arXiv subjects

Sergey Ershkov

Publications and source records attributed to Sergey Ershkov.

10 recordsLinked to original sources

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↗

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

Phoenix-Chess strategy or revisiting the algorithm for playing in Chess with incomplete information

We present here the new insight or revisiting the algorithm for playing in Chess with incomplete information (which can be recognized by its newly short-name as Phoenix-Chess strategy). The only difference with respect to the classical variant of Chess-game is that each rook after its having been captured by enemy chess piece in the proccess of gaming is not to be eliminated from the current game, but this rook is assumed being under virtual repairing during next N-steps (the required number of N is discussed in the current research). Then afterwards, such rook will be introduced in game again during maximal N-steps if only the chessboard square (on which it was captured previously) has not been occupied at previous step. In this case, Phoenix-Chess can be classified as game without predictable horizon of planning, so this kind of game should be considered as Chess-like games with incomplete information.

physics.soc-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↗

arXiv2020

Sitnikov-type solution for the motion of infinitesimal mass in BiER4BP

In this paper, we present a new ansatz for approximated solving equations of motion of the infinitesimal mass m in case of bi-elliptic restricted problem of four bodies (BiER4BP) (where three primaries M1, M2, M3 are rotating around their common centre of mass on elliptic orbits with hierarchical configuration M3 < M2 << M1). A new type of the solving procedure is implemented here to obtain the coordinates of the infinitesimal mass m. Meanwhile, the system of equations of motion has been successfully explored with respect to the existence of semi-analytical (approximated) way for presentation of the solution. We obtain as follows: 1) the solution for coordinates {x, y} = {0, 0} is approximately satisfied both the first and second equations of motion if we take into consideration assumption {M3, M2} << M1, 2) the expression for coordinate z(f) is given by the equation of 2-nd order, which describes Sitnikov-type approximated solution. It means that test particle is moving along the z-axis, outward the common barycenter of the system (but perpendicular to the plane of the mutual rotation of all the primaries).

physics.gen-ph↗

arXiv2020

Semi-analytical solution for the trapped orbits of satellite near the planet in ER3BP

In this paper, we present a new ansatz for solving equations of motion for the trapped orbits of the infinitesimal mass (satellite), which is locked in the space trap to be moving near the planet in case of the elliptic restricted problem of three bodies, ER3BP (with Keplerian elliptic trajectories of primaries Sun and planet around each other). A new type of the solving procedure is implemented here to obtain the coordinates of the infinitesimal mass (satellite) with its orbit located near the planet. The system of equations of motion was applied for obtaining of the semi-analytic and analytic solutions. It is obtained that two cartesian coordinates (in a plane of mutual rotation of primaries Sun and planet around each other) depend on the true anomaly and a function which determines the quasi periodic character of solution, while the third coordinate (perpendicular to the plane of rotation of primaries) is quasi-periodically varying with true anomaly.

physics.gen-ph↗

arXiv2019

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↗

arXiv2015

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↗

arXiv2010

Revisiting solving procedure for Ermakov-Pinney equation (with applications in the field of cosmology)

It is known that Ermakov-Pinney equation is a nonlinear equation with wide applications in dynamics, physics, cosmology (e.g., Ermakov equation can be connected to Bose-Einstein Condensate cosmology which unifies the dark energy and the dark matter). In this analytical study, we have presented a new type of solving procedure to obtain analytical solution of Ermakov-Pinney equation, specifically for the case of rotating early Universe with vortex. The particular case of solution of the aforementioned equation is presented also (such the solution of special kind is important for cosmological applications) which corresponds to the class of solutions with symmetry reduction.

physics.gen-ph↗