arXiv subjects

Hexi Baoyin

Publications and source records attributed to Hexi Baoyin.

At least 37 records · Page 2Linked to original sources

arXiv2017

Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems

We present the analysis and computational results for the inclination relative effect of moonlets of triple asteroidal systems. Perturbations on moonlets due to the primarys non-sphericity gravity, the solar gravity, and moonlets relative gravity are discussed. The inclination vector for each moonlet follows a periodic elliptical motion; the motion period depends on the moonlets semi-major axis and the primarys J2 perturbations. Perturbation on moonlets from the Solar gravity and moonlets relative gravity makes the motion of the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 to be periodic.The mean motion of x component and the y component of the inclination vector of each moonlet forms an ellipse. However, the instantaneous motion of x component and the y component of the inclination vector may be an elliptical disc due to the coupling effect of perturbation forces. Furthermore, the x component of the inclination vector of moonlet 1 and the y component of the inclination vector of moonlet 2 form a quasi-periodic motion. Numerical calculation of dynamical configurations of two triple asteroidal systems (216) Kleopatra and (153591) 2001 SN263 validates the conclusion.

astro-ph.EP↗

arXiv2017

Hamiltonian Formulation and Perturbations for Dust Motion around Cometary Nuclei

In this paper we analyze the dynamical behavior of large dust grains in the vicinity of a cometary nucleus. To this end we consider the gravitational field of the irregularly shaped body, as well as its electric and magnetic fields. Without considering the effect of gas friction and solar radiation, we find that there exist grains which are static relative to the cometary nucleus; the positions of these grains are the stable equibria. There also exist grains in the stable periodic orbits close to the cometary nucleus. The grains in the stable equibria or the stable periodic orbits will not escape or impact on the surface of the cometary nucleus. The results are applicable for large charge dusts with small area-mass ratio which are near the cometary nucleus and far from the Solar. It is found that the resonant periodic orbit can be stable, and there exist stable non-resonant periodic orbits, stable resonant periodic orbits and unstable resonant periodic orbits in the potential field of cometary nuclei. The comet gravity force, solar gravity force, electric froce, magnetic force, solar radiation pressure, as well as the gas drag force are all considered to analyze the order of magnitude of these forces acting on the grains with different parameters. Let the distance of the dust grain relative to the mass centre of the cometary nucleus, the charge and the mass of the dust grain vary, respectively, fix other parameters, we clacluated the strengths of different forces.

astro-ph.EP↗

arXiv2016

Periodic Orbit Families in the Gravitational Field of Irregular-shaped Bodies

The discovery of binary and triple asteroids in addition to the execution of space missions to minor celestial bodies in the past several years have focused increasing attention on periodic orbits around irregular-shaped celestial bodies. In the present work, we adopt a polyhedron shape model for providing an accurate representation of irregular-shaped bodies, and employ the model to calculate their corresponding gravitational and effective potentials. We also investigate the characteristics of periodic orbit families and the continuation of periodic orbits. We prove a fact, which provides a conserved quantity that permits restricting the number of periodic orbits in a fixed energy curved surface about an irregular-shaped body. The collisions of Floquet multipliers are maintained during the continuation of periodic orbits around the comet 1P/Halley. Multiple bifurcations in the periodic orbit families about irregular-shaped bodies are also discussed. Three bifurcations in the periodic orbit family have been found around the asteroid 216 Kleopatra, which include two real saddle bifurcations and one period-doubling bifurcation.

astro-ph.EP↗

arXiv2016

Dynamical Configurations of Celestial Systems Comprised of Multiple Irregular Bodies

This manuscript considers the main features of the nonlinear dynamics of multiple irregular celestial body systems. The gravitational potential, static electric potential, and magnetic potential are considered. Based on the three established potentials, we show that three conservative values exist for this system, including a Jacobi integral. The equilibrium conditions for the system are derived and their stability analyzed. The equilibrium conditions of a celestial system comprised of n irregular bodies are reduced to 12n minus 9 equations. The dynamical results are applied to simulate the motion of multiple-asteroid systems. The simulation is useful for the study of the stability of multiple irregular celestial body systems and for the design of spacecraft orbits to triple asteroid systems discovered in the solar system. The dynamical configurations of the five triple-asteroid systems 45 Eugenia, 87 Sylvia, 93 Minerva, 216 Kleopatra, and 136617 1994CC, and the six-body system 134340 Pluto are calculated and analyzed.

