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Let us consider the elliptic restricted three body problem (Elliptic RTBP) for the Jupiter Sun system with eccentricity $e=0.048$ and $\mu=0.000953339$. Let us denote by $T$ the period of their orbits. In this paper we provide initial…
Posing Kepler's problem of motion around a fixed "sun" requires the geometric mechanician to choose a metric and a Laplacian. The metric provides the kinetic energy. The fundamental solution to the Laplacian (with delta source at the "sun")…
We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is…
Given a volume preserving dynamical system with non-compact phase space, one is sometimes interested in special subsets of its wandering set. One example from celestial mechanics is the set of initial values leading to collision. Another…
We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose…
In a model of nonlinear system of three scalar fields the problem on dynamics of a massive particle moving in effective potential provided by two relativistic fields is solving. The potentials for these fields are chosen in the form of…
We investigate the symmetry of point vortices with one dominant vortex and four vortices with infinitesimal circulations in the (1+4)-vortex problem, a subcase of the five-vortex problem. The four infinitesimal vortices inscribe…
We consider a special relativistic effect, known as the Poynting-Robertson effect, on various types of trajectories of solar sails. Since this effect occurs at order $v^{\phi}/c$, where $v^{\phi}$ is the tangential speed relative to the…
Based on the kinetic energy theorem, as one of the fundamental theorems from the classical mechanics, throughout the first part of the article an attempt has been made to derive the mathematical model of a material point motion in the…
The problem of determining the radiation reaction force experienced by a scalar charge moving in flat spacetime is investigated. A consistent renormalization procedure is used, which exploits the Poincar\'e invariance of the theory.…
Convection in the solar interior is thought to comprise structures on a spectrum of scales. This conclusion emerges from phenomenological studies and numerical simulations, though neither covers the proper range of dynamical parameters of…
In a recent papers, Turner and Turner (2010 {\em Am. J. Phys.} {\bf 78} 905-7) and Jensen (2011 {\em Eur. J. Phys.} {\bf 32} 389-397) analysed the motion of asymmetric rolling rigid bodies on a horizontal plane. These papers addressed the…
Coronal mass ejections (CMEs) are large-scale ejections of plasma and magnetic field from the solar corona, which propagate through interplanetary space at velocities of $\sim$100--2500~km~s$^{-1}$. Although plane-of-sky coronagraph…
This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
Higher mass dimension terms in an effective field theory framework for tests of spacetime symmetries are studied. Using a post-Newtonian expansion method, we derive the spacetime metric and the equations of motion for a binary system. This…
In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity [1]. When the scalar field vacuum is in a broken symmetry state, an effective…
When a solid body is freely rotating at an angular velocity ${\bf \Omega}$, the ellipsoid of constant angular momentum, in the space $\Omega_1, \Omega_2, \Omega_3$, has poles corresponding to spinning about the minimal-inertia and…
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…
The forces acting on solar Coronal Mass Ejections (CMEs) in the interplanetary medium have been evaluated so far in terms of an empirical drag coefficient $C_{\rm D} \sim 1$ that quantifies the role of the aerodynamic drag experienced by a…