arXiv subjects

Dmytro Leshchenko

Publications and source records attributed to Dmytro Leshchenko.

11 recordsLinked to original sources

arXiv2023

On the analytical solution in non-inertial frame of R2BP

In this analytical study, we have presented a new type of solving procedure with aim to obtain the coordinates of small mass m, which moves around primary M_Sun, referred to non-inertial frame of restricted two-body problem (R2BP) with modified potential function (taking into account the components of variable velocity of central body M_Sun motion) instead of classical potential function for Kepler formulation of R2BP. Meanwhile, system of equations of motion has been successfully explored with respect to the existence of analytical way for presentation of the solution in polar coordinates with radial distance r = r(t). We have obtained analytical formula for function t = t(r) via appropriate elliptic integral. Having obtained the inversed dependence r = r(t), we can obtain the time-dependence for the polar angle as well. Also, we have pointed out how to express components of solution (including initial conditions) from cartesian to polar coordinates.

physics.gen-ph↗

arXiv2023

Revisiting the dynamics of finite-sized satellite near the planet in ER3BP

A novel approach for solving equations of motion of finite-sized satellite supposed to be moving in a proximity and around the planet in the elliptic restricted three-body problem, ER3BP is presented in this semi-analytical investigation. We consider two primaries, M_Sun and m_planet (the last is secondary in that binary system), both are orbiting around their barycenter on elliptic orbits. Satellite is considered to be the solid ellipsoid having nearly spherical form, with its gravitational potential to be given by a formula of MacCullagh type. Our aim is to revisit previously presented in work [Ashenberg, 1996] approach and to investigate the updated type of the satellite dynamics correlated implicitly to a kind of trapped motion (in the synodic co-rotating Cartesian coordinate system) in so way that satellite will always to be located near the secondary planet, m_planet, moving on quasi-stable elliptic orbit.

physics.gen-ph↗

arXiv2023

On the motion of satellite around the natural moons of planets using the concept of ER3BP with variable eccentricity

In the current study, we explore stability of motion of satellite around the natural moons of planets in Solar system using the novel concept of ER3BP with variable eccentricity. This concept was introduced earlier when novel type of ER3BP (Sun-planet-satellite) was investigated with variable spin state of secondary planet correlated implicitly to the motion of satellite (in the synodic co-rotating Cartesian coordinate system) for its trapped orbit near the secondary planet (which is involved in kepler duet ). But it is of real interest to explore another kind of aforedescribed problem, ER3BP (planet-moon-satellite) with respect to investigation of motion of satellite m around the natural moon m_moon of planet in Solar system with variable eccentricity of the moon in its motion around the planet. So, we consider here two primaries, M_planet and m_moon, the last is orbiting around their common barycenter on quasi-elliptic orbit with slow-changing, not constant eccentricity (on a large-time scale) due to tidal phenomena. Our aim is to investigate motion of small dot satellite around the natural moon of planet on quasi-stable elliptic orbit. Both novel theoretical and numerical findings (for various cases of trio ) are presented in the current research.

physics.gen-ph↗

arXiv2022

Dynamics of a small planetoid in Newtonian gravity field of Lagrangian configuration of three primaries

Novel method for semi-analytical solving of equations of a trapped dynamics for a planetoid m4 close to the plane of mutual motion of main bodies around each other (in case of a special type of Bi-Elliptic Restricted 4-Bodies Problem) is presented. We consider here three primaries m1, m2, m3 orbiting around their center of mass on elliptic orbits which are permanently forming Lagrangian configuration of an equilateral triangle. Our aim is to obtain appoximate coordinates of quasi planar trajectory of the infinitesimal planetoid m4, when the primaries have masses equal to 1/3. Results are as follows: 1) equations for coordinates {x, y} are described by system of coupled 2-nd order ordinary differential equations with respect to true anomaly f, 2) expression for z stems from solving second order Riccati ordinary differential equation that determines the quasi-periodical oscillations of planetoid m4 not far from invariant plane {x, y, 0}.

physics.gen-ph↗

arXiv2022

Revisiting Apophis 2029 approach to Earth (staying on shoulders of NASA experts) or Can we be sure in almost ricocheting fly-by of Apophis on 13 of April 2029 near the Earth?

The main idea of this challenging research is to revisit the solar-centric dynamics of Earth around the Sun in analysis of its position on 13 April 2029 close to asteroid Apophis which is supposed to be moving in fly-by near the Earth on its orbit. As of now, we can be sure that trajectory of Apophis is well-known with respect to the center of Sun. Also, NASA experts calculated that relative distance between center of Earth and Apophis should be less than 38 thousands of kilometers during closest Apophis approach to the Earth. But the reasonable question is: will the center of Earth be at the predicted position at the beginning of April 2029? The matter is that NASA solving procedure disregards influence of Milankovich cycles to the orbit of Earth but alternative concept suggests another solution (with additional quasi-periodic deviation from their solution, proportional to square of eccentricity of Earth orbit around the Sun equals to ~ 0.017). So, possible perturbation of Earth orbit is likely to be proportional to (0.017)$^2$ ~ 0.03% from 1 a.e. or ~ 43 200 km which could be compared with gap between Earth and Apophis during closest Apophis approach to Earth in April 2029.

physics.gen-ph↗

arXiv2021

Analysis of the size of Solar system close to the state with zero total angular momentum via Sundman inequality

In this paper, we present a new mathematical approach or solving procedure for analysis of the Sundman inequality (for estimating the moment of inertia of the Solar system configuration) with the help of Lagrange-Jacobi relation, under additional assumption of decreasing of the total angular momentum close to the zero absolute magnitude in the final state of Solar system in a future. By assuming such the final state for Solar system, we have estimated the mean-size of Solar system R via analysis of the Sundman inequality. So, to answer the question "Does the ninth planet exist in Solar system?", one should meet the two mandatory criteria for such the ninth planet, first is that it should have the negligible magnitude of inclination of its orbit with respect to the invariable plane. The second condition is that the orbit of the ninth planet should be located within the estimation for the mean-size of Solar system R.

