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Among the nearly 30,000 known near-Earth asteroids (NEAs), only tens of them possess Earth co-orbital characteristics with semi-major axes $\sim$1 au. In particular, 469219 Kamo`oalewa (2016 HO3), upcoming target of China's Tianwen-2 asteroid sampling mission, exhibits a meta-stable 1:1 mean-motion resonance with Earth. Intriguingly, recent ground-based observations show that Kamo`oalewa has spectroscopic characteristics similar to space-weathered lunar silicates, hinting at a lunar origin instead of an asteroidal one like the vast majority of NEAs. Here we use numerical simulations to demonstrate that Kamo`oalewa's physical and orbital properties are compatible with a fragment from a crater larger than 10--20 km formed on the Moon in the last few million years. The impact could have ejected sufficiently large fragments into heliocentric orbits, some of which could be transferred to Earth 1:1 resonance and persist today. This leads us to suggest the young lunar crater Giordano Bruno (22 km diameter, 1--10 Ma age) as the most likely source, linking a specific asteroid in space to its source crater on the Moon. The hypothesis will be tested by the Tianwen-2 mission when it returns a sample of Kamo`oalewa. And the upcoming NEO Surveyor mission will possibly help us to identify such a lunar-derived NEA population., Comment: 29 pages, 4 figures. Published in Nature Astronomy, 19 April 2024

The rotational mass loss has been realized to be a prevalent mechanism to produce low-speed debris near the asteroid, and the size composition of the asteroid's surface regolith has been closely measured by in situ explorations. However, the full-scale evolution of the shedding debris has not been examined using the observed particle sizes, which may hold vital clues to the initial growth of an asteroid moonlet, and help us to understand the general mechanisms that dominate the formation of asteroid systems. This paper presented our study on the cumulative evolution of the debris cloud formed by a rotationally unstable asteroid. A semi-analytical model is developed to characterize the spatial-temporal evolution of the debris cloud posterior to a shedding event. Large-scale DEM simulations are performed to quantify the clustering behavior of the debris particles in the mechanical environment near the asteroid. As a result, we found the cumulation of a steady debris cloud is dominated by large pieces of debris, and the shedding particles follow a common migration trend, which fundamentally determines the mass distribution of the debris cloud. For the accretion analysis, we sketched the life cycle of a debris cluster, and showed its dependency on particle size. The DEM simulations adopt physical parameters estimated from observations and asteroid missions. The results confirm porous fluffy cluster structures can form shortly after a shedding event with magnitudes as the observed shedding activities. Measurements to these structures show they possess certain strength and adsorption capacity to collisions from dissociative debris particles.

Asteroid 2016 HO3, a small asteroid (<60 m) in super fast rotation state (~28 min), and is the target of China's Tianwen-2 asteroid sample-return mission. In this work, we investigate its structural stability using an advanced soft-sphere-discrete-element-model code, DEMBody, which is integrated with bonded-aggregate models to simulate highly irregular boulders. The asteroid body is numerically constructed by tens of thousands particles, and then is slowly spin up until structural failure. Rubble piles with different morphologies, grain size distributions and structures are investigated. We find a 2016 HO3 shaped granular asteroid would undergo tensile failure at higher cohesive strengths as opposed to shear failure in lower strengths, regardless of its shape and constituent grain size ratio. Such a failure mode transition is consistent with the priority between the Maximum Tensile Stress criterion criterion and the Drucker-Prager criterion. Therefore, previous works that solely considered the Drucker-Prager failure criterion have underestimated the minimal cohesion strength required for fast-rotating asteroids. We predict that the high spin rate of asteroid 2016 HO3 requires a surface cohesion over ~1 Pa and a bulk cohesion over ~10-20 Pa. Through comparing these strength conditions with the latest data from asteroid missions, we suggest a higher likelihood of a monolithic structure over a typical rubble pile structure. However, the possibility of the latter cannot be completely ruled out. In addition, the asteroid's surface could retain a loose regolith layer globally or only near its poles, which could be the target for sampling of Tianwen-2 mission.

An asteroid spun up to its critical limit has unique surface mechanical properties that its gravity and the centrifugal force largely balance, creating a relaxation environment where low-energy events such as mass shedding may trigger subsequent long complex motion of an asteroid's regolith grains. Exploring such an evolution process may provide key clues for understanding the early formation of multi-asteroid systems. This paper investigates the complex evolution process of loose particles becoming triggered by shedding events and the dependency of their dynamical propagation on the contact mechanical properties of the asteroid surface. We present a numerical model for tracking the trajectory of a shed particle that considers the collision between the particle and the surface of an asteroid. Monte Carlo simulations are performed to reflect the statistical behavior of shed particles. We also introduce zero-velocity surfaces to our data-based analysis in order to reveal the intrinsic invariance of the evolutionary processes. We used the average mechanical energy of the particle cloud to check the connection between contact property and the temporal-spatial distribution of the shed particles. We sketch a common evolutionary path of the particle in the vicinity of a fast-rotating asteroid, that is, particles dislodged from the unstable region will eventually enter, through several collisions with the surface, non-return orbits that launch from the minimum geopotential area of the unstable region. The common trend is independent of any particular asteroid morphology, and all shed particles enter the same evolutionary path. We also find that the orbital energy of the particle cloud is statistically independent of the surface contact property, meaning that the collision coefficient of restitution is a nonsensitive parameter in the outward spreading process of the shed particles., Comment: Accepted for publication in A&A

