Orbits Of Asteroids Research Articles

Comparison of Solar Sail Spacecraft Flight and Low Thrust Spacecraft Flight to Potentially Hazardous Asteroid Orbit

This paper outlines the nonlinear flight simulation of a low thrust spacecraft and a solar sail spacecraft. The main purpose of the work is ballistic comparison of solar sail spacecraft flight and low thrust spacecraft flight. The mathematical motion model for such types of spacecraft is formulated and described. The work considers the mathematical motion models within the heliocentric system of coordinates. Motion simulation process is the best way to assess the reasonableness of the mathematical model. On the basis of the formulated mathematical models, a special software for nonlinear flight simulation is developed. In particular, the flight of the low thrust spacecraft from Earth's orbit to the potentially hazardous asteroid is simulated. The findings of the work consist of heliocentric trajectories, time dependency graphs of flight parameters, the values of flight duration and the value of propellant consumption.

Study of the Effects of Projectile Shape in the Asteroid Orbit Change by Spacecraft Impact

NEO (Near Earth Object) are the celestial bodies which pass near the Earth. One NEO deflection method is spacecraft impact. In order to estimate its results, it is necessary to clarify mechanism of momentum change of NEO. Generally, β is used as an evaluation index in this field and affected by various factors, so this study focuses on spacecraft shape. Five types of projectile shape were tested and compared in term of two aspects. In addition, we made comparison by using scaling law in order to compare the shape effect in the speed region which is assumed to using actual NEO deflection.

Probability of coincidental similarity among the orbits of small bodies – I. Pairing

Probability of coincidental clustering among orbits of comets, asteroids and meteoroids depends on many factors like: the size of the orbital sample searched for clusters or the size of the identified group, it is different for groups of 2,3,4,… members. Probability of coincidental clustering is assessed by the numerical simulation, therefore, it depends also on the method used for the synthetic orbits generation.We have tested the impact of some of these factors. For a given size of the orbital sample we have assessed probability of random pairing among several orbital populations of different sizes. We have found how these probabilities vary with the size of the orbital samples.Finally, keeping fixed size of the orbital sample we have shown that the probability of random pairing can be significantly different for the orbital samples obtained by different observation techniques. Also for the user convenience we have obtained several formulae which, for given size of the orbital sample can be used to calculate the similarity threshold corresponding to the small value of the probability of coincidental similarity among two orbits.

SEARCH SMALL BODIES IMAGES IN COLLECTIONS DIGITIZED PHOTOGRAPHIC OBSERVATIONS OF PREVIOUS YEARS

Photographic observations of XX century is an important source of information on small bodies of the Solar system. The observations of chronologically earlier oppositions, photometric evaluation of brightness for long periods of time allow refining the orbits of asteroids and identifying various non-stationaries. Unfortunately international databases were contained a very little observable data for accurate estimates of geometric and kinematic parameters of asteroids. We analyzed the results of digital processing of 338 photographic plates of Northern Sky Survey (FON) project. Modern approach to processing early observations using new digital technologies provides a sufficiently high accuracy of coordinates and magnitudes for all objects on astroplates. As a result 570 images of asteroids and 4 images of comets from 8-16 magnitudes were detected on these plates. Equatorial coordinates and stellar magnitudes of them were composed to catalog of asteroids. All positions were compared with ephemeris. Analysis of ephemeris calculations with known today about the several hundred small planets with observation data showed some interesting results.

On the problem of designing small spacecraft with electric propulsion power plants for studying minor bodies of the Solar System

Aspects of the design of small spacecraft with electric propulsion power plants for investigating minor bodies in the Solar System are examined. The results of design and ballistic analysis of transfer into an orbit of terrestrial asteroids using electric propulsion thrusters are given. The possible concept design of the spacecraft is determined and the structure of a small spacecraft with an electric propulsion power plant is presented. Parameters of the electric propulsion power plant of a small spacecraft for a flight to the minor bodies of the Solar System are estimated.

