Photometric Analysis for Asteroid(81)Terpsichore using Convex Inversion and Phase Function Fitting Methods

The shapes and rotation states(periods and pole orientations)of main-belt asteroids are important for understanding their formation and evolution.In order to obtain sufficient photometric data covering different apparitions for asteroid(81)Terpsichore,ground-based photometric observations in 2020 and 2021 were carried out.By combining published and newly obtained photometric data,we calculated the shape and spin parameters for(81)Terpsichore using the convex inversion method.With this method,we have derived a best fitted pole orientation—(22.2±_(3.1)^(3.3°),17.5±_(5.5)^(10.8°))with a spin period of 10.94±_(0.01)^(0.01)h.Based on the derived convex shape of(81)Terpsichore,we have fitted the H,G+1,G_(2)phase function using the calibrated TESS data and Gaia data after accounting for the lightcurve amplitude correction.As a result,we have derived its absolute magnitude H=8.68±_(0.19)^(0.22)mag with corresponding phase function parameters G_(1)=0.82±_(0.10)^(0.09)and G_(2)=0.02±_(0.02)^(0.03).

A Rendezvous Mission to the Second Earth Trojan Asteroid 2020 XL_5 with Low-Thrust Multi-Gravity Assist Techniques

As the second of Earth's Trojan asteroids, 2020 XL_(5) is worthy of rendezvous and even sample return missions in many aspects. In this paper, a rendezvous mission to Earth's second Trojan asteroid 2020 XL_(5) is proposed.However, due to its high inclination and large eccentricity, direct impulsive transfer requires large amounts of fuel consumption. To address this challenge, we explore the benefits of electric propulsion and multi-gravity assist techniques for interplanetary missions. These two techniques are integrated in this mission design. The design of a low-thrust gravity-assist(LTGA) trajectory in multi-body dynamics is thoroughly investigated,which is a complex process. A comprehensive framework including three steps is presented here for optimization of LTGA trajectories in multi-body dynamics. The rendezvous mission to 2020 XL_(5) is designed with this three-step approach. The most effective transfer sequence among the outcomes involves Earth–Venus–Earth–Venus-2020 XL_(5). Numerical results indicate that the combination of electric propulsion and multi-gravity assists can greatly reduce the fuel consumption, with fuel consumption of 9.03%, making it a highly favorable choice for this rendezvous mission.

Accelerating Asteroidal Period and Pole Inversion from Multiple Lightcurves Using Parallel Differential Evolution and Cellinoid Shape Model

Determining asteroid properties provides valuable physical insights but inverting them from photometric lightcurves remains computationally intensive.This paper presents a new approach that combines a simplified Cellinoid shape model with the Parallel Differential Evolution(PDE)algorithm to accelerate inversion.The PDE algorithm is more efficient than the Differential Evolution algorithm,achieving an extraordinary speedup of 37.983 with 64 workers on multicore CPUs.The PDE algorithm accurately derives period and pole values from simulated data.The analysis of real asteroid lightcurves validates the method’s reliability:in comparison with results published elsewhere,the PDE algorithm accurately recovers the rotational periods and,given adequate viewing geometries,closely matches the pole orientations.The PDE approach converges to solutions within 20,000 iterations and under one hour,demonstrating its potential for large-scale data analysis.This work provides a promising new tool for unveiling asteroid physical properties by overcoming key computational bottlenecks.

Characteristics and close-range exploration methods of near- Earth asteroid 2016HO_(3)

The characteristics of asteroids are vital parameters for planning asteroid exploration missions.These characteristics have been explored in close range for some typical asteroids,and are summarized in the article.This allows estimates of the characteristics of asteroid 2016HO_(3),the target of the first Chinese asteroid exploration mission,Tianwen 2.We obtain 80 characteristic parameters in 9 categories and analyze their impacts on the mission.By comparing three close-range exploration modes,we provide advantages and disadvantages of each,and propose suitable methods for the exploration of 2016HO_(3).Owing to the weak gravity and small size of 2016HO_(3),a combination of multiple hovering positions and active orbiting is recommended for scientific exploration.

