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.

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.

Autonomous determination of orbit for probe around asteroids using unscented Kalman filter

The observed images of the asteroid and the asteroid reference images are used to obtain the probe-to-asteroid direction and the location of the limb features of the asteroid in the inertial coordinate. These informa-tion in combination with the shape model of the asteroid and attitude information of the probe are utilized to ob-tain the position of the probe. The position information is then input to the UKF which determines the real-timeorbit of the probe. Finally, the autonomous orbit determination algorithm is validated using digital simulation.The determination of orbit using UKF is compared with that using extended Kalman filter (EKF), and the resultshows that UKF is superior to EKF.

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.

Generating Periodic Orbits for Explorations of Elongated Asteroids

A practical method is proposed to search for periodic orbits of elongated asteroids.The method obtains required initial variables of periodic orbits by using the rotating mass dipole with appropriate parameters,and then implement local iterations to obtain the real orbits over an asteroid in the polyhedral model.In this paper the dipole and polyhedral models,and list detailed procedures of the searching method are introduced.A planar single lobe orbit is presented to evaluate the effectiveness of the method,with the asteroid 216 Kleopatra of the triple asteroid system as a representative elongated body.By applying the above method,ten families of periodic orbits around Kleopatra are identified and discussed with respect to their orbital stabilities and periods.One sample of the sombrero orbit is checked by calculating 1000 hours to examine its orbital behavior.Besides the above orbits,the intriguing head-surrounding orbit is also analyzed.

The research objectives and observational possibilities for fast moving near-Earth asteroids

The paper describes observations of fast-moving near-Earth asteroids(NEAs) made with the small ground-based telescopes of National Time Service Center of Chinese Academy of Science(NTSC of CAS) and Research Institute "Mykolaiv Astronomical Observatory"(RI MAO) by the rotating-drift-scan CCD(RDS CCD) technique. This technique is used to obtain the point images of both the studied objects and reference stars. The results of ongoing follow-up observations of NEAs are discussed. The residual differences(O-C) between the observed and calculated positions from JPL ephemeris were generally small for these asteroids. The standard deviations of these differences were typically ±(0.2′′-0.3′′) in both coordinates for objects with apparent velocity which substantially exceed FWHM for the given exposure time. The results of comparative statistics for such observations from the MPC database show that this is a good level of precision for NEAs. Moreover, the telescopes with the RDS CCD technique implemented can observe the NEAs that closely approach the Earth and with enough observations can improve the precision of determining their orbital elements and impact predictions.

Optical spectroscopy and photometry of main-belt asteroids with a high orbital inclination

We carried out low-resolution optical spectroscopy of 51 main-belt asteroids, most of which have highly-inclined orbits. They are selected from D-type candidates in the SDSS-MOC 4 catalog. Using the University of Hawaii 2.2 m telescope and the Inter-University Centre for Astronomy and Astrophysics 2 m telescope in India, we determined the spectral types of 38 asteroids. Among them, eight asteroids were classified as D-type asteroids. Fractions of D-type asteroids are 3.0 ± 1.1% for low orbital inclination main-belt asteroids and 7.3 ± 2.0% for high orbital inclination main-belt asteroids. The results of our study indicate that some D-type asteroids were formed within the ecliptic region between the main belt and Jupiter, and were then perturbed by Jupiter.

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.

BGLS-based method of estimating the rotational periods of asteroids

As the asteroid rotational period is important to the study of the properties of asteroids(e.g.,super-fast rotators have structures owing an internal cohesion(rather than being rubble piles bounded by gravity only) so as not to fly apart), constructing an effective and fast method used to search the period attracts much researchers' attention. Recently, the Bayesian generalized Lomb–Scargle(BGLS)periodogram was developed to improve the convergence efficiency of the Lomb–Scargle method. However,the result of BGLS varies with the frequency range and cannot meet the two minimum/maximum requirements for a complete rotation of the asteroid. We propose a robust BGLS-based method that efficiently determines rotational periods. The proposed method employs a polynomial series to fit folded light curves with potential periods, initially calculated using the BGLS periodogram, and adopts a merit function to estimate and refine best-fit periods. We estimate the rotational periods of 30 asteroids applying the new method to light curves from the Palomar Transient Factory. Results confirm the effectiveness of the BGLS-based method in deriving rotational periods from ground-based observations of asteroids. Further application of the BGLS-based method to sparse light curves, such as Gaia data, is discussed.

Close Approaches of Potentially Hazardous Asteroids during Two Centuries

Asteroids are the most important small bodies in the solar system and the near-earth asteroids (NEAs) are of especial concern to the world. The reason is that they will make close approaches to the earth in the near future. We use a reasonable dynamical model and an efficient computing method to calculate the orbits of over 160 Potentially Hazardous Asteroids (PHAs) for two centuries.

