Orbits Of Asteroids Research Articles

Nonlinearity in Inverse Problems of Asteroid Dynamics

A collision of an asteroid with the Earth in the future is always considered as a probabilistic event because the asteroid orbit determined from observations with random errors inevitably contains an uncertainty in its parameters. To establish the probability of collision, the parametric uncertainty as a probabilistic distribution of virtual objects is mapped by the orbital model into the physical space for the period of the asteroid rendezvous with the Earth, and then the probabilistic mass penetrating into the planet body is estimated. The asteroid impact on the Earth is a very significant phenomenon because it can have fatal consequences for mankind. Therefore, probabilistic estimation of collision with potentially hazardous asteroids must be carried out very carefully with allowance for various subtle aspects. In this work, nonlinearity in inverse problems of asteroid dynamics under different observation conditions for various types of determined orbits is studied. The main problem we set ourselves is to examine to what extent nonlinearity can affect the accuracy of a probabilistic estimation when the parametric uncertainty is simulated using classical linear stochastic methods. To study the total, parameter-effect, and intrinsic nonlinearities, we introduce original indices with justified threshold values determined from the maximum tolerable biases of probabilistic estimates due to nonlinearity. The general analysis of nonlinearity is carried out for potentially hazardous asteroids observed in one appearance before June 2020. In particular, it is shown that main factors of strong nonlinearity are the short observed orbital arc (less than one degree) and the small observation period (less than ten days). Moreover, the situation is aggravated if the asteroid moves during the observation along the ecliptic and near it on an arc with small curvature. It is also established that, due to strong nonlinearity in problems of probabilistic estimation, nonlinear stochastic methods are required to simulate the orbital uncertainty for almost half of the potentially hazardous asteroids (44%).

О методе радиомаяка для уточнения орбиты астероида

Приводятся аргументы в пользу неизбежной интенсификации полетов к астероидам. Это обусловлено ростом внимания к проблеме астероидно-кометной опасности, а также быстрым ростом интереса к освоению астероидных ресурсов. Массовость полетов ставит задачу оптимизации технологии уточнения параметров движения астероидов. Метод радиопередатчика (маяка), размещенного на околоастероидной орбите, позволяет уточнить положение астероида по сравнению с обычными средствами на 2-3 порядка. Отработка такой возможности была заложена в космическом проекте «Апофис», который ранее предлагался для включения в Федеральную космическую программу, а сейчас может быть частично реализован в рамках проекта «Бумеранг». Arguments are given in favor of the inevitable intensification of flights to the asteroids. This is due to the growing attention to the problem of asteroid/comet hazard, as well as the rapid growth of interest in exploration of asteroid resources. The massive flights require an optimal technology for refining the motion parameters of asteroid. The method of a radio transmitter (beacon) placed into a near-asteroid orbit makes it possible to refine the position of the asteroid by 2-3 orders of magnitude in comparison to conventional techniques. Working out this possibility was laid down in the “Apophis” space project, which was previously proposed for inclusion in the Federal space program, and now can be implemented in the “Boomerang” project.

Dynamical Systems, Celestial Mechanics, and Music: Pythagoras Revisited

Gioseffo Zarlino reintroduced the Pythagorean paradigm into Renaissance musical theory. In a similar fashion, Nicolaus Copernicus, Galileo Galilei, Johannes Kepler, and Isaac Newton reinvigorated Pythagorean ideas in celestial mechanics; Kepler and Newton explicitly invoked musical principles. Today, the theory of dynamical systems allows us to describe very different applications of physics, from the orbits of asteroids in the Solar System to the pitch of complex sounds. Our aim in this text is to review the overarching aims of our research in this field over the past quarter of a century. We demonstrate with a combination of dynamical systems theory and music theory the thread running from Pythagoras to Zarlino that allowed the latter to construct musical scales using the ideas of proportion known to the former, and we discuss how the modern theory of dynamical systems, with the study of resonances in nonlinear systems, returns to Pythagorean ideas of a Musica Universalis.