astro-ph.EP↗

arXiv2016

Surface Motion Relative to the Irregular Celestial Bodies

We study the motion and equilibria of the grains on the surface of the irregular celestial body (hereafter called irregular bodies). Motions for the grains on the smooth and unsmooth surfaces are discussed, respectively. The linearized equations of motion relative to a surface equilibrium point and its characteristic equations are presented. Considering the stick-slip effect, the damping forces and the spring forces for the grain are calculated, then the linearized equations of motion and the characteristic equations relative to the surface equilibrium points are derived. The number of non-degenerate surface equilibria is an even number. We compute the motion of a grain released above three different regions relative to the irregular asteroid 6489 Golevka, including the flat surface, the concave region, and the convex region. Following the grain release and initial bounce, three kinds of motions exist, the orbital motion, the impact motion and the surface motion. We find that the maximum height of the next hop may be bigger than the maximum height of the current hopping. We also used Monte Carlo simulations to calculate 100 grains hopping motions, the results shows that the stable surface equilibria are on the concave region and flat surface of the asteroid.

astro-ph.EP↗

arXiv2016

Multiple Bifurcations in the Periodic Orbit around Eros

We investigate the multiple bifurcations in periodic orbit families in the potential field of a highly irregular-shaped celestial body. Topological cases of periodic orbits and four kinds of basic bifurcations in periodic orbit families are studied. Multiple bifurcations in periodic orbit families consist of four kinds of basic bifurcations. We found both binary period-doubling bifurcations and binary tangent bifurcations in periodic orbit families around asteroid 433 Eros. The periodic orbit family with binary period-doubling bifurcations is nearly circular, with almost zero inclination, and is reversed relative to the body of the asteroid 433 Eros. This implies that there are two stable regions separated by one unstable region for the motion around this asteroid. In addition, we found triple bifurcations which consist of two real saddle bifurcations and one period-doubling bifurcation. A periodic orbit family generated from an equilibrium point of asteroid 433 Eros has five bifurcations, which are one real saddle bifurcation, two tangent bifurcations, and two period-doubling bifurcations.

astro-ph.EP↗

arXiv2016

Capillary Action in a Crack on the Surface of Asteroids with an Application to 433 Eros

Some asteroids contain water ice, and a space mission landing on an asteroid may take liquid to the surface of the asteroid. Gas pressure is very weak on the surface of asteroids. Here we consider the capillary action in a crack on the surface of irregular asteroids. The crack is modelled as a capillary which has a fixed radius. An asteroid s irregular gravitational potential influences the height of the liquid in the capillary. The height of the liquid in the capillary on the surface of such asteroids is derived from the asteroid s irregular gravitational potential. Capillary mechanisms are expected to produce an inhomogeneaous distribution of emergent liquid on the surface. This result is applied to asteroid 433 Eros, which has an irregular, elongated, and concave shape. Two cases are considered 1) we calculate the height of the liquid in the capillary when the direction of the capillary is perpendicular to the local surface of the asteroid; 2) we calculate the height of the liquid in the capillary when the direction of the capillary is parallel to the vector from the center of mass to the surface position. The projected height in the capillary on the local surface of the asteroid seems to depend on the assumed direction of the capillary.

astro-ph.EP↗

arXiv2015

Debris Engine: A Potential Thruster for Space Debris Removal

We present a design concept for a space engine that can continuously remove the orbit debris by using the debris as a propellant. Space robotic cleaner is adopted to capture the targeting debris and to transfer them into the engine. Debris with larger size is first disintegrated into small pieces by using a mechanical method. The planetary ball mill is then adopted to grind the pieces into micrometer or smaller powder. The energy needed in this process is get from the nuclear and solar power. By the effect of gamma-ray photoelectric or the behavior of tangently rub of tungsten needles, the debris powered is charged. This behavior can be used to speed up the movement of powder in a tandem electrostatic particle accelerator. By ejecting the high-temperture and high-pressure charged powered from the nozzle of the engine,the continuously thrust is obtained. This thrust can be used to perform orbital maneuver and debris rendezvous for the spacecraft and robotic cleaner. The ejected charged particle will be blown away from the circumterrestrial orbit by the solar wind. By digesting the space debris, we obtain not only the previous thrust but also the clean space. In the near future, start trek will not just a dream, human exploration will extend to deep universe. The analysis shown, the magnitude of the specific impulse for debris engine is determined by the accelerating electrostatic potential and the charge-to-mass ratio of the powder.