Modeling and Analysis of the Impacts of Temporal-Spatial Variant Troposphere on Ground-Based SAR Imaging of Asteroids

The near-Earth asteroid collisions could cause catastrophic disasters to humanity and the Earth,so it is crucial to monitor asteroids.Ground-based synthetic aperture radar(SAR)is an observation technique for high resolution imaging of asteroids.The ground-based SAR requires a long integration time to achieve a large synthetic aperture,and the echo signal will be seriously affected by temporal-spatial variant troposphere.Traditional spatiotemporal freezing tropospheric models are ineffective.To cope with this,this paper models and analyses the impacts of temporal-spatial variant troposphere on ground-based SAR imaging of asteroids.For the background tropo-sphere,a temporal-spatial variant ray tracing method is proposed to trace the 4D(3D spatial+temporal)refractive index network provided by the numerical weather model,and calculate the error of the background troposphere.For the tropospheric turbulence,the Andrew power spectral model is used in conjunction with multiphase screen theory,and varying errors are obtained by tracking the changing position of the pierce point on the phase screen.Through simulation,the impact of temporal-spatial variant tropospheric errors on image quality is analyzed,and the simulation results show that the X-band echo signal is seriously affected by the troposphere and the echo signal must be compensated.

Study of photometric phase curve:assuming a cellinoid ellipsoid shape for asteroid(106)Dione

We carried out new photometric observations of asteroid （106） Dione at three apparitions （2004, 2012 and 2015） to understand its basic physical properties. Based on a new brightness model, new photometric observational data and published data of （106） Dione were analyzed to characterize the morphology of Dione＇s photometric phase curve. In this brightness model, a cellinoid ellipsoid shape and three-parameter （H, G1, G2） magnitude phase function system were involved. Such a model can not only solve the phase function system parameters of （106） Dione by considering an asymmetric shape of an asteroid, but also can be applied to more asteroids, especially those without enough photometric data to solve the convex shape. Using a Markov Chain Monte Carlo （MCMC） method, Dione＇s absolute magnitude of H = 7.66＋0.03-0.03 mag, and phase function parameters G1 = 0.682＋0.077-0.077 and G2 = 0.081＋0.042-0.042 were obtained. Simultaneously, Dione＇s simplistic shape, orientation of pole and rotation period were also determined preliminarily.

Study of photometric phase curve with new brightness model:refining phase function system parameters of asteroid(107)Camilla

We characterize the morphology of the photometric phase curve model of an asteroid with a three- parameter magnitude phase function H - G1 - G2 system by considering the effect of brightness variation arising from a triaxial ellipsoid representing the asteroid＇s shape. Applying this new model and a Markov Chain Monte Carlo method, we refine the photometric phase curve of asteroid （107） Camilla and obtain its absolute magnitude H = 7.026-0.054^＋0.052 mag, and phase function parameters G1=0.489-0.044^＋0.043 and G2 = 0.259-0.023^＋0.023.Meanwhile, we also determine （107） Camilla＇s orientation of pole （74.1°-4.5°^＋4.3°,50.2°-5.0°^＋5.4°）. with rotational period of 4.843928-0.000001^＋0.000001 h, and axial ratios a/b ： 1.409-0.020^＋0.020 And b/c =1.249-0.060^＋0.063. Furthermore, according to the values of phase function parameters G1 and G2, we infer that asteroid （107） Camilla is an X-type asteroid.

Nocardia asteroides XI的鉴定及抗菌活性研究

目的为了筛选出具有生物活性的放线菌,并研究其可能存在的潜在研究及商业价值。方法从台州市剑门港海区海底淤泥中采样并分离到3株具有抗菌活性的放线菌,通过分子生物学、(G+C)mol%含量、菌落及形态学进行菌种鉴定,应用BLAST Clustal W(V 1.83)和Mega(V 5.1)等软件进行系统发育树分析,以鉴定其分离地位,并对其发酵产物进行活性检测。结果经研究发现一株菌株经不同发酵配方发酵,其胞内胞外物质均具有较好的抑菌效果,该菌经鉴定为星状诺卡菌,命名为Nocardia asteroids X1。结论 Nocardia asteroides X1筛选与鉴定丰富了抗生素产生菌资源,有潜在的开发出新的抗菌药物的可能性,值得进一步深入研究。

A Tiny Piece of Basalt Probably from Asteroid 4 Vesta

Grove Mountains (GRV) 99018 is a new eucrite (0.23 g), consisting mainly of pyroxene (50.5 vol%) and plagioclase (37.2 vol%) with minor silica minerals (7.0 Vol%) and opaque minerals (5.2 vol%). It was intensely shocked, leading to partial melting, formation of abundant tiny inclusions in pyroxenes and plagioclase, and heavy brecciation. Exsolution of most pyroxenes (1-3μm in width of the lamellae), recrystallization of the shpck-induced melt pockets and veins (5-20μm in size), and homogeneous compositions of pyroxenes of various occurrences suggest the intense thermal metamorphism of GRV 99018 in the asteroidal body Vesta. This new eucrite will bring additional constraints on the chemical composition and multi-stage thermal and shock history of Vesta.