GROUPS OF METEORITE-PRODUCING METEOROIDS AND METEORITES IN ASTEROIDAL ORBITS AND THEIR SOURCES

This paper presents the results of theanalysis of possible existence of nine near-Earthmeteorite-producing groups in asteroidal orbits, consistingof sporadic fireballs from the IAU MDC 2007 database,sporadic meteors from the SonotaCo database, meteorites– namely, L5, L6 and H4-H6 ordinary chondrites and anureilite, for which atmospheric and orbital parameters areknown from instrumental observations – and theirplausible parent bodies, that is, near-Earth asteroids(NEAs). Orbits of the selected members of meteorite-producing groups were classified as asteroidal accordingto the Tisserand parameter T J > 3.1.In order to test the link between meteorite-producinggroups in asteroidal orbits and their plausible parentbodies, we carried out an investigation into the possibleexistence of some known NEAs that move in similarorbits. Based on the orbital similarity, determined usingthe Drummond (D D ) and Southworth & Hawkins (D SH )orbital similarity criteria, some associations between theidentified NEAs, known meteorites in asteroidal orbitsand small, as well as meteorite-dropping, meteoroids havebeen suggested. As a result, several meteorite-droppingsporadic fireballs and small meteors, whose orbits arecurrently similar to the orbits of known meteorites, havebeen detected and reckoned as possible members of thegroups in asteroidal orbits; their plausible source regionshave also been considered.

Encounter trajectories for deep space mission ASTER to the triple near Earth asteroid 2001-SN263. The laser altimeter (ALR) point of view

In cooperation with Russia, the Brazilian deep space mission ASTER plans to send a small spacecraft to investigate the triple asteroid 2001-SN263. The nearest launch opportunities for this project include June 2022 and June 2025. One main exploration campaign is being planned with focus on the largest asteroid (Alpha). Among the instruments under development, a laser altimeter (named ALR) was preliminarily designed and presented in 2010–2011. Many studies to define mission and instruments requirements were performed aiming at the characterization of important issues for the successful realization of the mission. Among them, the identification of a suitable trajectory that could be followed by the ASTER spacecraft in the encounter phase, when the main campaign will take place. This paper describes the effort undertaken with focus on the laser altimeter operation. Possible encounter trajectories were modelled and simulated to identify suitable approach parameters and conditions allowing the accomplishment of the intended investigation. The simulation also involves the instrument operation, considering approach geometry, attitude, relative motion, time/date, and the dynamics of the main asteroid. From the laser altimeter point of view, keeping in mind the desired coverage results (50% minimum surface coverage of asteroid Alpha, complying with horizontal and vertical resolution requirements), results point out crucial features for the encounter trajectory, like the need for a small inclination (10-6 degrees; with respect to the asteroid's orbit), the most favourable spacecraft positioning (between the Sun and the asteroid) and pointing condition (back to the Sun), the minimum amount of achievable surface coverage (58%, focused on central areas), and the most proper time to conduct the main campaign (January 2025). Concerning the instrument, results offer refined values for divergence angle (500 to 650 μrad, half-cone), pulse repetition frequencies (from 1/20 to 1 Hz), and consequent data generation rates. A simulation tool that can use any 3D generated trajectories as input data was created for the analyses presented here. Although created for the ALR in this mission, this simple analysis tool can be adapted to other instruments in this or other missions.

A 2-D Trajectory Design Algorithm for Multiple Asteroid Flyby Missions

Asteroid mining is one of the most promising private space ventures of the near future. Near-Earth Asteroids (NEAs), i.e. those with perihelion at less than 1.3 AU from the Sun, are among the best candidates for such venture. In preparation of mining expeditions, it is likely that prospector missions will be carried out well in advance so to assess the accessibility, potential for revenues and possible critical issues of target asteroids. This work is concerned with the problem of the feasibility of a single spacecraft prospector mission capable of visiting as many NEAs as possible in one shot, focusing on Apollo-class asteroids only. The search of possible trajectories is done assuming a chemically propelled spacecraft with realistic specific impulse and propellant mass ratio, so to allow for a credible mission design with a reasonable, cost-effective total duration. In order to restrict the number of possible trajectories, only those that lie in the plane of the ecliptic are examined; such trajectories can be reached from the Earth without expensive plane change maneuvers. The search for a maximum number of encounters is thus restricted to those occurring where the asteroid orbit crosses the ecliptic. A deterministic building blocks approach is adopted, dividing the optimization problem in two parts: a local optimization for possible target determination; and a global optimization for the choice of the overall trajectory. It is found that the combined approach leads to the identification of viable trajectories, able to perform a number of encounters that depends on the launch epoch; as an example, in one test case two different sets of 21 NEA’s each were identified that could be reached with a single launch, with a slightly different propellant expenditure. It is concluded that the method is well suited to perform feasibility studies of NEA missions with good accuracy and moderate computational cost.

