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The nearly circular (mean eccentricity <e>~0.06) and coplanar (mean mutual inclination <i>~3 deg) orbits of the Solar System planets motivated Kant and Laplace to put forth the hypothesis that planets are formed in disks, which has…
We address the problem of inertial property of matter through analysis of the motion of an extended charged particle. Our approach is based on the continuity equation for momentum (Newton's second law) taking due account of the vector…
It is shown that a recent result regarding the average rate of evolution of a dynamical system at equilibrium in combination with the quantization of geometric areas coming from LQG, implies the validity of Kepler's Second Law of planetary…
First post-Newtonian (PN) approximation of the scalar-tensor theory of gravity is used to discuss the effacing principle in N-body system, that is dependence of equations of motion of spherically-symmetric bodies comprising the system on…
We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular…
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle…
This study considers the periodic orbital period of an n-body system from the perspective of dimension analysis. According to characteristics of the n-body system with point masses $(m_1,m_2,...,m_n)$, the gravitational field parameter,…
Neural networks have provided powerful approaches to solve various scientific problems. Many of them are even difficult for human experts who are good at accessing the physical laws from experimental data. We investigate whether neural…
The field equations of a generalized $f(R)$ type gravity model, in which there is an arbitrary coupling between matter and geometry, are obtained. The equations of motion for test particles are derived from a variational principle in the…
We study the modification of Newton's second law, upto first order in the deformation parameter $a$, in the $\kappa$-space-time. We derive the deformed Hamiltonian, expressed in terms of the commutative phase space variables, describing the…
At gravitational interactions of bodies and particles there appears the defect of masses, i.e. the energy yields since the bodies (or particles) are attracted. It is shown that this changing of the effective mass of the body (or the…
Earth rotation is determined by polar motion (PM) and length of day (lod). The excitation sources of PM are torques linked to fluid circulations ("geophysical excitations"), and those of lod to luni-solar tides ("astronomical excitations").…
We analytically work out the long-term variations caused on the motion of a planet orbiting a star by a very distant, pointlike massive object X. Apart from the semi-major axis a, all the other Keplerian osculating orbital elements…
The study of our Solar System -- its formation, evolution, and long-term stability -- has been ongoing for centuries and is now a standard part of scientific education. While the formation of other Solar-like exoplanetary systems is…
We consider a non-rotating, massive test particle acted upon by a "pressure"-type, non-geodesic acceleration arising from a certain general class of gravitational theories with nonminimal coupling between the matter and the metric. The…
The probability of the detection of Earth-like exoplanets may increase in the near future after the launch of the space missions using the transit photometry as observation method. By using this technique only the semi-major axis of the…
This work introduces a novel path-following control strategy inspired by the famous two-body problem, aiming to stabilize any Keplerian orbit. Utilizing insights from the mathematical structure of the two-body problem, we derive a robust…
A new model of nonlinear electromagnetic fields possessing a dimensional parameter $\beta$ is proposed. Electromagnetic fields are considered as the source of the gravitation field and accelerated expansion of the universe is driven by…
Starting from the classical Newton's second law which, according to our assumption, is valid in any instantaneous inertial rest frame of body that moves in Minkowskian space-time we get the relativistic equation of motion…
We propose several descriptive measures to characterize the arrangements of planetary masses, periods, and mutual inclinations within exoplanetary systems. These measures are based in complexity theory and capture the global, system-level…