physics.gen-ph↗

arXiv2021

Revisiting dynamics of Sun center relative to barycenter of Solar system

We introduce here in the current research the revisiting of approach to the dynamics of Sun center relative to barycenter of Solar system by using self-resulting photo-gravitational force of the Sun as the main reason of such motion. In case of slowly moving in the direction outwards with respect to the initial position of barycenter of Solar system (together with the current position of Solar system barycenter, of course) with average established velocity not less than 1050 Km/day, we should especially note that hierarchical configuration of Solar system will be preferably the same during this motion. As the main findings, we have suggested algorithm how to move towards stars using Solar self-resulting photo-gravitational force. The obvious physically reasonable assumption is that the Solar system will have been increasing its size during the evolution in a future (due to losses of the total angular momentum taking into account the tidal phenomena).

physics.gen-ph↗

arXiv2021

A new solving procedure for the Kelvin&Kirchhoff equations in case of falling a rotating torus

We present in this communication a new solving procedure for Kelvin&Kirchhoff equations, considering the dynamics of falling the rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation for the rotating body, I_1 = I_2. Fundamental law of angular momentum conservation is used for the aforementioned solving procedure. The system of Euler equations for dynamics of torus rotation is explored in regard to the existence of an analytic way of presentation for the approximated solution (where we consider the case of laminar flow at slow regime of torus rotation). The second finding is associated with the fact that the Stokes boundary layer phenomenon on the boundaries of the torus is also been assumed at formulation of basic Kelvin&Kirchhoff equations (for which analytical expressions for the components of fluid torque vector {T_2, T_3} were obtained earlier). The results of calculations for the components of angular velocity should then be used for full solving the momentum equation of Kelvin&Kirchhoff system. Trajectories of motion can be divided into, preferably, 3 classes: zigzagging, helical spiral motion, and the chaotic regime of oscillations.

physics.gen-ph↗

arXiv2021

About influence of differential rotation in convection zone of gaseous or fluid giant Planet (Uranus) onto the parameters of orbits of satellites

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. We suggest in the current research to take into consideration the additional well-known effect of differential rotation which obviously takes place in the gaseous or fluid convection zone of primary giant Planet (indeed, the aforementioned effect exists even not depending on the orbital evolution of satellites around host Planet). Nevertheless, estimations for the contribution of the aforementioned effect of differential rotation in the Uranus system (including all its most massive satellites) let us exclude using such effect from calculations of mutual evolution of the eccentricity e along with the semi-major axis a for all satellites of Uranus (Planet of ice-type). It means that the Uranus can be considered in the analytic exploration of governing equations as to be the appropriate candidate for applying the modern ansatz [Efroimsky, 2015] (tidal dissipation effect depending on the tidal-flexure frequency) in regard to estimations of eccentricity e along with semi-major axis a for satellites of Uranus. We can see from the results of calculations in Section 3 that the combined system of governing equations (in the sense of combined contributions to the tidal dissipation from Uranus + from satellite) yields the really observed magnitudes of decelerations for semi-major axises of all the satellites of Uranus. Meanwhile, internal heat generation effects in the satellites (due to tidal dissipation effect) are much more than those which definitely take place in the Uranus, excepting the case of Ariel.

physics.gen-ph↗

arXiv2020

On the dynamics of non-rigid asteroid rotation

We have presented in this communication a new solving procedure for the dynamics of non-rigid asteroid rotation, considering the final spin state of rotation for a small celestial body (asteroid). The last condition means the ultimate absence of the applied external torques (including short-term effect from torques during collisions, long-term YORP effect, etc.). Fundamental law of angular momentum conservation has been used for the aforementioned solving procedure. The system of Euler equations for dynamics of non-rigid asteroid rotation has been explored with regard to the existence of an analytic way of presentation of the approximated solution. Despite of various perturbations (such as collisions, YORP effect) which destabilize the rotation of asteroid via deviating from the current spin state, the inelastic (mainly, tidal) dissipation reduces kinetic energy of asteroid. So, evolution of the spinning asteroid should be resulting by the rotation about maximal-inertia axis with the proper spin state corresponding to minimal energy with a fixed angular momentum. Basing on the aforesaid assumption (component K_1 is supposed to be fluctuating near the given appropriate constant of the fixed angular momentum), we have obtained that 2-nd component K_2 is the solution of appropriate Riccati ordinary differential equation of 1-st order, whereas component K_3 should be determined via expression for K_2.

physics.gen-ph↗

arXiv2019

Notes on approaches for solving the Euler-Poisson equations

In this paper, we proceed to develop a new approach which was formulated first in Ershkov (2017) for solving Poisson equations: a new type of the solving procedure for Euler-Poisson equations (rigid body rotation over the fixed point) is suggested in the current research. Meanwhile, the Euler-Poisson system of equations has been successfully explored for the existence of analytical way for presentation of the solution. As the main result, the new ansatz is suggested for solving Euler-Poisson equations: the Euler-Poisson equations are reduced to the system of 3 nonlinear ordinary differential equations of 1-st order in regard to 3 functions; the elegant approximate solution has been obtained via re-inversion of the proper analytical integral as a set of quasi-periodic cycles. So, the system of Euler-Poisson equations is proved to have the analytical solutions (in quadratures) only in classical simplifying cases: 1) Lagrange case, or 2) Kovalevskaya case or 3) Euler case or other well-known but particular cases.

physics.gen-ph↗