In this paper, the time- and propellant-optimal low-thrust rephasing problems in circular orbit are studied to depict their solution spaces in an atlas. The number of key parameters that settle the rephasing problems is reduced by developing a set of linearized equations of motion based on the Sundman transformation and by formulating two reduced shooting functions using the minimum principle and symmetry properties. Only one key parameter is identified for the time-optimal problem, while two key parameters are obtained for the propellant-optimal one. Numerical investigation of the relationships between these parameters and shooting variables reveals that they can be depicted by some curve (or contour) maps and approximated by piecewise functions (or linear interpolations). For the relatively short- or long-term rephasing cases, some analytical time- and propellant-optimal solutions are proposed and consistent with the numerical solutions. Numerical results demonstrate that the proposed solutions can provide good initial guesses to solve the low-thrust rephasing problems with nonlinear dynamics. Moreover, the approximations of the performance indexes can be used in the preliminary mission design.

We studied the creep motion of granular materials in a gradient potential field that is created using a slow spin-up experiment device. Natural sand confined in the acrylic box is spun up by a controlled turntable and the surface flows are captured using video-based measurements. Various spin-up accelerations were considered to understand the responses of creep motion on different accelerating paths. Convergent behaviors in the morphological change of sand surface were observed in the final steady state. To quantify the quasi-static spin-up process, we examined the net flux and the surface slope as a function of the spin rate and offset from the rotation axis. Evolution of sand creep motion demonstrated behaviors similar to regolith migration in numeric simulations, showing intermittency like general sheared granular systems. We noticed the sand surface approaches criticality as the spin-up proceeding, consistent with the observation that top-shaped asteroids near limiting spin rate take on critical shape. Comparisons to large-scale numeric simulations and analytical solutions reveal underlying similarities between our experiments and the million-year evolution of asteroid regolith under YORP acceleration, which raises the possibility of studying asteroid surface processes in laboratory analogue experiments.

Geostationary Earth orbit (GEO) satellites are of great significance in the space market. Low-thrust propulsion has been highly developed in the last decades because it is fuel-saving. Therefore, the design of GEO satellites is rapidly changing from classic high-thrust propulsion more and more toward low-thrust propulsion. However, the transfer time will be quite long using low-thrust propulsion and it will be very expensive if the ground supports the whole orbit raising. Therefore, autonomous orbit raising is necessary. Deep neural networks are trained to learn the optimal control. Results show that DNNs can be applied in this long-duration optimal control problem and have excellent performance.

In the design of multitarget interplanetary missions, there are always many options available, making it often impractical to optimize in detail each transfer trajectory in a preliminary search phase. Fast and accurate estimation methods for optimal transfers are thus of great value. In this paper, deep feed-forward neural networks are employed to estimate solutions to three types of optimization problems: the transfer time of time-optimal low-thrust transfers, fuel consumption of fuel-optimal low-thrust transfers, and the total dv of minimum-dv J2-perturbed multi-impulse transfers. To generate the training data, low-thrust trajectories are optimized using the indirect method and J2-perturbed multi-impulse trajectories are optimized using J2 homotopy and particle swarm optimization. The hyper-parameters of our deep networks are searched by grid search, random search, and the tree-structured Parzen estimators approach. Results show that deep networks are capable of estimating the final mass or time of optimal transfers with extremely high accuracy; resulting into a mean relative error of less than 0.5% for low-thrust transfers and less than 4% for multi-impulse transfers. Our results are also compared with other off-the-shelf machine-learning algorithms and investigated with respect to their capability of predicting cases well outside of the training data.

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., Comment: 63 pages, 17 figures

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 total angular momentum and total energy indicate 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 for understanding the complicated dynamical behaviors of the binary asteroid systems discovered in our Solar system., Comment: 22 pages, 12 figures

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., Comment: 35 pages, 8 figures, Advance in Space Research 2018

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., Comment: 28 pages, 4 figures

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., Comment: 31 pages, 4 figures, The Astronomical Journal 2016

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., Comment: 60 pages, 20 figures, The online version of this article (doi:10.1007/s10509-016-2884-z) contains supplementary material, which is available to authorized users. 6 videos, 5 rar files, 1 pdf file of figures

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., Comment: 30 pages and 8 figures. Besides, 3 videos are online at http://dx.doi.org/10.1016/j.pss.2016.04.007, Planetary and Space Science (2016)

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., Comment: 36pages, 12 figures

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., Comment: 4 figures in New Astronomy (2016)

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., Comment: 26 pages, 5 figures

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., Comment: This paper has been withdrawn by the author due to a crucial sign error in figure 1

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., Comment: 25pages, 3 figures, accepted by MNRAS