Routing the asteroid surface vehicle with detailed mechanics

The motion of a surface vehicle on/above an irregular object is inv.estigated for a potential interest in the insitu explorations to asteroids of the solar system. A global valid numeric method, including detailed gravity and geo- morphology, is developed to mimic the behaviors of the test particles governed by the orbital equations and surface cou- pling effects. A general discussion on the surface mechanical environment of a specified asteroid, 1620 Geographos, is presented to make a global evaluation of the surface vehicle＇s working conditions. We show the connections between the natural trajectories near the ground and differential features of the asteroid surface, which describes both the good and bad of typical terrains from the viewpoint of vehicles＇ dynamic performances. Monte Carlo simulations are performed to take a further look at the trajectories of particles initializing near the surface. The simulations reveal consistent conclusions with the analysis, i.e., the open- field flat ground and slightly concave basins/valleys are the best choices for the vehicles＇ dynamical security. The dependence of decending trajectories on the releasing height is studied as an application; the results show that the pole direction （where the centrifugal force is zero） is the most stable direction in which the shift of a natural trajectory will be well limited after landing. We present this work as an example for pre-analysis that provides guidance to engineering design of the exploration site and routing the surface vehicles.

Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

A survey on orbital dynamics and navigation of asteroid missions

Asteroid exploration is currently one of the most concerned topics among international space agencies. Or- bital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief review on the dynamics, control and navigation of asteroid reconnaissance orbits, including the heliocentric transfer orbit and near as- teroid orbit. The developments in optimization techniques of the transfer segment are discussed in detail. We surveyed global researches in this field and made comments on several important progresses. The final section proposed a prospec- tive of future studies with emphasis on the key techniques of these issues in the asteroid exploration missions.

Near-Earth asteroid flyby trajectories from the Sun-Earth L2 for Chang’e-2’s extended flight

Driven by curiosity about possible flight options for the Chang＇e-2 spacecraft after it remains at the Sun-Earth L2 point, effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroid flyby trajectories. The approaches include the use of modified unstable manifolds, grid search of the manifolds＇ parameters, and a two-impulse maneuver for orbital phase matching and z-axis bias change, and are demonstrated to be effective in asteroid target screening and trajectory optimization. Asteroid flybys are expected to be within a distance of 2 × 10^7 km from the Earth owing to the constrained Earth-spacecraft communication range. In this case, the spacecraft＇s orbital motion is significantly affected by the gravities of both the Sun and the Earth, and therefore, the concept of the ＂he- liocentric oscillating-Kepler orbit＂ is proposed, because the classical orbital elements of the flyby trajectories referenced in the heliocentric inertial frame oscillate significantly with respect to time. The analysis and results presented in this study show that, among the asteroids whose orbits are the most accurately predicted, ＂Toutatis＂, ＂2005 NZ6＂, or ＂2010 CL19＂ might be encountered by Chang＇e-2 in late 2012 or 2013 with total impulses less than 100 rn/s.

A particle-linkage model for non-axisymmetric elongated asteroids

This paper investigates a simplified model for describing the gravitational fields of non- axisymmetric elongated asteroids. The connection between the simplified model and the target aster-oid is built by considering the positions of equilibrium points. To improve the performance of po-sition matching for the equilibrium points associated with these non-axisymmetric asteroids, a non-axisymmetric triple-particle-linkage model is proposed based on two existing axisymmetric particle- linkage models. The unknown parameters of the simplified model are determined by minimizing the matching error using the nonlinear optimization method. The proposed simplified model is applied for three realistic elongated asteroids, 243 Ida, 433 Eros and （8567） 1996 HW1. The simulation re-sults verify that the current particle-linkage model has better matching accuracy than the two existing particle-linkage models. The comparison, between the simplified model and the polyhedral model, on the topological cases of the equilibrium points and the distribution of gravitational potential further validate the rationality and accuracy of the simplified model.

Adaptive Quasi Fixed-Time Orbit Control Around Asteroid with Performance Guarantees

This paper investigates a novel quasi fixed-time orbit tracking control method for spacecraft around an asteroid in the presence of uncertain dynamics and unknown uncertainties.To quantitatively characterize the transient and steady-state responses of orbit tracking error system,a continuous performance function is devised via using a quartic polynomial.Then,integrating backstepping control technique and barrier Lyapunov function leads to a quasi fixed-time convergent orbit tracking controller without using any fractional state information and symbolic functions.Finally,two groups of illustrative examples are employed to test the effectiveness of the proposed orbit control method.

