Relevant bibliographies by topics / Orbital Collisions

Academic literature on the topic 'Orbital Collisions'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Orbital Collisions"

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Abedin, Abedin Y., J. J. Kavelaars, Jean-Marc Petit, Brett Gladman, Michele Bannister, Mike Alexandersen, Ying-Tung Chen, Stephen Gwyn, and Kathryn Volk. "OSSOS. XXVI. On the Lack of Catastrophic Collisions in the Present Kuiper Belt." Astronomical Journal 164, no. 6 (November 30, 2022): 261. http://dx.doi.org/10.3847/1538-3881/ac9cdb.

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Abstract We investigate different conditions, including the orbital and size–frequency distribution (SFD) of the early Kuiper Belt, that can trigger catastrophic planetesimal destruction. The goal of this study is to test if there is evidence for collisional grinding in the Kuiper Belt that has occurred since its formation. This analysis has important implications for whether the present-day SFD of the cold classical trans-Neptunian objects (TNOs) is a result of collisional equilibrium or if it reflects the primordial stage of planetesimal accretion. As an input to our modeling, we use the most up-to-date debiased OSSOS++ ensemble sample of the TNO population and orbital model based on the present-day architecture of the Kuiper Belt. We calculate the specific impact energies between impactor–target pairs from different TNO groups and compare our computed energies to catastrophic disruption results from smoothed particle hydrodynamics simulations. We explore different scenarios by considering different total primordial Kuiper Belt masses and power slopes of the SFD and allowing collisions to take place over different timescales. The collisional evolution of the Kuiper Belt is a strong function of the unknown initial mass in the trans-Neptunian region, where collisional grinding of planetesimals requires a total primordial Kuiper Belt mass of M > 5 M ⊕, collision speeds as high as 3 km s−1, and collisions over at least 0.5 Gyr. We conclude that presently, most of the collisions in the trans-Neptunian region are in the cratering rather than disruption regime. Given the low collision rates among the cold classical Kuiper Belt objects, their SFD most likely represents the primordial planetesimal accretion.
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Zhang, Haitao, Zhi Li, Weilin Wang, Yasheng Zhang, and Hao Wang. "Geostationary Orbital Debris Collision Hazard after a Collision." Aerospace 9, no. 5 (May 10, 2022): 258. http://dx.doi.org/10.3390/aerospace9050258.

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Many space objects are densely distributed in the geostationary (GEO) band, and the long-term impact of the collision of GEO spacecraft and space debris on the GEO environment has attracted more and more attention. After summarizing the advantages and disadvantages of the long-term evolution model based on the “Cube” collision probability calculation model, the “Grid” model, a long-term evolution model especially suitable for GEO band, was established. For four types of collision and disintegration events, the “Grid” model was used to study the space environment in the GEO band after collisions between GEO spacecraft and space debris. Future collisions were simulated, and the number of space objects in the next 100 years was counted. Once space debris and massive spacecraft were completely disintegrated after collision, the number of space objects and the collision probability increased sharply, and this caused a collision cascading syndrome. Even if there was no initial disintegration event, collision and disintegration events occurred in the long-term evolution of the GEO band, which led to an increase in the number of space objects. However, the collision probability was much lower, and the number of space objects grew much more slowly without the initial collision.
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Knowles, Stephen H. "Space Object Traffic Control." International Astronomical Union Colloquium 112 (1991): 165. http://dx.doi.org/10.1017/s0252921100003912.

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ABSTRACTThe task of avoiding collisions between orbiting objects requires more than a statistical description of the objects’ positions. The paper describes the general procedures used for such cataloging, together with an indication of the accuracy required for orbital collision avoidance.
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Nicolas, Timothée. "Impact of azimuthal forcing on the Brillouin limit in a collisional two-species Ohkawa filter." Physics of Plasmas 29, no. 4 (April 2022): 042105. http://dx.doi.org/10.1063/5.0073198.