astro-ph.IM↗

arXiv2015

Periodic Motion near the Surface of Asteroids

We are interested in the periodic motion and bifurcations near the surface of an asteroid. The gravity field of an irregular asteroid and the equation of motion of a particle near the surface of an asteroid are studied. The periodic motions around the major body of triple asteroid 216 Kleopatra and the OSIRIS REx mission target asteroid 101955 Bennu are discussed. We find that motion near the surface of an irregular asteroid is quite different from the motion near the surface of a homoplastically spheroidal celestial body. The periodic motions around the asteroid 101955 Bennu and 216 Kleopatra indicate that the geometrical shapes of the orbits are probably very sophisticated. There exist both stable periodic motions and unstable periodic motions near the surface of the same irregular asteroid. This periodic motion which is unstable can be resonant or non resonant. The period doubling bifurcation and pseudo period doubling bifurcation of periodic orbits coexist in the same gravity field of the primary of the triple asteroid 216 Kleopatra. It is found that both of the period doubling bifurcations of periodic orbits and pseudo period-doubling bifurcation of periodic orbits have four different paths. The pseudo period doubling bifurcation found in the potential field of primary of triple asteroid 216 Kleopatra shows that there exist stable periodic orbits near the primary s equatorial plane, which gives an explanation for the motion stability of the triple asteroid 216 Kleopatra s two moonlets, Alexhelios and Cleoselene.

astro-ph.EP↗

arXiv2015

Order and Chaos near Equilibrium Points in the Potential of Rotating Highly Irregular-shaped Celestial Bodies

The order and chaos of the motion near equilibrium points in the potential of a rotating highly irregular-shaped celestial body are investigated from point of view of the dynamical system theory. The positions of the non-degenerate equilibrium points vary continuously when the parameter changes. The topological structures in the vicinity of equilibrium points are classified into several different cases. Bifurcations at equilibrium points and the topological transfers between different cases for equilibrium points are also discussed. The conclusions can be applied to all kinds of rotating celestial bodies, simple-shaped or highly irregular-shaped, including asteroids, comets, planets and satellites of planets to help one to understand the dynamical behaviors around them. Applications to asteroids 216 Kleopatra, 2063 Bacchus, and 25143 Itokawa are significant and interesting: eigenvalues affiliated to the equilibrium points for the asteroid 216 Kleopatra move and always belong to the same topological cases; while eigenvalues affiliated to two different equilibrium points for the asteroid 2063 Bacchus and 25143 Itokawa move through the resonant cases of equilibrium points, and the collision of eigenvalues in the complex plane occurs. Poincaré sections in the potential of the asteroid 216 Kleopatra show the chaos behaviors of the orbits in large scale.

astro-ph.EP↗

arXiv2015

Collision and Annihilation of Relative Equilibrium Points Around Asteroids with a Changing Parameter

In this work, we investigate the bifurcations of relative equilibria in the gravitational potential of asteroids. A theorem concerning a conserved quantity, which is about the eigenvalues and number of relative equilibria, is presented and proved. The conserved quantity can restrict the number of non-degenerate equilibria in the gravitational potential of an asteroid. It is concluded that the number of non-degenerate equilibria in the gravitational field of an asteroid varies in pairs and is an odd number. In addition, the conserved quantity can also restrict the kinds of bifurcations of relative equilibria in the gravitational potential of an asteroid when the parameter varies. Furthermore, studies have shown that there exist transcritical bifurcations, quasi-transcritical bifurcations, saddle-node bifurcations, saddle-saddle bifurcations, binary saddle-node bifurcations, supercritical pitchfork bifurcations, and subcritical pitchfork bifurcations for the relative equilibria in the gravitational potential of asteroids. It is found that for the asteroid 216 Kleopatra, when the rotation period varies as a parameter, the number of relative equilibria changes from 7 to 5 to 3 to 1, and the bifurcations for the relative equilibria are saddle-node bifurcations and saddle-saddle bifurcations.

