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The arrival of powerful instruments will provide valuable data for the characterization of rocky exoplanets. It is then crucial to accurately model the dynamical state of exoplanets. Rocky planets with sufficiently large orbits should have…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
We consider the orbital angular momentum of a free electron vortex moving in a uniform magnetic field. We identify three contributions to this angular momentum: the canonical orbital angular momentum associated with the vortex, the angular…
Modified Newtonian dynamics (MOND) is a possible way to explain the flat galaxy rotation curves without invoking the existence of dark matter. It is however quite difficult to predict such a phenomenology in a consistent field theory, free…
This paper uses an inductive method to investigate the factors responsible for variations in planetary-rotation periods. I began by showing the presence of a correlation between the masses of planets and their rotation periods. Then I…
The kinematics of about 2000 classical Cepheids of the Milky Way with data from Gaia\,EDR3 catalog has been studied. For some of these stars, there are line-of-sight velocities. On the basis of the nonlinear rotation model, the parameters…
The variation in the figure axis in the Earth owing to the geophysical causes directly reflects the physical state of the Earth and therefore, it is important for understanding the Earth. Of the variations in the figure axis arising from…
Venus' atmosphere shows highly variable warm vortices over both of the planet's poles. The nature of the mechanism behind their formation and properties is still unknown. Potential vorticity is a conserved quantity when advective processes…
It has been suggested that the ice shell of Jupiter's moon Europa may drift non-synchronously due to tidal torques. Here we argue that torques applied by the underlying ocean are also important and can result in non-synchronous rotation…
We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the variation of the undisturbed flow at the body scale is…
It is well known that a rigid motion of the Euclidean plane can be written as the composition of at most three reflections. It is perhaps not so widely known that a similar result holds for Euclidean space in any number of dimensions. The…
For a point mass residing in an expanding universe, within General Relativity (GR), a new metric [1} is found to lead to a cosmological background dependent MOND-like acceleration in addition to the Newtonian acceleration. In [2], we study…
The tidal deformations of a planet are often considered as markers of its inner structure. In this work, we use the tide excitations induced by the Sun on Venus for deciphering the nature of its internal layers. In using a Monte Carlo…
We perform direct numerical simulations of the tidal encounter of a rotating planet on a highly eccentric or parabolic orbit about a central star formulated as an initial value problem. This approach enables us to extend previous work of…
We consider a body immersed in a perfect gas, moving under the action of a constant force E along the x axis . We assume the gas to be described by the mean-field approximation and interacting elastically with the body, we study the…
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in…
We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk…
Geometrical properties of three-body orbits with zero angular momentum are investigated. If the moment of inertia is also constant along the orbit, the triangle whose vertexes are the positions of the bodies, and the triangle whose…
During the last few decades, there has been a growing interest in exact solutions of Einstein equations describing razor-thin disks. Despite the progress in the area, the analytical study of geodesic motion crossing the disk plane in these…
AIMS: An alternative to the traditional method for modeling kinematics of the Earth's rotation is proposed. The purpose of developing the new approach is to provide a self-consistent and simple description of the Earth's rotation in a way…