A fast ellipsoid model for asteroids inverted from lightcurves

Research about asteroids has recently attracted more and more attention, especially focusing on their physical structures, such as their spin axis, rotation period and shape. The long distance between observers on Earth and asteroids makes it impossible to directly calculate the shape and other parameters of asteroids, with the exception of Near Earth Asteroids and others that have passed by some spacecrafts. Photometric measurements are still generally the main way to obtain research data on asteroids, i.e. the lightcurves recording the brightness and positions of asteroids. Supposing that the shape of the asteroid is a triaxial ellipsoid with a stable spin, a new method is presented in this article to reconstruct the shape models of asteroids from the lightcurves, together with other physical parameters. By applying a special curvature function, the method calculates the brightness integration on a unit sphere and Lebedev quadrature is employed for the discretization. Finally, the method searches for the optimal solution by the Levenberg-Marquardt algorithm to minimize the residual of the brightness. By adopting this method, not only can related physical parameters of asteroids be obtained at a reasonable accuracy, but also a simple shape model of an ellipsoid can be generated for reconstructing a more sophisticated shape model.

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.

Averaging analyses for spacecraft orbital motions around asteroids

This paper summarizes a few cases of spacecraft orbital motion around asteroid for which averaging method can be applied, i.e., when central body rotates slowly, fast, and when a spacecraft is near to the resonant orbits between the spacecraft mean motion and the central body＇s rotation. Averaging conditions for these cases are given. As a major extension, a few classes of near resonant orbits are analyzed by the averaging method. Then some resulted conclusions of these averaging analyses are applied to understand the stabil- ity regions in a numerical experiment. Some stability conclu- sions are obtained. As a typical example, it is shown in detail that near circular 1 ： 2 resonant orbit is always unstable.

Possible Duplicities of Five Asteroids

Some evidences of possible duplicities of five asteroids are presented. A satellite of (279) Thule was convincingly detected by a stellar occultation on 2008 April 3 by Thule and also from follow-up light curve observations. The orbital period of the satellite is 3.007 or 6.014 days, and the minimum diameter is estimated to be 52 km. A satellite of (324) Bamberga was detected by secondary drops of the light curve in 2007. The rotation period of the primary is 1.22625 days, and the revolution period of the secondary is 3.00 or 6.00 days. Presumed contact duplicity of the main body of the L4 Trojan (624) Hektor was detected by a stellar occultation by Hektor on 2008 January 24. A possible satellite of (657) Gunl?d was suggested from a secondary occultation by Gunl?d on 2008 November 29. The minimum of the diameter is 7 km. A possible satellite of (739) Mandeville was suggested by stellar occultation observations on 1980 December 10.

Gravitational Potential of Asteroids of Diverse Shapes

Asteroid research is of global security interest, we are more afraid about any impact of these asteroids on Earth. We seek through this work to provide a study on the effect of the asteroid’s shape on the gravity aspect. Knowledge of the potential is crucial to bodies approaching the asteroid. There is a range of asteroid shapes to consider. Some well-known asteroids such Ceres, Vesta, Iris and Oumuamua are considered in this study. After determining the moment of inertia of the asteroids depending on their materials, the gravity fields and the potential gravity of the asteroids are established when varying their shapes. A representation of the gravity field is given in three dimensional coordinate systems. Also, the behavior of the potential gravity is drawing in the function of the object’s location. The second part is dealing with the interpretation of all the obtained results in order to deduce some rules and features which would be useful for the identification of the asteroids. Thus, by the best knowledge of the effect of the asteroid’s shape, we would be more informed in the survey of the hazardous near earth objects.

The problem of the near-earth asteroids encountering the earth

The asteroids are the most important small bodies in the solar system, while the movement of the near-earth-asteroids (NEAs) is specially concerned by the world. The focus on these asteroids is that they encounter the earth. The orbital evolution of this kind of asteroid is studied by analyzing and comparing them; reasonable dynamical models and corresponding algorithm are given, and the formal numbered NEAs are calculated. The results of the minimal distance and the very closeapproach time with the earth agree well with those announced by the Minor Planet Center (MPC).