astro-ph.EP↗

arXiv2015

Topological Classifications and Bifurcations of Periodic Orbits in the Potential Field of Highly Irregular-shaped Celestial Bodies

This paper studies the distribution of characteristic multipliers, the structure of submanifolds, the phase diagram, bifurcations and chaotic motions in the potential field of rotating highly irregular-shaped celestial bodies (hereafter called irregular bodies). The topological structure of the submanifolds for the orbits in the potential field of an irregular body is shown to be classified into 34 different cases, including 6 ordinary cases, 3 collisional cases, 3 degenerate real saddle cases, 7 periodic cases, 7 period-doubling cases, 1 periodic and collisional case, 1 periodic and degenerate real saddle case, 1 period-doubling and collisional case, 1 period-doubling and degenerate real saddle case, and 4 periodic and period-doubling cases. The different distribution of the characteristic multipliers has been shown to fix the structure of the submanifolds, the type of orbits, the dynamical behaviour and the phase diagram of the motion. Classifications and properties for each case are presented. Moreover, tangent bifurcations, period-doubling bifurcations, Neimark-Sacker bifurcations and the real saddle bifurcations of periodic orbits in the potential field of an irregular body are discovered. Submanifolds appear to be Mobius strips and Klein bottles when the period-doubling bifurcation occurs.

astro-ph.EP↗

arXiv2014

Orbit Maneuver of Spinning Tether via Tidal Force

Recently, the spinning tethered system is regarded as a typical and fundamental space structure attracting great interest of the aerospace engineers, and has been discussed primarily for specific space missions in past decades, including on-orbit capture and propellantless orbit transfer etc. The present work studies the dynamical behaviours of a fast spinning tethered binary system under central gravitational field, and derives principles of the basic laws of orbital maneuver. Considering the characteristics of coupled librational and orbital motions, an averaging method is introduced to deal with the slow-fast system equation, thus a definite equivalent model is derived. The general orbit motion is completely determined analytically, including the orbit geometry, periodicity, conversations and moving region etc. Since the possibility of orbit control using tether reaction has been proved by previous studies, special attention is paid to the transportation mode of angular momentum and mechanical energy between the orbit and libration. The effect of tether length change on the orbit shape is verified both in the averaged model and original model. The results show the orbit angular momentum and mechanical energy can be controlled independently, and the operating principles of tether reactions are derived for special modification of orbit shape.

physics.class-ph↗

arXiv2014

Analysis of potential locations of asteroidal moonlets

In this study, the potential locations of asteroidal small satellites (also called moonlets) with quasi-circular mutual orbit are analyzed. For the motion of the moonlets, only the solar gravity perturbation and the primary's 2nd degree-and-order gravity field are considered. By eliminating of short periodic terms, the dynamical behavior of the Hamiltonian for the moonlets is investigated. The observational data of some high size ratio binary asteroids show that the orbits of the moonlets lie close to the classical Laplace equilibria, which reach global minimum values of the Hamiltonian. It is found that tides or Yarkovsky effects alone cannot account for the reason why the orbits of asteroidal moonlets are not exactly at the classical Laplace equilibria. The analysis in this study is expected to provide useful information for the potential locations of asteroidal moonlets, and contribute to principles to relate predictions to observations.

astro-ph.EP↗

arXiv2014

Orbits and Manifolds near the Equilibrium Points around a Rotating Asteroid

We study the orbits and manifolds near the equilibrium points of a rotating asteroid. The linearised equations of motion relative to the equilibrium points in the gravitational field of a rotating asteroid, the characteristic equation and the stable conditions of the equilibrium points are derived and discussed. First, a new metric is presented to link the orbit and the geodesic of the smooth manifold. Then, using the eigenvalues of the characteristic equation, the equilibrium points are classified into 8 cases. A theorem is presented and proved to describe the structure of the submanifold as well as the stable and unstable behaviours of a massless particle near the equilibrium points. The linearly stable, the non-resonant unstable, and the resonant equilibrium points are discussed. There are three families of periodic orbits and four families of quasi-periodic orbits near the linearly stable equilibrium point. For the non-resonant unstable equilibrium points, there are four cases; for the periodic orbit and the quasi-periodic orbit, the structures of the submanifold and the subspace near the equilibrium points are studied for each case. For the resonant equilibrium points, the dimension of the resonant manifold is greater than four, and we find at least 1 family of periodic orbits near the resonant equilibrium points. Besides, this theory is applied to asteroids 216 Kleopatra, 1620 Geographos, 4769 Castalia, and 6489 Golevka.