Dynamics of Centaur Chariklo and evolution of its rings

It follows from observations that the asteroid Chariklo has two outer rings. The purpose of this paper is constructing the equilibrium model of asteroid and developing the kinetic mechanism of evolution of its rings. We have specified for Chariklo the density \(\rho_{0} \approx 2.71~\mbox{g}/\mbox{cm}^{3}\), the mass \(M_{0} \approx 8.817 \times 10^{21}~\mbox{g}\), and the average radius \(R_{0} \approx 128.16~\mbox{km}\). Its rings are modeled by circular gravitating tori consisting of the small rock-ice particles that orbit the asteroid. The method does not imply the presence of hidden satellites close to the asteroid, and the equilibrium of the rings is determined by the small velocity dispersion and gravity of particles. The problem of expansion of the internal torus gravitational potential in series in powers of its geometrical parameter is solved. This enables the gravitational energy of Chariklo’s rings to be found and to express their masses in terms of the mass of the asteroid \(M_{0}\). We calculated the mass of the inner ring to be \(M_{r1} \approx 9.8 \times 10^{18}~\mbox{g}\), and its relation to the mass of the asteroid is \(\frac{M_{r1}}{M_{0}} \approx 0.001\); similarly, for the outer ring \(M_{r2} \approx 10^{18}~\mbox{g}\), and \(\frac{M_{r2}}{M_{0}} \approx 0.0001\). The mass ratio \(\frac{M_{r1}}{M_{r2}} \approx 10\) is typical for satellites of other asteroids and dwarf planets. The velocity dispersion of particles in rings \(\upsilon_{1} \approx 1~\mbox{m}/\mbox{s}\) and \(\upsilon_{2} \approx 45~\mbox{cm}/\mbox{s}\) is no greater than \(1 \div 2~\%\) of its rotational velocity \(\upsilon_{rot} \approx 40~\mbox{m}/\mbox{s}\). The particle of medium radius \(r_{p} = 25~\mbox{cm}\) has the mean free path \(\lambda \approx 7~\mbox{m}\), and its diffusion time from center line on the surface of the torus is \(\frac{T'_{1}}{T_{rot1}} \approx 13\) and \(\frac{T'_{2}}{T_{rot2}} \approx 5\). The dissipation rate equation for Chariklo’s rings is derived. From this equation a surprising result follows: the time of energy dissipation (the time of evolution of rings) is only \(T_{d1} \approx 10^{3} \div 10^{4}~\mbox{years}\), which by astronomical measures is a very short time scale. We adduce the arguments supporting the idea that these rings in near future can become Chariklo’s satellites, and that the transformation of the rings into satellites energetically is favored.

Influence of the Centaurs and TNOs on the main belt and its families

Centaurs are objects whose orbits are found between those of the giant planets. They are supposed to originate mainly from the TransNeptunian objects, and they are among the sources of NearEarth Objects.TransNeptunian Objects (TNOs) cross Neptune's orbit and produce the Centaurs. We investigate their interactions with main belt asteroids to determine if chaotic scattering caused by close encounters and impacts by these bodies may have played a role in the dynamical evolution of the main belt. We find that Centaurs and TNOs that reach the inner Solar System can modify the orbits of main belt asteroids, though only if their mass is of the order of 1 billion less the mass of the sun for single encounters or, one order less in the case of multiple close encounters. Centaurs and TNOs are unlikely to have significantly dispersed young asteroid families in the main belt, but they can have perturbed some old asteroid families. Current main belt asteroids that originated as Centaurs or Trans-Neptunian Objects may lie in the outer belt with short lifetime less than 4 My, most likely between 2.8 au and 3.2 au at larger eccentricities than typical of main belt asteroids.

Modeling orbital gamma-ray spectroscopy experiments at carbonaceous asteroids.

