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This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of
Yongjie Liu; Yu Jiang; Hengnian Li; Hui Zhang. Some Special Types of Orbits around Jupiter. Aerospace 2021, 8, 183 .
AMA StyleYongjie Liu, Yu Jiang, Hengnian Li, Hui Zhang. Some Special Types of Orbits around Jupiter. Aerospace. 2021; 8 (7):183.
Chicago/Turabian StyleYongjie Liu; Yu Jiang; Hengnian Li; Hui Zhang. 2021. "Some Special Types of Orbits around Jupiter." Aerospace 8, no. 7: 183.
In this work, we study the continuation of a periodic orbit on a relatively large scale and discover the existence of convergence under certain conditions, which has profound significance in research on asteroids and can provide a total geometric perspective to understanding the evolution of the dynamic characteristics from a global perspective. Based on the polyhedron model, convergence is derived via a series of theoretical analyses and derivations, which shows that a periodic orbit will evolve into a nearly circular orbit with a normal periodic ratio (e.g., 2:1, 3:2, and 4:3) and almost zero torsion under proper circumstances. As an application of the results developed here, three asteroids, (2 1 6) Kleopatra, (22) Kalliope and (4 3 3) Eros, are studied, and several representative periodic orbit families are detected, with convergence in three different cases: bidirectional, increasing-directional and decreasing-directional continuation. At the same time, four commonalities among these numerical examples are concluded. First, a (pseudo) tangent bifurcation arises at the cuspidal points during the variations in the periodic ratios in a single periodic orbit family. In addition, these cuspidal points in the periodic ratio coincide with the turning points during the variations in the average radius, the maximal torsion and the maximal radius of curvature. Furthermore, the periodic ratio increases (or decreases) with an increase (or decrease) in the Jacobian constant overall. We find the relationship between periodic ratio and Jacobian constant. The results implies that the periodic ratios for a fixed resonant status have an infimum and a supremum. Finally, if the periodic orbit converges to a point, it can be an unstable equilibrium point of the asteroid.
Haokun Kang; Yu Jiang; Hengnian Li. Convergence of a periodic orbit family close to asteroids during a continuation. Results in Physics 2020, 19, 103353 .
AMA StyleHaokun Kang, Yu Jiang, Hengnian Li. Convergence of a periodic orbit family close to asteroids during a continuation. Results in Physics. 2020; 19 ():103353.
Chicago/Turabian StyleHaokun Kang; Yu Jiang; Hengnian Li. 2020. "Convergence of a periodic orbit family close to asteroids during a continuation." Results in Physics 19, no. : 103353.
From Jan. 6, 2019 to Feb. 18, 2019, OSIRIS-REx observed asteroid (101955) Bennu ejecting 11 plumes of dust, of which part is escaping and another part is re-captured by the asteroid. The relative magnitudes of the typical forces acting on the emitted dust are quite different from the environments of the planets and other minor planets in the solar system. Here we show that ejected dust grains from the surface of Bennu can be caught in the gravitational field of Bennu. To this end, we calculated numerically the trajectories of dust grains of various sizes, from the 0.1μm to the ten millimeter range. The shape and the fate of an emitted cloud of particles depend on the size of the grains: smaller grains form a more narrowly confined dust trail while trails formed by larger grains disperse more rapidly. Four different fates are possible for ejected dust. All grains with radius less than 1.0μm, directly re-impact on Bennu or they escape directly. In contrast, a fraction of grains with a radius larger than 10.0 μm will impact or escape only after performing a number of non-Keplerian revolutions around Bennu. Our findings show how dust grains may populate the vicinity of Bennu and other active asteroids and that they can reach interplanetary space and other celestial bodies, implying that organic matter can be transported from carbonaceous asteroids to other celestial bodies, including Earth.
Yu Jiang; Jürgen Schmidt. Motion of dust ejected from the surface of asteroid (101955) Bennu. Heliyon 2020, 6, 1 .
AMA StyleYu Jiang, Jürgen Schmidt. Motion of dust ejected from the surface of asteroid (101955) Bennu. Heliyon. 2020; 6 (10):1.
