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Hexi Baoyin - One of the best experts on this subject based on the ideXlab platform.
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periodic orbits related to the equilibrium points in the potential of irregular shaped minor Celestial Bodies
Results in physics, 2019Co-Authors: Yu Jiang, Hexi BaoyinAbstract:Abstract 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.
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annihilation of relative equilibria in the gravitational field of irregular shaped minor Celestial Bodies
Planetary and Space Science, 2018Co-Authors: Yu Jiang, Hexi BaoyinAbstract:Abstract The rotational speeds of irregular-shaped minor Celestial Bodies can be changed by the YORP effect. This variation in speed can make the numbers, positions, stabilities, and topological cases of the minor body's relative equilibrium points vary. The numbers of relative equilibrium points can be reduced through the collision and annihilation of relative equilibrium points, or increase through the creation and separation of relative equilibrium points. Here we develop a classification system of multiple annihilation behaviors of the equilibrium points for irregular-shaped minor Celestial Bodies. Most minor Bodies have five equilibrium points; there are twice the number of annihilations per equilibrium point when the number of equilibrium points is between one and five. We present the detailed annihilation classifications for equilibria of objects which have five equilibrium points. Additionally, the annihilation classification for the seven equilibria of Kleopatra-shaped objects and the nine equilibria of Bennu-shaped objects are also discussed. Equilibria of different objects fall into different annihilation classifications. By letting the rotational speeds vary, we studied the annihilations and creations of relative equilibria in the gravitational field of ten minor Bodies, including eight asteroids, one satellite of a planet, and one cometary nucleus: the asteroids were 216 Kleopatra, 243 Ida, 951 Gaspra, 1620 Geographos, 2063 Bacchus, 2867 Steins, 6489 Golevka, and 101955 Bennu; the satellite of the planet was S16 Prometheus; and the comet was 1682 Q1/Halley. For the asteroid 101955 Bennu, which has the largest number of equilibria among the known asteroids, we find that the equilibrium points with different indices approach each other as the rotational speed varies and thus annihilate each other successively. The equilibrium in the gravitational field and the smooth surface equilibrium collides when the equilibrium touches the surface of the body.
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the periodic dynamics of the irregular heterogeneous Celestial Bodies
Astrophysics and Space Science, 2017Co-Authors: Lei Lan, Mo Yang, Hexi BaoyinAbstract:In this paper, we develop a methodology to study the periodic dynamics of irregular heterogeneous Celestial Bodies. Heterogeneous Bodies are not scarce in space. It has been found that Bodies, such as 4 Vesta, 624 Hektor, 87 Sylvia, 16 Psyche and 25143 Itokawa, may all have varied internal structures. They can be divided into large-scale and small-scale cases. The varied internal structures of large-scale Bodies always result from gradient pressure inside, which leads to compactness differences of the inner material. However, the heterogeneity of a small-scale body is always reflected by the different densities of different areas, which may originate from collision formation from multiple objects. We propose a modeling procedure for the heterogeneous Bodies derived from the conventional polyhedral method and then compare its dynamical characteristics with those of the homogeneous case. It is found that zero-velocity curves, positions of equilibrium points, types of bifurcations in the continuation of the orbital family and the stabilities of periodic orbits near the heterogeneous body are different from those in the homogeneous case. The suborbicular orbits near the equatorial plane are potential parking orbits for a future mission, so we discuss the switching of the orbital stability of the family because it has fundamental significance to orbit maintenance and operations around actual asteroids.
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periodic orbit families in the gravitational field of irregular shaped Bodies
The Astronomical Journal, 2016Co-Authors: Yu Jiang, Hexi BaoyinAbstract: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.
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surface motion relative to the irregular Celestial Bodies
Planetary and Space Science, 2016Co-Authors: Yu Jiang, Yun Zhang, Hexi BaoyinAbstract:Abstract 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.
Yu Jiang - One of the best experts on this subject based on the ideXlab platform.
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periodic orbits related to the equilibrium points in the potential of irregular shaped minor Celestial Bodies
Results in physics, 2019Co-Authors: Yu Jiang, Hexi BaoyinAbstract:Abstract 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.