A Perturbative Treatment of the Retrograde Co-orbital Motion

Abstract An important area of research in celestial mechanics is the analysis of dynamics in mean-motion resonances (MMR). In this paper, we consider a retrograde MMR 1:1 corresponding to a co-orbital motion, in which the asteroid and the planet revolve around the Sun in opposite directions. The motivation was provided by the recent discovery of real celestial bodies moving in such resonances with giant planets (the most famous example being 514107 Ka‘epaoka‘awela, a retrograde co-orbital asteroid of Jupiter). Our study is conducted in the context of a spatial restricted circular three-body problem. Applying double numerical averaging, we construct the equations describing the secular evolution of the asteroid's orbit and generate phase portraits in an e − ω space. In some cases, the averaging procedure is complicated by the coexistence of several modes of resonant motion. It leads to different scenarios of the long-term behavior and, consequently, to the splitting of the phase portrait into several sheets.

Asteroid satellite ephemeride service. Mutual occultations and eclipses

A tool has been developed for computing the ephemerides of asteroid satellites, which are needed to plan and verify new observations, as well as for space missions.The proposed ephemeris server is available online at http://www.sai.msu.ru/neb/nss/html/multisat/nssAsthe.htm and http://nsdb.imcce.fr/multisat/nssAsthe.htm.Motion models for 62 asteroid satellites are included, which are computed based on all available observations. The proposed ephemeris server can provide relative satellite positions for a series of time instants specified by the user. The server displays the time intervals of mutual occultations and eclipses in asteroid systems with satellites, as well as times of satellite elongations, when the observing conditions are most favorable.The circumstances of all mutual occultations and eclipses in the satellite systems are determined. During the years 2021–2025, events are to occur in 21 of the 62 systems considered. The plots show the time intervals of the phenomena.The reliability of the computed ephemerides is verified by comparing their predictions with the results published by other authors.We use our original method to estimate the accuracy of asteroid satellite ephemerides. Thus the asteroid satellite ephemeris server provides not only ephemerides but also the uncertainties of the predicted satellite positions. The low accuracy of the ephemerides of some satellites is due to the fact that their orbits are determined from a small number of observations spanning a short time interval.Our tool can be used with more accurate orbital parameters and for new satellites to be discovered in the future. We hope to work on this initial release and to consider adding updates including refined astrometry and additional systems.

Precise astrometry and diameters of asteroids from occultations – a data set of observations and their interpretation

ABSTRACT Occultations of stars by asteroids have been observed since 1961, increasing from a very small number to now over 500 annually. We have created and regularly maintain a growing data set of more than 5000 observed asteroidal occultations. The data set includes the raw observations, astrometry at the 1 mas level based on centre of mass or figure (not illumination), where possible the asteroid’s diameter to 5 km or better, and fits to shape models, the separation and diameters of asteroidal satellites, and double star discoveries with typical separations being in the tens of mas or less. The data set is published at NASA’s Planetary Data System and is regularly updated. We provide here an overview of the data set, discuss the issues associated with determining the astrometry and diameters, and give examples of what can be derived from the data set. We also compare the occultation diameters of asteroids with the diameters measured by the satellites NEOWISE, AKARI AcuA, and IRAS, and show that the best satellite-determined diameter is a combination of the diameters from all three satellites.