On-board modeling of gravity fields of elongated asteroids using Hopfield neural networks

To rapidly model the gravity field near elongated asteroids,an intelligent inversion method using Hopfield neural networks(HNNs)is proposed to estimate on-orbit simplified model parameters.First,based on a rotating mass dipole model,the gravitational field of asteroids is characterized using a few parameters.To solve all the parameters of this simplified model,a stepped parameter estimation model is constructed based on different gravity field models.Second,to overcome linearization difficulties caused by the coupling of the parameters to be estimated and the system state,a dynamic parameter linearization technique is proposed such that all terms except the parameter terms are known or available.Moreover,the Lyapunov function of the HNNs is matched to the problem of minimizing parameter estimation errors.Equilibrium values of the Lyapunov function areused as estimated values.The proposed method is applied to natural elongated asteroids 216 Kleopatra,951 Gaspra,and 433 Eros.Simulation results indicate that this method can estimate the simplified model parameters rapidly,and that the estimated simplified model provides a good approximation of the gravity field of elongated asteroids.

Structural analysis of rubble-pile asteroids applied to collisional evolution

Solar system small bodies come in a wide variety of shapes and sizes,which are achieved following very individual evolutional paths through billions of years.Nevertheless,some common mechanisms can still be found during these processes,e.g.,rubble-pile asteroids tend towards fluid equilibrium as they are reshaped by external disturbances.This paper focuses on the reshaping process of rubble-pile asteroids driven by meteorite impacts.A mesoscale cluster of solid spheres is employed as the principal model for a rubble-pile asteroid,for which little is actually known about their interior structure.We take this simple model as a rough guide to the qualitative aspects of the reshaping processes,and it can reveal,to some degree,the inner workings of rubble-pile asteroids.In our study,numerous possible equilibrium configurations are obtained via Monte Carlo simulation,and the structural stability of these configurations is determined via eigen analysis of the geometric constructions.The eigen decomposition reveals a connection between the cluster’s reactions and the types of external disturbance.Numerical simulations are performed to verify the analytical results.The gravitational N-body code pkdgrav is used to mimic the responses of the cluster under intermittent non-dispersive impacts.We statistically confirm that the stability index I S,the total gravitational potential P G,and the volume of inertia ellipsoid V E show consistent tendency of variation.A common regime is found in which the clusters tend towards crystallization under intermittent impacts,i.e.,only the configurations with high structural stability survive under the external disturbances.The results suggest the trivial non-disruptive impacts might play an important role in the rearrangement of the constituent blocks,which may strengthen these rubble piles and help to build a robust structure under impacts of similar magnitude.The final part of this study consists of systematic simulations over two parameters,the projectile momentum and the rotational speed of the cluster.The results show a critical value exists for the projectile momentum,as predicted by theory,below which all clusters become responseless to external disturbances;and the rotation proves to be significant for it exhibits an“enhancing”effect on loose-packed clusters,which coincides with the observation that several fast-spinning asteroids have low bulk densities.

New image processing algorithm for terminal guidance of multiple kinetic-energy impactors for disrupting hazardous asteroids

This paper describes the preliminary study results of developing a hypervelocity terminal intercept guidance system of a multiple kinetic-energy impactor vehicle(MKIV).The proposed MKIV system is intended to fragment or pulverize an asteroid of smaller than approximately 150 m in diameter that is detected with a mission lead time of shorter than 10 years,without using nuclear explosive devices.This paper focuses on the development of a new image processing algorithm based on Otsu’s method for the coordinated terminal intercept guidance and control of multiple kinetic-energy impactors employing visual and/or infrared sensors.A scaled polyhedron shape model of asteroid(216)Kleopatra is used as a fictional target asteroid.GPU-based simulation results demonstrate the feasibility of impacting a small irregular-shaped asteroid by using the proposed new image processing algorithm and a classical pulsed TPN(true proportional navigation)terminal guidance law.

Target selection for a small low-thrust mission to near-Earth asteroids

The preliminary mission design of spacecraft missions to asteroids often involves,in the early phases,the selection of candidate target asteroids.The final result of such an analysis is a list of asteroids,ranked with respect to the necessary propellant to be used,that the spacecraft could potentially reach.In this paper we investigate the sensitivity of the produced asteroids rank to the employed trajectory model in the specific case of a small low-thrust propelled spacecraft beginning its journey from the Sun–Earth L2 Lagrangian point and heading to a rendezvous with some near-Earth asteroid.We consider five increasingly complex trajectory models:impulsive,Lambert,nuclear electric propulsion,nuclear electric propulsion including the Earth’s gravity,solar electric propulsion including the Earth’s gravity and we study the final correlation between the obtained target rankings.We find that the use of a lowthrust trajectory model is of great importance for target selection,since the use of chemical propulsion surrogates leads to favouring less attractive options 19%of times,a percentage that drops to 8%already using a simple nuclear electric propulsion model that neglects the Earth’s gravity effects and thrust dependence on the solar distance.We also find that for the study case considered,a small interplanetary CubeSat named M-ARGO,the inclusion of the Earth’s gravity in the considered dynamics does not affect the target selection significantly.