To evaluate the feasibility of measuring differences in bulk composition among carbonaceous meteorite parent bodies from an asteroid or comet orbiter, we present the results of a performance simulation of an orbital gamma-ray spectroscopy (GRS) experiment in a Dawn-like orbit around spherical model asteroids with a range of carbonaceous compositions. The orbital altitude was held equal to the asteroid radius for 4.5 months. Both the asteroid gamma-ray spectrum and the spacecraft background flux were calculated using the MCNPX Monte-Carlo code. GRS is sensitive to depths below the optical surface (to ≈20-50 cm depth depending on material density). This technique can therefore measure underlying compositions beneath a sulfur-depleted (e.g., Nittler et al. 2001) or desiccated surface layer. We find that 3σ uncertainties of under 1 wt% are achievable for H, C, O, Si, S, Fe, and Cl for five carbonaceous meteorite compositions using the heritage Mars Odyssey GRS design in a spacecraft-deck-mounted configuration at the Odyssey end-of-mission energy resolution, FWHM = 5.7 keV at 1332 keV. The calculated compositional uncertainties are smaller than the compositional differences between carbonaceous chondrite subclasses.

Asteroids 87887 – 415992: the youngest known asteroid pair?

Context. Pairs of asteroids, that is, couples of single bodies on tightly similar heliocentric orbits, were recently postulated as a new category of objects in the solar system. They are believed to be close twins to binary and multiple systems. Aims. Ages of the known pairs range from about 15 kyr to nearly a million years. Beyond the upper limit, the pairs disperse in the background population of asteroids and become difficult to detect. Below the lower limit, the pairs should be easily recognizable if they exist and are discovered by surveys. Using the available data, we analyze the possible existence of very young asteroid pairs with clearly proven ages ≤ 10 kyr. Methods. We searched for candidate very young asteroid pairs in the current catalog of asteroid orbits. After a preliminary analysis, we selected the most promising case of the small asteroids (87887) 2000 SS286 and (415992) 2002 AT49. We collected photometric observations to determine their rotation periods and absolute magnitudes. Results. The rotation period of (87887) 2000 SS286 is 5.7773 ± 0.0004 h. Analysis of the data for (415992) 2002 AT49 indicates as the most probable period 2.6366 ± 0.0003 h, but other solutions are still possible. The composite light curves of the two asteroids have very low amplitudes, 0.22 and 0.12 mag, suggesting roundish shapes. Our observations also allow us to determine the absolute magnitude in R band H R = 14.99 ± 0.04 and H R = 16.24 ± 0.03 for the primary and secondary components. A transformation to the visible band provides H = 15.44 ± 0.05 and H = 16.69 ± 0.04. These two asteroids experienced a very close encounter, probably a formation event, some 7.4 ± 0.3 kyr ago. The formal extension of our numerical runs backward in time reveal that these close encounters may have continued, starting from ≃ 45 kyr ago. However, based on tests using synthetic fission events, we argue that the older age solutions might be the true solution only at ≃ (10−15)% level, assuming their low initial separation velocity is of between 10−20 cm s -1 . This means that 87887–415992 probably is the youngest known asteroid pair in our dataset with a reliable determined age.

Asteroid retrieval missions enabled by invariant manifold dynamics

Near Earth Asteroids are attractive targets for new space missions; firstly, because of their scientific importance, but also because of their impact threat and prospective resources. The asteroid retrieval mission concept has thus arisen as a synergistic approach to tackle these three facets of interest in one single mission. This paper reviews the methodology used by the authors (2013) in a previous search for objects that could be transported from accessible heliocentric orbits into the Earth's neighbourhood at affordable costs (or Easily Retrievable Objects, a.k.a. EROs). This methodology consisted of a heuristic pruning and an impulsive manoeuvre trajectory optimisation. Low thrust propulsion on the other hand clearly enables the transportation of much larger objects due to its higher specific impulse. Hence, in this paper, low thrust retrieval transfers are sought using impulsive trajectories as first guesses to solve the optimal control problem. GPOPS-II is used to transcribe the continuous-time optimal control problem to a nonlinear programming problem (NLP). The latter is solved by IPOPT, an open source software package for large-scale NLPs. Finally, a natural continuation procedure that increases the asteroid mass allows to find out the largest objects that could be retrieved from a given asteroid orbit. If this retrievable mass is larger than the actual mass of the asteroid, the asteroid retrieval mission for this particular object is said to be feasible. The paper concludes with an updated list of 17 EROs, as of April 2016, with their maximum retrievable masses by means of low thrust propulsion. This ranges from 2000tons for the easiest object to be retrieved to 300tons for the least accessible of them.