Asteroid control through surface restructuring

A novel concept for asteroid orbit control by restructuring asteroid surfaces to manipulate albedo and respective radiation pressure effects is introduced. The method itself is propellant-less allowing for prolonged operation and permitting the adaption and even reversing reflection changes. Microscopic restructuring of asteroid surface material allows further for asymmetric manipulation of reflective properties, which can be exploited for influencing orbit and attitude parameters. Asymmetric radiation pressures are well known for their ability to change the orbit of an asteroid through the Yarkovsky effect or rotational parameters by the YORP effect. It is shown that in the simplest form albedo manipulation of a solid surface asteroid can be achieved with a single spacecraft mission. A spacecraft will locally focus energy from a very low (pseudo-)orbit onto the asteroids surface. One technology candidate are CO2 laser systems, while other options exist. First, CO2 laser are used as conventional laser engravers to brighten mineralic and metallic surfaces. Second, CO2 laser cleaning systems are often used to remove silicate residue of industrial processes.It is calculated that an asteroid with a high albedo will experience significantly less Yarkovsky forces, resulting in reduced orbit drift and improved future predictability.Laser technology can further be exploited to create surface structures that represent an asymmetric saw tooth pattern (i.e. repeating sharp right triangles) by using femto second laser pulses or by an angled focal point. This asymmetric surface pattern leads to an angular dependent reflectivity, which can be exploited to create radiation pressure differences. When properly applied, countering spin-rate changes and rotation axis drift of the YORP effect is possible. A preliminary analysis indicates feasibility for a medium size probe equipped for laser treatment of Near Earth Object surfaces.

Using atmospheric impact data to model meteoroid close encounters

ABSTRACT Based on telescopic observations of Jupiter-family comets (JFCs), there is predicted to be a paucity of objects at sub-kilometre sizes. However, several bright fireballs and some meteorites have been tenuously linked to the JFC population, showing metre-scale objects do exist in this region. In 2017, the Desert Fireball Network (DFN) observed a grazing fireball that redirected a meteoroid from an Apollo-type orbit to a JFC-like orbit. Using orbital data collected by the DFN, in this study, we have generated an artificial data set of close terrestrial encounters that come within 1.5 lunar distances (LD) of the Earth in the size-range of 0.01–100 kg. This range of objects is typically too small for telescopic surveys to detect, so using atmospheric impact flux data from fireball observations is currently one of the only ways to characterize these close encounters. Based on this model, we predict that within the considered size-range 2.5 × 108 objects ($0.1{{\ \rm per\ cent}}$ of the total flux) from asteroidal orbits (TJ > 3) are annually sent on to JFC-like orbits (2 < TJ < 3), with a steady-state population of about 8 × 1013 objects. Close encounters with the Earth provide another way to transfer material to the JFC region. Additionally, using our model, we found that approximately 1.96 × 107 objects are sent on to Aten-type orbits and ∼104 objects are ejected from the Solar system annually via a close encounter with the Earth.

Simultaneous estimation of spacecraft position and asteroid diameter during final approach of Hayabusa2 to Ryugu

This paper presents the optical navigation results of the asteroid explorer Hayabusa2 during the final rendezvous approach phase with the asteroid Ryugu. The orbit determination of Hayabusa2 during the cruising phase uses a triangulation-based method that estimates the probe and asteroid orbits using the directions from which they are observed. Conversely, the asteroid size is available as optical information just prior to arrival. The size information allows us to estimate the relative distance between the probe and the asteroid with high accuracy, that is strongly related to the success or failure of the rendezvous. In this study, the relative distance and asteroid size in real space are simultaneously estimated in real time by focusing on the rate of change of the asteroid size observed in sequential images. The real-time estimation results coincided with those of precise analyses performed after arrival.