Chicago/Turabian StyleYu Jiang; Jürgen Schmidt. 2020. "Motion of dust ejected from the surface of asteroid (101955) Bennu." Heliyon 6, no. 10: 1.
Understanding the motion of debris cloud produced by the anti-satellite test can help us to know the danger of these tests. This study presents the orbit status of 57 fragments observed by the CelesTrak and presented in the NORAD Two-Line Element Sets of India Anti-Satellite Test. There are 10 of these observed fragments have altitudes of the apogee larger than 1000.0km, the maximum one is 1725.7km. We also numerical calculated the number of debris, the results show that the number of debris with the diameter larger than 0.2m is 14, the number of debris with the diameter larger than 0.01m is 6587, and the number of debris with the diameter larger than 0.001m is 7.22×105. The results of the secondary collision of the debris will produced more fragments in the space. The life time of the fragments depends on the initial orbit parameters and the sizes of the debris.
Yu Jiang. Debris cloud of India anti-satellite test to Microsat-R satellite. Heliyon 2020, 6, e04692 .
AMA StyleYu Jiang. Debris cloud of India anti-satellite test to Microsat-R satellite. Heliyon. 2020; 6 (8):e04692.
Chicago/Turabian StyleYu Jiang. 2020. "Debris cloud of India anti-satellite test to Microsat-R satellite." Heliyon 6, no. 8: e04692.
We investigate the dynamical environment in the first announced triple asteroid system 87 Sylvia. The 3D shape of the primary is rebuilt from shape data using the polyhedral model method. The dynamical characteristics of the primary, such as the surface height, the surface effective potential, the surface gravitational acceleration, the structure of the zero-velocity surfaces, and the locations and stability of the equilibrium points, have been investigated. Five equilibrium points are in the potential of 87 Sylvia. Both unstable periodic orbits and stable periodic orbits coexist near the surface of the primary of the triple asteroid system 87 Sylvia. Under the full perturbation force of two moonlets, the semi-major axis, the eccentricity, the inclination, and the mechanical energy vary periodically and have no secular terms. Among them, the semi-major axis, the eccentricity, and the mechanical energy have two period terms, namely, a long period term and a short period term; the inclination has three period terms, i.e., a long period term, a short period term, and an intermediate period term. Unlike these orbital parameters, the argument of the pericenter and the longitude of the ascending node have a secular term, a long period term and a short period term. A simulation of the trajectories of 1000 grains generated in the system considering the gravity of the irregular shape and two moonlets of the primary has been presented. The grains may impact on the surface of the primary, escape the system, or move in the system.
Yu Jiang. Dynamical environment in the triple asteroid system 87 Sylvia. Astrophysics and Space Science 2019, 364, 60 .
AMA StyleYu Jiang. Dynamical environment in the triple asteroid system 87 Sylvia. Astrophysics and Space Science. 2019; 364 (4):60.
Chicago/Turabian StyleYu Jiang. 2019. "Dynamical environment in the triple asteroid system 87 Sylvia." Astrophysics and Space Science 364, no. 4: 60.
This paper studies the orbital dynamics of the potential of asteroid 22 Kalliope using observational data of the irregular shape. The zero-velocity surface are calculated and showed with different Jacobian values. All five equilibrium points are found, four of them are outside and unstable, and the other one is inside and linearly stable. The movement and bifurcations of equilibrium points during the variety of rotation speed and density of the body are investigated. The Hopf bifurcations occurs during the variety of rotational speed from ω=1.0ω 0 to 0.5ω 0, and the Saddle-Node bifurcation occurs during the variety of rotational speed from ω=1.0ω 0 to 2.0ω 0. Both unstable and stable resonant periodic orbits around Kalliope are coexisting. The perturbation of an unstable periodic orbit shows that the gravitational field of Kalliope is strongly perturbed.
Yu Jiang; Hengnian Li. Equilibria and orbits in the dynamical environment of asteroid 22 Kalliope. Open Astronomy 2019, 28, 154 -164.
AMA StyleYu Jiang, Hengnian Li. Equilibria and orbits in the dynamical environment of asteroid 22 Kalliope. Open Astronomy. 2019; 28 (1):154-164.
Chicago/Turabian StyleYu Jiang; Hengnian Li. 2019. "Equilibria and orbits in the dynamical environment of asteroid 22 Kalliope." Open Astronomy 28, no. 1: 154-164.