EXTREME AO OBSERVATIONS OF TWO TRIPLE ASTEROID SYSTEMS WITH SPHERE

ABSTRACT We present the discovery of a new satellite of asteroid (130) Elektra—S/2014 (130) 1—in differential imaging and in integral field spectroscopy data over multiple epochs obtained with Spectro-Polarimetric High-contrast Exoplanet Research/Very Large Telescope. This new (second) moonlet of Elektra is about 2 km across, on an eccentric orbit, and about 500 km away from the primary. For a comparative study, we also observed another triple asteroid system, (93) Minerva. For both systems, component-resolved reflectance spectra of the satellites and primary were obtained simultaneously. No significant spectral difference was observed between the satellites and the primary for either triple system. We find that the moonlets in both systems are more likely to have been created by sub-disruptive impacts as opposed to having been captured.

THE SCHULHOF FAMILY: SOLVING THE AGE PUZZLE

ABSTRACT The Schulhof family, a tight cluster of small asteroids around the central main belt body (2384) Schulhof, belongs to a so far rare class of very young families (estimated ages less than 1 Myr). Characterization of these asteroid clusters may provide important insights into the physics of the catastrophic disruption of their parent body. The case of the Schulhof family has been up to now complicated by the existence of two proposed epochs of its origin. In this paper, we first use our own photometric observations, as well as archival data, to determine the rotation rate and spin axis orientation of the largest fragment (2384) Schulhof. Our data also allow us to better constrain the absolute magnitude of this asteroid, and thus also improve the determination of its geometric albedo. Next, using the up-to-date catalog of asteroid orbits, we perform a new search of smaller members in the Schulhof family, increasing their number by 50%. Finally, the available data are used to access Schulhof's family age anew. We now find that the younger of the previously proposed two ages of this family is not correct, resulting from a large orbital uncertainty of single-opposition members. Our new runs reveal a single age solution of about 800 kyr with a realistic uncertainty of 200 kyr.

Shadowing Lemma and chaotic orbit determination

Orbit determination is possible for a chaotic orbit of a dynamical system, given a finite set of observations, provided the initial conditions are at the central time. In a simple discrete model, the standard map, we tackle the problem of chaotic orbit determination when observations extend beyond the predictability horizon. If the orbit is hyperbolic, a shadowing orbit is computed by the least squares orbit determination. We test both the convergence of the orbit determination iterative procedure and the behaviour of the uncertainties as a function of the maximum number $n$ of map iterations observed. When the initial conditions belong to a chaotic orbit, the orbit determination is made impossible by numerical instability beyond a computability horizon, which can be approximately predicted by a simple formula. Moreover, the uncertainty of the results is sharply increased if a dynamical parameter is added to the initial conditions as parameter to be estimated. The uncertainty of the dynamical parameter decreases like $n^a$ with $a<0$ but not large (of the order of unity). If only the initial conditions are estimated, their uncertainty decreases exponentially with $n$. If they belong to a non-chaotic orbit the computational horizon is much larger, if it exists at all, and the decrease of the uncertainty is polynomial in all parameters, like $n^a$ with $a\simeq 1/2$. The Shadowing Lemma does not dictate what the asymptotic behaviour of the uncertainties should be. These phenomena have significant implications, which remain to be studied, in practical problems of orbit determination involving chaos, such as the chaotic rotation state of a celestial body and a chaotic orbit of a planet-crossing asteroid undergoing many close approaches.