Required deflection impulses as a function of time before impact for Earth-impacting asteroids

For any asteroid on an impact trajectory, the amount of time prior to impact a deflection can be implemented can drastically change the amount of deflection impulse required. In this study we use the precision cloud-based asteroid orbit propagation and targeting capabilities of the Asteroid Institute’s Asteroid Decision Analysis and Mapping (ADAM) platform to investigate the distribution of deflection Δv required to divert asteroids on Earth-impacting trajectories (Chesley and Spahr, 2004) as a function of time prior to impact for 10,000 synthetic impacting asteroids. We target a miss distance of one Earth radius above the surface of the Earth and calculate the distribution of deflection Δv required if applied 10, 20, 30, 40, and 50 years prior to impact. We find that the median required deflection impulse decreases as approximately t−1 for increasing time before impact (Ahrens and Harris, 1992), where the median required Δv is 1.4 cm/s, 0.76 cm/s, 0.55 cm/s, 0.46 cm/s, and 0.38 cm/s for 10, 20, 30, 40, & 50 years before impact, respectively. We find a considerable spread in the distribution of required deflection Δv including a small fraction of asteroids that require an order of magnitude smaller or larger deflection Δv than the median for each decade of time before impact studied.

Study of highly perturbed spacecraft formation dynamics via approximation

This paper explores methods for approximating and analyzing the dynamics of highly perturbed spacecraft formations with an emphasis on computationally efficient approaches. This facilitates on-board computation or rapid preliminary mission design analysis. Perturbed formation dynamics are often approximated as linear time-varying (LTV) systems, for which Floquet theory can be used to analyze the degree of system instability. Furthermore, the angular momentum of the relative orbital state can be computed with the approximate dynamics to provide additional insight. A general methodology is developed first and then applied to the problem of unstable formation dynamics in asteroid orbits. Here the dominant perturbative effects due to low-order gravitational harmonics and solar radiation pressure are modeled. Numerical simulations validate the approach and illustrate the approximation accuracy achieved.

Particle Ejection Contributions to the Rotational Acceleration and Orbit Evolution of Asteroid (101955) Bennu.

This paper explores the implications of the observed Bennu particle ejection events for that asteroid's spin rate and orbit evolution, which could complicate interpretation of the Yarkovsky‐O'Keefe‐Radzievskii‐Paddack (YORP) and Yarkovsky effects on this body's spin rate and orbital evolution. Based on current estimates of particle ejection rates, we find that the overall contribution to Bennu's spin and orbital drift is small or negligible as compared to the Yarkovsky and YORP effects. However, if there is a large unseen component of smaller mass ejections or a strong directionality in the ejection events, it could constitute a significant contribution that could mask the overall YORP effect. This means that the YORP effect may be stronger than currently assumed. The analysis is generalized so that the particle ejection effect can be assessed for other bodies that may be subject to similar mass loss events. Further, our model can be modified to address different potential mechanisms of particle ejection, which are a topic of ongoing study.

Asteroid mass estimation with the robust adaptive Metropolis algorithm

Context. The bulk density of an asteroid informs us about its interior structure and composition. To constrain the bulk density, one needs an estimated mass of the asteroid. The mass is estimated by analyzing an asteroid’s gravitational interaction with another object, such as another asteroid during a close encounter. An estimate for the mass has typically been obtained with linearized least-squares methods, despite the fact that this family of methods is not able to properly describe non-Gaussian parameter distributions. In addition, the uncertainties reported for asteroid masses in the literature are sometimes inconsistent with each other and are suspected to be unrealistically low. Aims. We aim to present a Markov-chain Monte Carlo (MCMC) algorithm for the asteroid mass estimation problem based on asteroid-asteroid close encounters. We verify that our algorithm works correctly by applying it to synthetic data sets. We use astrometry available through the Minor Planet Center to estimate masses for a select few example cases and compare our results with results reported in the literature. Methods. Our mass-estimation method is based on the robust adaptive Metropolis algorithm that has been implemented into the OpenOrb asteroid orbit computation software. Our method has the built-in capability to analyze multiple perturbing asteroids and test asteroids simultaneously. Results. We find that our mass estimates for the synthetic data sets are fully consistent with the ground truth. The nominal masses for real example cases typically agree with the literature but tend to have greater uncertainties than what is reported in recent literature. Possible reasons for this include different astrometric data sets and weights, different test asteroids, different force models or different algorithms. For (16) Psyche, the target of NASA’s Psyche mission, our maximum likelihood mass is approximately 55% of what is reported in the literature. Such a low mass would imply that the bulk density is significantly lower than previously expected and thus disagrees with the theory of (16) Psyche being the metallic core of a protoplanet. We do, however, note that masses reported in recent literature remain within our 3-sigma limits. Results. The new MCMC mass-estimation algorithm performs as expected, but a rigorous comparison with results from a least-squares algorithm with the exact same data set remains to be done. The matters of uncertainties in comparison with other algorithms and correlations of observations also warrant further investigation.