In the current study, we use the polyhedral model to compute the potential of the asteroid. There are five equilibrium points in the gravitational field of the asteroid 283 Emma. We concluded that the zero-velocity surfaces and the equilibrium points change with the suppositive variation of the rotational speed of the asteroid. It is found that if the rotational speed equals a half as it is in present, the number of equilibrium points is also five. However, if the rotational speed equals twice as it is in present, there are only three equilibrium points left. Four different periodic orbits are calculated using the hierarchical grid searching method. We calculated characteristic multipliers of periodic orbits to invistigate the stability of these periodic orbits. The orbit near the primary's equatorial plane is more likely to be stable when the separation/ primary-radius is a large number.
Yu Jiang; Xiaodong Liu. Equilibria and orbits around asteroid using the polyhedral model. New Astronomy 2018, 69, 8 -20.
AMA StyleYu Jiang, Xiaodong Liu. Equilibria and orbits around asteroid using the polyhedral model. New Astronomy. 2018; 69 ():8-20.
Chicago/Turabian StyleYu Jiang; Xiaodong Liu. 2018. "Equilibria and orbits around asteroid using the polyhedral model." New Astronomy 69, no. : 8-20.
We presented an overview of detailed continuation results of periodic orbit families which emanate from the equilibrium points (EPs) of irregular-shaped minor celestial bodies (hereafter called minor bodies). The generation and annihilation of periodic orbits (POs) related to the EPs are discussed in detail. The branch points of families of POs are also investigated. We presented 3D bifurcation diagrams for periodic orbits families emanating from the EPs of minor bodies which have five EPs totally. Structures of the 3D bifurcation diagrams depend on the distribution of EPs with different topological classifications. We calculated orbit families emanating from the EPs of asteroids 433 Eros and 216 Kleopatra, including the Lyapunov orbit family, the Vertical orbit family, the orbit families bifurcating from the Vertical orbit family, as well as the nonplanar orbit family.
Yu Jiang; Hexi Baoyin. Periodic orbits related to the equilibrium points in the potential of Irregular-shaped minor celestial bodies. Results in Physics 2018, 12, 368 -374.
AMA StyleYu Jiang, Hexi Baoyin. Periodic orbits related to the equilibrium points in the potential of Irregular-shaped minor celestial bodies. Results in Physics. 2018; 12 ():368-374.
Chicago/Turabian StyleYu Jiang; Hexi Baoyin. 2018. "Periodic orbits related to the equilibrium points in the potential of Irregular-shaped minor celestial bodies." Results in Physics 12, no. : 368-374.
Yu Jiang; Hexi Baoyin. Annihilation of relative equilibria in the gravitational field of irregular-shaped minor celestial bodies. Planetary and Space Science 2018, 161, 107 -136.
AMA StyleYu Jiang, Hexi Baoyin. Annihilation of relative equilibria in the gravitational field of irregular-shaped minor celestial bodies. Planetary and Space Science. 2018; 161 ():107-136.
Chicago/Turabian StyleYu Jiang; Hexi Baoyin. 2018. "Annihilation of relative equilibria in the gravitational field of irregular-shaped minor celestial bodies." Planetary and Space Science 161, no. : 107-136.
We used binary octahedrons to investigate the dynamical behaviors of binary asteroid systems. The mutual potential of the binary polyhedron method is derived from the fourth order to the sixth order. The irregular shapes, relative orbits, attitude angles, as well as the angular velocities of the binary asteroid system are included in the model. We investigated the relative trajectory of the secondary relative to the primary, the total angular momentum and total energy of the system, the three-axis attitude angular velocity of the binary system, as well as the angular momentum of the two components. The relative errors of the total angular momentum and the total energy indicate that the calculation has a high precision. It is found that the influence of the orbital and attitude motion of the primary from the gravitational force of the secondary is obvious. This study is useful in understanding the complicated dynamical behaviors of the binary asteroid systems discovered in our Solar system.
Yu Jiang; Hexi Baoyin; Mo Yang. Dynamical model of binary asteroid systems using binary octahedrons. Journal of Astrophysics and Astronomy 2018, 39, 54 .