A method for classifying orbits near asteroids

A method for classifying orbits near asteroids under a polyhedral gravitational field is presented, and may serve as a valuable reference for spacecraft orbit design for asteroid exploration. The orbital dynamics near aster- oids are very complex. According to the variation in orbit characteristics after being affected by gravitational perturbation during the periapsis passage, orbits near an as- teroid can be classified into 9 categories： （1） surrounding- to-surrounding, （2） surrounding-to-surface, （3） surrounding- to-infinity, （4） infinity-to-infinity, （5） infinity-to-surface, （6） infinity-to-surrounding, （7） surface-to-surface, （8） surface- to-surrounding, and （9） surface-to- infinity. Assume that the orbital elements are constant near the periapsis, the gravitation potential is expanded into a harmonic series. Then, the influence of the gravitational perturbation on the orbit is studied analytically. The styles of orbits are dependent on the argument of periapsis, the periapsis radius, and the periapsis velocity. Given the argument of periapsis, the orbital energy before and after perturbation can be derived according to the periapsis radius and the periapsis velocity. Simulations have been performed for orbits in the gravitational field of 216 Kleopatra. The numerical results are well consistent with analytic predictions.

Modeling method and preliminary model of Asteroid Toutatis from Chang'E-2 optical images

Shape modeling is fundamental to the analysis of dynamic environment and motion around asteroid. Chang＇E- 2 successfully made a flyby of Asteroid 4179 Toutatis and obtained plenty of high-resolution images during the mis- sion. In this paper, the modeling method and preliminary model of Asteroid Toutatis are discussed. First, the optical images obtained by Chang＇E-2 are analyzed. Terrain and silhouette features in images are described. Then, the modeling method based on previous radar model and preliminary information from optical images is proposed. A preliminary polyhedron model of Asteroid Toutatis is established. Finally, the spherical harmonic coefficients of Asteroid Toutatis based on the polyhedron model are obtained. Some parameters of model are analyzed and compared. Although the model proposed in this paper is only a preliminary model, this work offers a valuable reference for future high-resolution models.

Utilization of an H-reversal trajectory of a solar sail for asteroid deflection

Near Earth Asteroids have a possibility of impacting the Earth and always represent a threat. This paper proposes a way of changing the orbit of the asteroid to avoid an impact. A solar sail evolving in an H-reversal trajectory is utilized for asteroid deflection. Firstly, the dynamics of the solar sail and the characteristics of the H-reversal trajectory are analyzed. Then, the attitude of the solar sail is optimized to guide the sail to impact the target asteroid along an H-reversal trajectory. The impact velocity depends on two important parameters： the minimum solar distance along the trajectory and lightness number of the solar sail. A larger lightness number and a smaller solar distance lead to a higher impact velocity. Finally, the deflection capability of a solar sail impacting the asteroid along the H-reversal trajectory is discussed. The results show that a 10kg solar sail with a lead-time of one year can move Apophis out of a 600-m keyhole area in 2029 to eliminate the possibility of its resonant return in 2036.

Parametric resonance orbit analysis for irregular shaped asteroids based on the perturbed particle-linkage model

There are plentiful asteroids moving periodically around their central primaries, such as the Sun. Due to the perturbation of the central primary, the gravitational force of the perturbed asteroid system varies periodically. In this paper, based on the idea of integrating the solar gravitational force as a part of the system instead of treating it as perturbation, the parametric resonance response is investigated. A novel type of stable parametric resonance orbits has been detected. It is found that the steady-state motion amplitude of parametric resonance orbit is determined by the frequency-response equation. The stability of the novel orbits has also been demonstrated. The new type of orbits may contribute to possible asteroid exploration missions.

Dynamic Problems of the Planets and Asteroids, and Their Discussion

The problems of dynamics of celestial bodies are considered which in the literature are explained by instability and randomness of movements. The dynamics of planets orbits on an interval 100 million years was investigated by new numerical method and its stability is established. The same method is used for computing movements of two asteroids Apophis and 1950DA. The evolution of their movement on an interval of 1000 is investigated. The moments of their closest passages at the Earth are defined. The different ways of transformation of asteroids trajectories into orbits of the Earth’s satellites are considered. The problems of interest are discussed from the different points of view.