The global impact distribution of Near-Earth objects

Asteroids that could collide with the Earth are listed on the publicly available Near-Earth object (NEO) hazard web sites maintained by the National Aeronautics and Space Administration (NASA) and the European Space Agency (ESA). The impact probability distribution of 69 potentially threatening NEOs from these lists that produce 261 dynamically distinct impact instances, or Virtual Impactors (VIs), were calculated using the Asteroid Risk Mitigation and Optimization Research (ARMOR) tool in conjunction with OrbFit. ARMOR projected the impact probability of each VI onto the surface of the Earth as a spatial probability distribution. The projection considers orbit solution accuracy and the global impact probability. The method of ARMOR is introduced and the tool is validated against two asteroid-Earth collision cases with objects 2008 TC3 and 2014 AA. In the analysis, the natural distribution of impact corridors is contrasted against the impact probability distribution to evaluate the distributions’ conformity with the uniform impact distribution assumption. The distribution of impact corridors is based on the NEO population and orbital mechanics. The analysis shows that the distribution of impact corridors matches the common assumption of uniform impact distribution and the result extends the evidence base for the uniform assumption from qualitative analysis of historic impact events into the future in a quantitative way. This finding is confirmed in a parallel analysis of impact points belonging to a synthetic population of 10,006 VIs. Taking into account the impact probabilities introduced significant variation into the results and the impact probability distribution, consequently, deviates markedly from uniformity. The concept of impact probabilities is a product of the asteroid observation and orbit determination technique and, thus, represents a man-made component that is largely disconnected from natural processes. It is important to consider impact probabilities because such information represents the best estimate of where an impact might occur.

Jupiter family comets in near-Earth orbits: Are some of them interlopers from the asteroid belt?

We analyze a sample of 58 Jupiter family comets (JFCs) in near-Earth orbits, defined as those whose perihelion distances at the time of discovery were qdisc<1.3au. In our definition JFCs have Tisserand parameters 2<T<3 and orbital periods P<20yr. We integrated the orbits of these objects, plus 50 clones for each one of them, for 104yr in the past and in the future. We find that most of them move on highly unstable orbits, having fallen in their current near-Earth orbits in the recent past, going from less than one hundred years to a few thousands years. They experience frequent close encounters with Jupiter down to distances ≲0.1au. This is the expected behavior for comets whose limited physical lifetimes in the near-Earth region make them unlikely to survive there for more than about a few hundred revolutions. In this sense the orbits of most JFCs are typically “cometary”, and they should be regarded as newcomers in the near-Earth region. Yet, a minor fraction of JFCs (less than about one third) are found to move on stable orbits for the past ∼104yr, and in some cases are found to continue to be stable at 5×104yr in the past. They also avoid very close encounters with Jupiter. Their orbital behavior is very similar to that of NEAs in cometary orbits. While “typical” JFCs in unstable orbits probably come from the trans-Neptunian region, the minor group of JFCs in asteroidal orbits may come from the main asteroid belt, like the NEAs. The asteroidal JFCs may have a more consolidated structure and a higher mineral content than that of comets coming from the trans-Neptunian belt or the Oort cloud, which could explain their much longer physical lifetimes in the near-Earth region. In particular, we mention comets 66P/du Toit, 162P/Siding Spring, 169P/NEAT, 182P/LONEOS, 189P/NEAT, 249P/LINEAR, 300P/Catalina, and P/2003 T12 (SOHO) as the most likely candidates to have an origin in the main asteroid belt. Another interesting case is 207P/NEAT, which stays near the 3:2 inner mean motion resonance with Jupiter, possibly evolving from the Hilda asteroid zone.

Sizes, Shapes, and Satellites of Asteroids from Occultations

AbstractFor 40 years, the sizes and shapes of many dozens of asteroids have been determined from observations of asteroidal occultations, and over a thousand high-precision positions of the asteroids relative to stars have been measured. Some of the first evidence for satellites of asteroids was obtained from the early efforts; now, the orbits and sizes of some satellites discovered by other means have been refined from occultation observations. Also, several close binary stars have been discovered, and the angular diameters of some stars have been measured from analysis of these observations. The International Occultation Timing Association (IOTA) coordinates this activity worldwide, from predicting and publicizing the events, to accurately timing the occultations from as many stations as possible, and publishing and archiving the observations.

