different types of spin-orbit evolution in compact multiplanet systems perturbed by an…
Images of both rotating celestial bodies (e.g., asteroids) and spheroidal planets with banded atmospheres (e.g., Jupiter) can contain features that are well-modeled as a circle of latitude (CoL). The projections of these CoLs appear as…
The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz $\gamma$-factor…
All the four giant planets in our Solar System have rings, but their characteristics are very different. The rings consist of a number of small particles, although individual particles have not been directly imaged. Near the central planet,…
Comet-type periodic orbits of the circular restricted three-body problem (CR3BP) are periodic solutions that are generated from very large retrograde and direct circular Keplerian motions around the common center of mass of the primaries.…
We propose new algebraic methods for extracting cylinders and cones from minimal point sets, including oriented points. More precisely, we are interested in computing efficiently cylinders through a set of three points, one of them being…
Our galaxy is full with planets. We now know that planets and planetary systems are diverse and come with different sizes, masses and compositions, as well as various orbital architectures. Although there has been great progress in…
Recent discoveries of circumbinary planets in Kepler data show that there is a viable channel of planet formation around binary main sequence stars. Motivated by these discoveries, we have investigated the caustic structures and…
The four longest period Kuiper belt objects have orbital periods close to integer ratios with each other. A hypothetical planet with orbital period $\sim$17,117 years, semimajor axis $\sim$665 AU, would have N/1 and N/2 period ratios with…
In the current study, the existence of periodic orbits around a fixed homogeneous cube is investigated, and the results have powerful implications for examining periodic orbits around non-spherical celestial bodies. In the two different…
The Kepler satellite has discovered a number of transiting planets around close binary stars. These circumbinary systems have highly aligned planetary and binary orbits. In this paper, we explore how the mutual inclination between the…
Circumstellar debris disks are the extrasolar analogues of the asteroid belt and the Kuiper belt. They consist of comets and leftover planetesimals that continuously collide and produce circumstellar dust that can be observed as infrared…
We consider the Lorenz equations, a system of three dimensional ordinary differential equations modeling atmospheric convection. These equations are chaotic and hard to study even numerically, and so a simpler "geometric model" has been…
Planetary atmospheres, and models of them, are discussed from the viewpoint of condensed matter physics. Atmospheres are a form of condensed matter, and many interesting phenomena of condensed matter systems are realized by them. The…
A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…
In this article, we describe a very simple technique to locate naked-eye planets in the sky, to an accuracy of $\sim 1^{\circ}$. The procedure, comprising just three steps, involves very simple manual calculations for planetary orbits…
We consider the geometry of four spatial displacements, arranged in cyclic order, such that the relative motion between neighbouring displacements is a pure rotation. We compute the locus of points whose homologous images lie on a circle,…
The closedness of orbits of central forces is addressed in a three dimensional space in which the Poisson bracket among the coordinates is that of the SU(2) Lie algebra. In particular it is shown that among problems with spherically…
We present a review of the interplay between the evolution of circumstellar disks and the formation of planets, both from the perspective of theoretical models and dedicated observations. Based on this, we identify and discuss fundamental…
We address the claim of Weiss et al. (2018) that the radii of adjacent planets in Kepler multi-planet systems are correlated. We explore two simple toy models---in the first the radii of the planets are chosen at random from a single…