AMA StyleYu Jiang, Hexi Baoyin, Mo Yang. Dynamical model of binary asteroid systems using binary octahedrons. Journal of Astrophysics and Astronomy. 2018; 39 (5):54.
Chicago/Turabian StyleYu Jiang; Hexi Baoyin; Mo Yang. 2018. "Dynamical model of binary asteroid systems using binary octahedrons." Journal of Astrophysics and Astronomy 39, no. 5: 54.
We investigate the equilibrium points and orbits around asteroid 1333 Cevenola by considering the full gravitational potential caused by the 3D irregular shape. The gravitational potential and effective potential of asteroid 1333 Cevenola are calculated. The zero-velocity curves for a massless particle orbiting in the gravitational environment have been discussed. The linearized dynamic equation, the characteristic equation, and the conserved quantity of the equilibria for the large-size-ratio binary asteroid system have been derived. It is found that there are totally five equilibrium points close to 1333 Cevenola. The topological cases of the outside equilibrium points have a staggered distribution. The simulation of orbits in the full gravitational potential caused by the 3D irregular shape of 1333 Cevenola shows that the moonlet’s orbit is more likely to be stable if the orbit inclination is small.
Yu Jiang. Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape. Astrodynamics 2018, 2, 361 -373.
AMA StyleYu Jiang. Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape. Astrodynamics. 2018; 2 (4):361-373.
Chicago/Turabian StyleYu Jiang. 2018. "Equilibrium points and orbits around asteroid with the full gravitational potential caused by the 3D irregular shape." Astrodynamics 2, no. 4: 361-373.
In this work, we investigate variations in the positions, eigenvalues, Jacobi integrals, topological cases, as well as the stability of equilibrium points around the asteroid 243 Ida when varying the external shape of the body. First, we employ a polyhedral shape model to calculate the surface height, gravitational force acceleration on the surface, and effective potential on the surface of 243 Ida. We then adopt the homotopy analysis method to generate variations in the external shape of a generic body within a continuum between the modeled external shape of 243 Ida and that of a sphere while maintaining a constant volume. Then, we calculated the positions, eigenvalues, Jacobi integrals, as well as the Hessian matrices of the equilibrium points in the gravitational potential of the generic body. We analyzed the topological cases and stability of the equilibrium points based on the obtained eigenvalues and Hessian matrices. It is concluded that the positions, eigenvalues, and Jacobi integrals change when varying the external shape of the body. For the four external equilibrium points E1–E4, the norm of the position vectors increases; however, the norm of the position vector for the internal equilibrium point E5 decreases. Equilibrium points E2 and E4 are subject to Hopf bifurcation when varying the external shape of the body, and the topological cases and stability of E2 and E4 are correspondingly changed. In contrast, the topological cases and stability of equilibrium points E1, E3, and E5 remain unchanged when varying the external shape of the body.
Yu Jiang; Hexi Baoyin. Parameters and bifurcations of equilibrium points in the gravitational potential of irregular-shaped bodies subjected to a varying external shape. Advances in Space Research 2018, 62, 3199 -3213.
AMA StyleYu Jiang, Hexi Baoyin. Parameters and bifurcations of equilibrium points in the gravitational potential of irregular-shaped bodies subjected to a varying external shape. Advances in Space Research. 2018; 62 (11):3199-3213.
Chicago/Turabian StyleYu Jiang; Hexi Baoyin. 2018. "Parameters and bifurcations of equilibrium points in the gravitational potential of irregular-shaped bodies subjected to a varying external shape." Advances in Space Research 62, no. 11: 3199-3213.
This study presents a study of equilibrium points, periodic orbits, stabilities, and manifolds in a rotating plane-symmetric potential field. It has been found that the dynamical behaviour near equilibrium points is completely determined by the structure of the submanifolds and subspaces. The non-degenerate equilibrium points are classified into twelve cases. The necessary and sufficient conditions for linearly stable, non-resonant unstable and resonant equilibrium points are established. Furthermore, the results show that a resonant equilibrium point is a Hopf bifurcation point. In addition, if the rotating speed changes, two non-degenerate equilibria may collide and annihilate each other. The theory developed here is lastly applied to two particular cases, motions around a rotating, homogeneous cube and the asteroid 1620 Geographos. We found that the mutual annihilation of equilibrium points occurs as the rotating speed increases, and then the first surface shedding begins near the intersection point of the –x axis and the surface. The results can be applied to planetary science, including the birth and evolution of the minor bodies in the Solar system, the rotational breakup and surface mass shedding of asteroids, etc.