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annihilation of relative equilibria in the gravitational field of irregular shaped minor Celestial Bodies
Planetary and Space Science, 2018Co-Authors: Yu Jiang, Hexi BaoyinAbstract:Abstract The rotational speeds of irregular-shaped minor Celestial Bodies can be changed by the YORP effect. This variation in speed can make the numbers, positions, stabilities, and topological cases of the minor body's relative equilibrium points vary. The numbers of relative equilibrium points can be reduced through the collision and annihilation of relative equilibrium points, or increase through the creation and separation of relative equilibrium points. Here we develop a classification system of multiple annihilation behaviors of the equilibrium points for irregular-shaped minor Celestial Bodies. Most minor Bodies have five equilibrium points; there are twice the number of annihilations per equilibrium point when the number of equilibrium points is between one and five. We present the detailed annihilation classifications for equilibria of objects which have five equilibrium points. Additionally, the annihilation classification for the seven equilibria of Kleopatra-shaped objects and the nine equilibria of Bennu-shaped objects are also discussed. Equilibria of different objects fall into different annihilation classifications. By letting the rotational speeds vary, we studied the annihilations and creations of relative equilibria in the gravitational field of ten minor Bodies, including eight asteroids, one satellite of a planet, and one cometary nucleus: the asteroids were 216 Kleopatra, 243 Ida, 951 Gaspra, 1620 Geographos, 2063 Bacchus, 2867 Steins, 6489 Golevka, and 101955 Bennu; the satellite of the planet was S16 Prometheus; and the comet was 1682 Q1/Halley. For the asteroid 101955 Bennu, which has the largest number of equilibria among the known asteroids, we find that the equilibrium points with different indices approach each other as the rotational speed varies and thus annihilate each other successively. The equilibrium in the gravitational field and the smooth surface equilibrium collides when the equilibrium touches the surface of the body.
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stable periodic orbits for spacecrafts around minor Celestial Bodies
arXiv: Earth and Planetary Astrophysics, 2018Co-Authors: Yu Jiang, Xiaodong Liu, Juergen Schmidt, Yue YangAbstract:We are interested in stable periodic orbits for spacecrafts 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: A) Stable periodic orbits generated from the stable equilibrium points outside the minor Celestial body, B) Stable periodic orbits continued from the unstable periodic orbits around the unstable equilibrium points, C) Retrograde and nearly circular periodic orbits with zero-inclination around minor Celestial Bodies, D) Resonance periodic orbits, E) Near-surface inclined periodic orbits. We take asteroid 243 Ida, 433 Eros, 6489 Golevka, 101955 Bennu, and the comet 1P/Halley for examples.
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Stable periodic orbits for spacecraft around minor Celestial Bodies
Astrodynamics, 2017Co-Authors: Yu Jiang, Jürgen Schmidt, Xiaodong Liu, Yue YangAbstract: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.
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periodic orbit families in the gravitational field of irregular shaped Bodies
The Astronomical Journal, 2016Co-Authors: Yu Jiang, Hexi BaoyinAbstract: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.
B. M. Shustov - One of the best experts on this subject based on the ideXlab platform.
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Space System for Detecting Hazardous Celestial Bodies Approaching Earth from the Daytime Sky (SODA)
Cosmic Research, 2018Co-Authors: A. S. Shugarov, B. M. Shustov, S. A. Naroenkov, M. A. ZverevaAbstract:The concept of the System for the Observation of Daytime Asteroids ( SODA system) has been developed, the purpose of which is to detect at least 95% of hazardous Celestial Bodies larger than 10 m in size that fly towards Earth from the Sun side. Spacecraft, equipped with the optimum version, which has three wide-angle optical telescopes of small aperture (20–30 cm) will be placed in a halo orbit around the L _1 libration point of the Sun–Earth system. This will provide a warning on the hazardous object, approaching from the Sun side, and will allow one to determine the orbit and the point of body entering Earth atmosphere to a sufficient accuracy, at least a few hours before the body collides with Earth. The requirements to the system are considered, the results of a preliminary design of the set of instruments have been described, the areas of visibility are calculated, and the versions of data transmission modes have been proposed. It has been shown that, in cooperation with other (particularly ground-based) projects aimed to observing objects flying from the night sky side, it is possible to detect in advance all hazardous Bodies in the near-Earth space larger than 10 m in size that approach Earth from almost any direction.
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on population of hazardous Celestial Bodies in the near earth space
Solar System Research, 2017Co-Authors: B. M. Shustov, S. A. Naroenkov, E V EfremovaAbstract:In recent years, following the Chelyabinsk event of February 15, 2013, the lower size limit for presumably dangerous near-Earth objects has been decreased manyfold (essentially, from 140 m to ~10 m). This has drawn an increased attention to the properties of the population of decameter-sized Bodies, in particular, the Bodies that approach the Earth from the sunward side (daytime sky). The current paper is concerned with various properties of this population. The properties of the ensemble are analyzed using both observational data from other authors and theoretical estimates obtained by cloning virtual Bodies. This question is of great practical importance, as the means for detecting such Bodies (for example, the SODA project) need to be developed with consideration for the requirements imposed by the population properties. We have shown that the average rate of entering near-Earth space (NES), i.e., at distances less than ~1 million km from the Earth, for decameter-sized and larger Bodies from the daytime sky (elongation values of entry points less than 90°) is approximately 620 objects per year for elongation angles of the detection point <90° and approximately 220 objects per year for elongation angles of the detection point <45°.