astro-ph.EP↗

arXiv2014

Orbital Mechanics near a Rotating Asteroid

This study investigates the different novel forms of the dynamical equations of a particle orbiting a rotating asteroid and the effective potential, the Jacobi integral, etc. on different manifolds. Nine new forms of the dynamical equations of a particle orbiting a rotating asteroid are presented, and the classical form of the dynamical equations has also been found. The dynamical equations with the potential and the effective potential in scalar form in the arbitrary body-fixed frame and the special body-fixed frame are presented and discussed. Moreover, the simplified forms of the effective potential and the Jacobi integral have been derived. The dynamical equation in coefficient-matrix form has been derived. Other forms of the dynamical equations near the asteroid are presented and discussed, including the Lagrange form, the Hamilton form, the symplectic form, the Poisson form, the Poisson-bracket form, the cohomology form, and the dynamical equations on the Kähler manifold and another complex manifold. Novel forms of the effective potential and the Jacobi integral are also presented. The dynamical equations in scalar form and coefficient-matrix form can aid in the study of the dynamical system, the bifurcation, and the chaotic motion of the orbital dynamics of a particle near a rotating asteroid. The dynamical equations of a particle near a rotating asteroid are presented on several manifolds, including the symplectic manifold, the Poisson manifold, and complex manifolds, which may lead to novel methods of studying the motion of a particle in the potential field of a rotating asteroid.

astro-ph.EP↗

arXiv2012

Five Special Types of Orbits Around Mars

The abstract is additional with repect to the paper published in JGCD. Ordinary Earth satellites are usually placed into five categories of special orbits: sun-synchronous orbits, orbits at the critical inclination, frozen orbits, repeating ground track orbits, and geostationary orbits. This paper investigates their counterparts around Mars and examines the basic nature of these orbits, which are of special interest for missions conducted around Mars, including Mars reconnaissance. Mars' gravity field is much more complicated, with relatively smaller J2, compared to Earth's, which makes the behaviors of these Martian orbits different from those of Earth. Analytical formulations and numerical simulations are used to analyze these Martian orbits and compare them with their Earth counterparts. First, mean element theory is employed to describe variations of orbital elements and give the constraint conditions for achieving these special orbits. Then, numerical verifications based on the PSODE algorithm (particle swarm optimization combined with differential evolution) are adopted to provide more accurate conditions for achieving these orbits when considering an Mars gravity field. Using the numerical method can significantly improve the design in the full gravity field, and it is therefore possible to select these usable orbits for Mars that can reduce or eliminate the need for stationkeeping.

astro-ph.EP↗

arXiv2012

The Hill Stability of Triple Minor Planets in the Solar System

The triple asteroids and triple Kuiper belt objects (collectively called the triple minor planets) in the Solar system are of particular interest to the scientific community since the discovery of the first triple asteroid system in 2004. In this paper, the Hill stability of the nine known triple minor planets in the Solar system is investigated. Seven of the systems are of large size ratio, i.e. they consist of a larger primary and two moonlets, while the other two systems have components of comparable size. Each case is treated separately. For the triple minor planets that have large size ratio, the sufficient condition for Hill stability is expressed in closed form. This is not possible for the systems with comparable size components, for which the Hill stability is assessed by a combination of analytical and numerical means. It is found that all the known triple minor planets are Hill stable, except 3749 Balam, for which the incomplete orbital parameters make the Hill stability of the system uncertain. This suggests that there might be more such stable triple minor planets in the Solar system yet to be observed. It is also shown that the Hill stability regions increase as the mutual inclination between the inner orbit and outer orbit decreases, the semimajor axis ratio of the inner orbit with respect to the outer orbit decreases, and the mass ratio of the outer satellite with respect to the inner satellite increases. This study therefore provides useful information about dynamical properties of the triple minor planets in the Solar system.

astro-ph.EP↗