Yu Jiang; Hexi Baoyin; Xianyu Wang; Hengnian Li. Stability and motion around equilibrium points in the rotating plane-symmetric potential field. Results in Physics 2018, 10, 487 -497.
AMA StyleYu Jiang, Hexi Baoyin, Xianyu Wang, Hengnian Li. Stability and motion around equilibrium points in the rotating plane-symmetric potential field. Results in Physics. 2018; 10 ():487-497.
Chicago/Turabian StyleYu Jiang; Hexi Baoyin; Xianyu Wang; Hengnian Li. 2018. "Stability and motion around equilibrium points in the rotating plane-symmetric potential field." Results in Physics 10, no. : 487-497.
We studied the dynamical environment in the vicinity of the primary of the binary asteroid. The gravitational field of the primary is calculated by the polyhedron model with observational data of the irregular shape. The equilibrium points, zero-velocity surfaces, as well as Jacobi integral have been investigated. The results show that the deviations of equilibrium points are large from the principal axes of moment of inertia. We take binary asteroid (41) Daphne and S/2008 (41) 1 for example. The distribution of topological cases of equilibrium points around (41) Daphne is different from other asteroids. The topological cases of the outer equilibrium points E1-E4 are Case 2, Case 5, Case 2, and Case 1. The topological case of the inner equilibrium point E5 is Case 1. Among the four outer equilibrium points E1-E4, E4 is linearly stable and other outer equilibrium points are unstable. Considering the shape variety of the body from Daphne to a sphere, we calculated the zero-velocity surfaces and the locations as well as eigenvalues of equilibrium points. It is found that the topological case of the outer equilibrium point E2 change from Case 5 to Case 1, and its stability change from unstable to linearly stable. Using the gravitational force acceleration calculated by the polyhedron model with the irregular shape, we simulated the orbit for the moonlet in the potential of (41) Daphne.
Yu Jiang. Dynamical environment in the vicinity of asteroids with an application to 41 Daphne. Results in Physics 2018, 9, 1511 -1520.
AMA StyleYu Jiang. Dynamical environment in the vicinity of asteroids with an application to 41 Daphne. Results in Physics. 2018; 9 ():1511-1520.
Chicago/Turabian StyleYu Jiang. 2018. "Dynamical environment in the vicinity of asteroids with an application to 41 Daphne." Results in Physics 9, no. : 1511-1520.
This paper is focused on the pseudo bifurcations and the variety of periodic ratio in the periodic orbits near the primary of binary irregular asteroid system (22) Kalliope, which would help on trajectory design for asteroid missions and give a practical insight into the generation and dynamic behaviour of binary asteroid systems. In this paper, we find three basic pseudo bifurcations in the periodic orbit families near (22) Kalliope during the numerical continuation with the variation of Jacobian constant. We also discover a nonuple mixed bifurcations which possess the highest multiplicity of bifurcations ever found and consist of three pseudo tangent bifurcations, two period-doubling bifurcations, one pseudo period-doubling bifurcation, one Neimark-Sacker bifurcation, one pseudo Neimark-Sacker bifurcation, and one real saddle bifurcation. Moreover, we find that the periodic ratio in the periodic orbit family may change during the continuation. Based on plenty of numerical evidences, we summarize three astonishing and exciting conclusions about the relationship of the periodic ratio and (pseudo) bifurcations in the periodic motion near (22) Kalliope. Firstly, the pseudo period-doubling bifurcation shows up when the periodic ratio comes near a half-integer (i.e. 1.5:1, 2.5:1, 3.5:1). Furthermore, almost all the cuspidal changes of the periodic ratio are accompanied with tangent bifurcation or pseudo tangent bifurcation. In addition, an integer can be admitted as the asymptotic value of the periodic ratio at the end of continuation, if the Jacobian constant isn't stuck into its local extremum, yet a half-integer can not.