Dealing with uncertainties in asteroid deflection demonstration missions: NEOTωIST

AbstractDeflection missions to near-Earth asteroids will encounter non-negligible uncertainties in the physical and orbital parameters of the target object. In order to reliably assess future impact threat mitigation operations such uncertainties have to be quantified and incorporated into the mission design. The implementation of deflection demonstration missions offers the great opportunity to test our current understanding of deflection relevant uncertainties and their consequences, e.g., regarding kinetic impacts on asteroid surfaces. In this contribution, we discuss the role of uncertainties in the NEOTωIST asteroid deflection demonstration concept, a low-cost kinetic impactor design elaborated in the framework of the NEOShield project. The aim of NEOTωIST is to change the spin state of a known and well characterized near-Earth object, in this case the asteroid (25143) Itokawa. Fast events such as the production of the impact crater and ejecta are studied via cube-sat chasers and a flyby vehicle. Long term changes, for instance, in the asteroid's spin and orbit, can be assessed using ground based observations. We find that such a mission can indeed provide valuable constraints on mitigation relevant parameters. Furthermore, the here proposed kinetic impact scenarios can be implemented within the next two decades without threatening Earth's safety.

Bayesian statistical approach to binary asteroid orbit determination

AbstractThe problem of binary asteroids orbit determination is of particular interest, given knowledge of the orbit is the best way to derive the mass of the system. Orbit determination from observed points is a classic problem of celestial mechanics. However, in the case of binary asteroids, particularly with a small number of observations, the solution is not evident to derive. In the case of resolved binaries the problem consists in the determination of the relative orbit from observed relative positions of a secondary asteroid with respect to the primary. In this work, the problem is investigated as a statistical inverse problem. Within this context, we propose a method based on Bayesian modelling together with a global optimisation procedure that is based on the simulated annealing algorithm.

Autonomous navigation of a spacecraft formation in the proximity of an asteroid

This paper presents a multi-sensor navigation approach to allow a formation of spacecraft to autonomously navigate in the proximity of a Near Earth Asteroid. Multiple measurements collected by on-board cameras, attitude sensors and LIDAR are used to estimate the state of each spacecraft with respect to the asteroid. Inter-spacecraft position measurements are then combined with spacecraft-to-asteroid position measurements to improve accuracy. The paper analyses the use of different filtering techniques to estimate the state of a 4-spacecraft formation with respect to the asteroid. Different combinations of measurements are constructed to evaluate the improvement in navigation performance offered by the data fusion of the measurements gathered by the four spacecraft. Moreover the robustness of the navigation system is tested against the occurrence of failures. Results show that the navigation performance is significantly improved by adding the inter-spacecraft position measurements. Finally, an asteroid orbit determination method is proposed that combines asteroid’s line of sight measurements from multiple spacecraft and Sun Doppler shift sensor with spacecraft-to-ground tracking data. Different approach configurations are evaluated for a 2-spacecraft formation and it is shown that the integrated use of spacecraft-to-asteroid and ground-to-spacecraft measurements provides an effective way to improve the ephemerides of the asteroid.

Asteroid rotation and orbit control via laser ablation

This paper presents an approach to control the rotational motion of an asteroid while a spacecraft is deflecting its trajectory through laser ablation. During the deflection, the proximity motion of the spacecraft is coupled with the orbital and rotational motion of the asteroid. The combination of the deflection acceleration, solar radiation pressure, gravity field and plume impingement will force the spacecraft to drift away from the asteroid. In turn, a variation of the motion of the spacecraft produces a change in the modulus and direction of the deflection action which modifies the rotational and orbital motion of the asteroid. An on-board state estimation and control algorithm is then presented that simultaneously provides an optimal proximity control and a control of the rotational motion of the asteroid. It will be shown that the simultaneous control of the rotational and proximity motions of asteroid and spacecraft has a significant impact on the required deflection time.