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On the modern approach to the problem of detecting hazardous Celestial Bodies
Kinematics and Physics of Celestial Bodies, 2016Co-Authors: B. M. ShustovAbstract:The problem of detecting dangerous (in the sense of a collision with the Earth) Celestial Bodies of natural origin and the modern concept of building a system of detection of such Bodies are discussed. The concept includes two items: remote detection of large (>50 m) hazardous objects providing warning time of several tens of days, which is sufficient to allow the active counteraction and detection of hazardous Bodies larger than 10 m in near-Earth space providing warning time of few hours, which is sufficient to issue a warning and to carry out mitigation activities. Some examples of this approach and prospects of the international cooperation are discussed.
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On the concept of a low-cost space system for detecting hazardous Celestial Bodies
Cosmic Research, 2015Co-Authors: A. S. Shugarov, B. M. Shustov, M. B. Martynov, V. A. Kudryashov, V. Yu. TerebizhAbstract:We present the concept of a space system for detecting hazardous Celestial Bodies larger than 100 m 15–30 days before their possible collision with the Earth on the base of a wide-angle telescope with the aperture of 0.75 m and a field of view with a diameter of 7°. A preliminary configuration of a spacecraft using the low-sized Lavochkin Association platform is proposed. Preliminary estimates of the main system parameters are given. The main advantage of the system is a combination of high productivity, penetrating force, moderate technical complexity, and low cost of the implementation.
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on the possibility of the guidance of small asteroids to dangerous Celestial Bodies using the gravity assist maneuver
Solar System Research, 2013Co-Authors: N Eismont, M N Boyarskii, Anton Ledkov, R R Nazirov, D Dunham, B. M. ShustovAbstract:In this paper, the method of changing the trajectories of hazardous asteroids with orbits known for some years to be on a possible collision course with the Earth is considered. The method relies on the use of small asteroids (asteroid-projectiles) directed at hazardous Celestial Bodies by giving the projectile a sufficiently small velocity impulse ensuring the Earth gravity assist. As a result, the asteroid-projectile vector can be controllably changed over a wide range. Apophis is considered as an example of the target asteroid. The technical feasibility of this method is discussed. It is noted that despite the potential use of this elegant method, its practical implementation requires further research and development.
Andreas Knauf - One of the best experts on this subject based on the ideXlab platform.
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asymptotic velocity for four Celestial Bodies
arXiv: Dynamical Systems, 2018Co-Authors: Andreas KnaufAbstract:Asymptotic velocity is defined as the Cesaro limit of velocity. As such, its existence has been proven for bounded interaction potentials. This is known to be wrong in Celestial mechanics with four or more Bodies. Here we show for a class of pair potentials including the homogeneous ones of degree -a for 0
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asymptotic velocity for four Celestial Bodies
Philosophical Transactions of the Royal Society A, 2018Co-Authors: Andreas KnaufAbstract:Asymptotic velocity is defined as the Cesro limit of velocity. As such, its existence has been proved for bounded interaction potentials. This is known to be wrong in Celestial mechanics with four ...
E Mysen - One of the best experts on this subject based on the ideXlab platform.
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on the predictability of unstable satellite motion around elongated Celestial Bodies
Astronomy and Astrophysics, 2009Co-Authors: E MysenAbstract:Context. Close satellite orbits around small and elongated Celestial Bodies can experience massive aperiodic changes in shape. According to a number of published works, the changes are continuous functions of the orbit elements of the satellite's unperturbed trajectory. Aims. Later research, however, has revealed that the onset of instability is discrete, and highly correlated with the overlap of spin-orbit resonances. Since the interaction of resonances also can induce stochasticity in the orbiter's motion, we want to investigate more closely to what extent it is possible to predict the orbit evolution from the unperturbed elements. Methods. Numerical simulations of a natural or artificial satellite's motion in a rotating gravity field of second order and degree are conducted using different algorithms and software.Results. Consistent with the identification of resonance overlap as the responsible mechanism for the onset of orbit instability, we find that it is not always possible to predict qualitatively the outcome of a close encounter between satellite and the central body from the unperturbed orbit elements of the orbiter.Conclusions. The massive aperiodic changes in orbit energy experienced by natural and artificial satellites in orbit around small elongated Bodies exhibit properties characteristic for stochasticity.