Haokun Kang; Yu Jiang; Hengnian Li. Pseudo bifurcation and variety of periodic ratio for periodic orbit families close to asteroid (22) Kalliope. Planetary and Space Science 2018, 158, 69 -86.
AMA StyleHaokun Kang, Yu Jiang, Hengnian Li. Pseudo bifurcation and variety of periodic ratio for periodic orbit families close to asteroid (22) Kalliope. Planetary and Space Science. 2018; 158 ():69-86.
Chicago/Turabian StyleHaokun Kang; Yu Jiang; Hengnian Li. 2018. "Pseudo bifurcation and variety of periodic ratio for periodic orbit families close to asteroid (22) Kalliope." Planetary and Space Science 158, no. : 69-86.
We investigate the orbital stability close to the unique L4-point Jupiter binary Trojan asteroid 624 Hektor. The gravitational potential of 624 Hektor is calculated using the polyhedron model with observational data of 2038 faces and 1021 vertexes. Previous studies have presented three different density values for 624 Hektor. The equilibrium points in the gravitational potential of 624 Hektor with different density values have been studied in detail. There are five equilibrium points in the gravitational potential of 624 Hektor no matter the density value. The positions, Jacobian, eigenvalues, topological cases, stability, as well as the Hessian matrix of the equilibrium points are investigated. For the three different density values the number, topological cases, and the stability of the equilibrium points with different density values are the same. However, the positions of the equilibrium points vary with the density value of the asteroid 624 Hektor. The outer equilibrium points move away from the asteroid’s mass center when the density increases, and the inner equilibrium point moves close to the asteroid’s mass center when the density increases. There exist unstable periodic orbits near the surface of 624 Hektor. We calculated an orbit near the primary’s equatorial plane of this binary Trojan asteroid; the results indicate that the orbit remains stable after 28.8375 d.
Yu Jiang; Hexi Baoyin; Hengnian Li. Orbital stability close to asteroid 624 Hektor using the polyhedral model. Advances in Space Research 2018, 61, 1371 -1385.
AMA StyleYu Jiang, Hexi Baoyin, Hengnian Li. Orbital stability close to asteroid 624 Hektor using the polyhedral model. Advances in Space Research. 2018; 61 (5):1371-1385.
Chicago/Turabian StyleYu Jiang; Hexi Baoyin; Hengnian Li. 2018. "Orbital stability close to asteroid 624 Hektor using the polyhedral model." Advances in Space Research 61, no. 5: 1371-1385.
The motion of the moonlet Dactyl in the binary system 243 Ida is investigated in this paper. First, periodic orbits in the vicinity of the primary are calculated, including the orbits around the equilibrium points and large-scale orbits. The Floquet multipliers’ topological cases of periodic orbits are calculated to study the orbits’ stabilities. During the continuation of the retrograde near-circular orbits near the equatorial plane, two period-doubling bifurcations and one Neimark–Sacker bifurcation occur one by one, leading to two stable regions and two unstable regions. Bifurcations occur at the boundaries of these regions. Periodic orbits in the stable regions are all stable, but in the unstable regions are all unstable. Moreover, many quasi-periodic orbits exist near the equatorial plane. Long-term integration indicates that a particle in a quasi-periodic orbit runs in a space like a tire. Quasi-periodic orbits in different regions have different styles of motion indicated by the Poincare sections. There is the possibility that moonlet Dactyl is in a quasi-periodic orbit near the stable region I, which is enlightening for the stability of the binary system.
Lei Lan; Y. Ni; Y. Jiang; J. Li. Motion of the moonlet in the binary system 243 Ida. Acta Mechanica Sinica 2017, 34, 214 -224.
AMA StyleLei Lan, Y. Ni, Y. Jiang, J. Li. Motion of the moonlet in the binary system 243 Ida. Acta Mechanica Sinica. 2017; 34 (1):214-224.
Chicago/Turabian StyleLei Lan; Y. Ni; Y. Jiang; J. Li. 2017. "Motion of the moonlet in the binary system 243 Ida." Acta Mechanica Sinica 34, no. 1: 214-224.