Study of the Characteristics of the Possible Region of the Apophis Asteroid Impact with Earth in 2036

In this study the possible region of the impact of the dangerous Apophis asteroid with Earth in 2036 according to the asteroid orbit of 2005 is determined and studied. Algorithms are developed to searching the entire probable set of Apophis asteroid trajectories falling into Earth using Monte Carlo and gradient descent methods. For this set, the search was realized for several probable families of collisions with Earth in 2036 asteroid trajectories corresponding to subsets of the perigee distance of the Apophis orbit from the minimum possible distance, ~2069 km, to the maximum corresponding to touching Earth’s surface, ~6376 km. A mapping of the entire set of trajectories falling onto Earth’s surface was obtained, as well as a collisional band was also constructed on the world map. The features of this collisional path and the properties of collision trajectories of Apophis were studied. A comparison of the results of this study with others is given.

The partial banana mapping: a robust linear method for impact probability estimation

ABSTRACT This paper presents a robust linear method for impact probability estimation of near-Earth asteroids with the Earth. This method is a significantly modified and improved method, which uses a special curvilinear coordinate system associated with the nominal orbit of an asteroid. One of the coordinates of this system is the mean anomaly in the osculating orbit of an asteroid. A normal distribution of errors of coordinates and velocities of this system is assumed. Because of the usage of the curvilinear coordinate system, the fact that the confidence region is curved and stretched mainly along the nominal asteroid orbit is taken into account. On the main axis of the curvilinear confidence ellipsoid the virtual asteroid, which is the closest to the Earth, is found. The part of the curvilinear confidence ellipsoid, around the found virtual asteroid, is obtained and mapped on to its target plane. The impact probability is calculated as the probability of the asteroid being in the region of the found virtual asteroid multiplied by the probability of a collision of the found virtual asteroid with the Earth. This approach is shown to give more accurate and trustworthy results than the target plane method.

Secular resonance sweeping and orbital excitation in decaying disks

We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in the light of recent models of solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance is verified by analytical calculations. The secular response of fictitious asteroids, under perturbations from Jupiter, Saturn and a decaying disk, is thoroughly studied. Note that the existence of a symmetry plane induced by the disk, lifts the inherent degeneracy of the two-planet system, such that the '$s_5$' nodal frequency can also play a major role. We examine different resonant configurations for the planets (2:1, 3:2, 5:3), disk models and depletion scenarios. For every case we compute the corresponding time paths of secular resonances, which show when and where resonance crossing occurs. The excitation of asteroids, particularly in inclination, is studied in the various models and compared to analytical estimates. We find that inclination excitation in excess of $\sim 10^{\circ}$ is possible in the asteroid belt, but the nearly uniform spread of $\Delta i\sim 20^{\circ}$ observed calls for the combined action of secular resonance sweeping with other mechanisms (e.g. scattering by Mars-sized embryos) that would be operating during terrestrial planet formation. Our results are also applicable to extrasolar planetary systems.

Analysis of the possibility of creating a stable satellite about the asteroid Apophis as a homogeneous triaxial ellipsoid

The task of creating a stable orbit of the Apophis asteroid satellite as a homogeneous triaxial ellipsoid is investigated. The simulation of the motion of the spacecraft around the asteroid was performed taking into account the main perturbations: from the attraction of celestial bodies, asteroids non-sphericity and solar radiation pressure, and taking into account the asteroids own rotation. It is shown that it is possible to create a stable orbit of an asteroid satellite. This orbit can be used for a detailed study of the characteristics of the asteroid and the refinement of its orbit using ground radio measurements of the motion of a satellite equipped with a radio beacon.