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 equilibria. There also exist grains in the stable periodic orbits close to the cometary nucleus. The grains in the stable equilibria or the stable periodic orbits won’t 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 force, 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 calculated the strengths of different forces. The motion of the dust grain depends on the area-mass ratio, the charge, and the distance relative to the comet’s mass center. For a large dust grain (> 1 mm) close to the cometary nucleus which has a small value of area-mass ratio, the comet gravity is the largest force acting on the dust grain. For a small dust grain (< 1 mm) close to the cometary nucleus with large value of area-mass ratio, both the solar radiation pressure and the comet gravity are two major forces. If the a small dust grain which is close to the cometary nucleus have the large value of charge, the magnetic force, the solar radiation pressure, and the electric force are all major forces. When the large dust grain is far away from the cometary nucleus, the solar gravity and solar radiation pressure are both major forces.
Yu Jiang; Juergen Schmidt; Hexi Baoyin; Hengnian Li; Junfeng Li. Hamiltonian Formulation and Perturbations for Dust Motion Around Cometary Nuclei. The Moon and the Planets 2017, 120, 147 -168.
AMA StyleYu Jiang, Juergen Schmidt, Hexi Baoyin, Hengnian Li, Junfeng Li. Hamiltonian Formulation and Perturbations for Dust Motion Around Cometary Nuclei. The Moon and the Planets. 2017; 120 (3):147-168.
Chicago/Turabian StyleYu Jiang; Juergen Schmidt; Hexi Baoyin; Hengnian Li; Junfeng Li. 2017. "Hamiltonian Formulation and Perturbations for Dust Motion Around Cometary Nuclei." The Moon and the Planets 120, no. 3: 147-168.
We are interested in stable periodic orbits for spacecraft in the gravitational field of minor celestial bodies. The stable periodic orbits around minor celestial bodies are useful not only for the mission design of the deep space exploration, but also for studying the long-time stability of small satellites in the large-size-ratio binary asteroids. The irregular shapes and gravitational fields of the minor celestial bodies are modeled by the polyhedral model. Using the topological classifications of periodic orbits and the grid search method, the stable periodic orbits can be calculated and the topological cases can be determined. Furthermore, we find five different types of stable periodic orbits around minor celestial bodies: (1) stable periodic orbits generated from the stable equilibrium points outside the minor celestial body; (2) stable periodic orbits continued from the unstable periodic orbits around the unstable equilibrium points; (3) retrograde and nearly circular periodic orbits with zero-inclination around minor celestial bodies; (4) resonance periodic orbits; (5) near-surface inclined periodic orbits. We take asteroids 243 Ida, 433 Eros, 6489 Golevka, 101955 Bennu, and the comet 1P/Halley for examples.
Yu Jiang; Jürgen Arno Schmidt; Hengnian Li; Xiaodong Liu; Yue Yang. Stable periodic orbits for spacecraft around minor celestial bodies. Astrodynamics 2017, 2, 69 -86.
AMA StyleYu Jiang, Jürgen Arno Schmidt, Hengnian Li, Xiaodong Liu, Yue Yang. Stable periodic orbits for spacecraft around minor celestial bodies. Astrodynamics. 2017; 2 (1):69-86.
Chicago/Turabian StyleYu Jiang; Jürgen Arno Schmidt; Hengnian Li; Xiaodong Liu; Yue Yang. 2017. "Stable periodic orbits for spacecraft around minor celestial bodies." Astrodynamics 2, no. 1: 69-86.
We present the analysis and computational results for the inclination relative effect of moonlets of triple asteroidal systems. Perturbations on moonlets due to the primary’s 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 moonlet’s semi-major axis and the primary’s J2 perturbations. Perturbation on moonlets from the Solar gravity and moonlet’s 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.
Yu Jiang; Hexi Baoyin; Yun Zhang. Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems. The Moon and the Planets 2016, 119, 65 -83.
AMA StyleYu Jiang, Hexi Baoyin, Yun Zhang. Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems. The Moon and the Planets. 2016; 119 (2-3):65-83.
Chicago/Turabian StyleYu Jiang; Hexi Baoyin; Yun Zhang. 2016. "Relative Effect of Inclinations for Moonlets in the Triple Asteroidal Systems." The Moon and the Planets 119, no. 2-3: 65-83.