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This paper investigates the physics of plasma separation in a two species rotating collisional Ohkawa filter, when the source of rotation is an orbital angular momentum carrying wave. The electric field is treated self-consistently with ion and electron radial motion. The injection of angular momentum causes radial currents leading to charge penetration and electric field build up. The electric field varies until an equilibrium with the friction forces is reached. Both collisions with neutrals and Coulomb collisions are considered. In the case where the electric field is driven by the resonant wave, there is no collisional breakdown of the Brillouin limit [Rax et al., Phys. Plasmas 22, 092101 (2015)]; on the contrary, the maximum achievable electric field decreases when the collision frequency is increased. When two species are present, one that undergoes the wave forcing while the second does not interact with the wave, we find the following: the first species is confined, while the second species can be expelled or confined depending on the charge to mass ratio and the collisionalities. Assuming equal charge numbers, if the second species is the heavy one, it is always expelled, which is a standard result. When the second species is the light one, it can also be expelled in the common case where neutral collisions dominate over Coulomb collisions, which constitutes a new result.
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TROSHIN, S. M., and N. E. TYURIN. "ELLIPTIC FLOW IN pp-COLLISIONS AT THE LHC." Modern Physics Letters A 26, no. 15 (May 20, 2011): 1095–102. http://dx.doi.org/10.1142/s0217732311035559.

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We consider collective effects in pp-collisions at the LHC energies related to presence of the large orbital angular momentum in the initial state and role of this orbital momentum in the elliptic flow behavior.
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Appleton, P. N. "Collisional Ring Galaxies." Symposium - International Astronomical Union 186 (1999): 97–104. http://dx.doi.org/10.1017/s007418090011232x.

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Ring galaxies are believed to represent a special case of a collision between two galaxies, in which one of the galaxies impacts and passes through the center of another disk system (e.g. Lynds & Toomre 1976). Although rare, this kind of low orbital-angular-momentum collision leads to a recognizable structure, namely a luminous blue star-forming ring (Appleton & Marston 1997), which should be easily identifiable even at moderate redshift. Indeed, Lavery et al. (1996) have used this fact, and their relative rarity at low-redshift, to conclude that rings (and therefore presumably all collisions) are over-represented in deep HST fields.
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Mikhailov V. S., Babenko P. Yu., Shergin A. P., and Zinoviev A. N. "Auger transition probabilities and electron emission cross sections for vacancy decay into the 2pπ-orbital in the Ne-=SUP=-+-=/SUP=--Ne quasimolecule." Technical Physics Letters 48, no. 1 (2022): 70. http://dx.doi.org/10.21883/tpl.2022.01.52475.19018.

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The paper reports the calculation of the probabilities of Auger transitions taking place in the process of filling a vacancy on the 2pπ-orbital in an Ne+-Ne quasimolecule, a short-lived system which arises when the ion and atom approach each other and decays when they fly apart. Calculations for various ionization degrees of the quasimolecule particles were performed for the first time. It was found out that the system ionization degree increases very significantly (from 2 to 6) with increasing collision energy and decreasing distance of the particles closest approach. Using of the quantum mechanical approach and taking into account the collision dynamics made it possible to quantitatively describe for the first time the experimental Auger electron spectra of a complex many-electron quasimolecule. The contribution of the transition from the initial 3dπ-3dπ state to the 2pπ orbital was shown to be predominant among the whole variety of possible Auger decay channels. Keywords: atomic collisions, quasimolecule, Auger transitions, electron emission cross sections, vacancy decay
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Crespi, Samuele, Ian Dobbs-Dixon, Nikolaos Georgakarakos, Nader Haghighipour, Thomas I. Maindl, Christoph M. Schäfer, and Philip Matthias Winter. "Protoplanet collisions: Statistical properties of ejecta." Monthly Notices of the Royal Astronomical Society 508, no. 4 (October 13, 2021): 6013–22. http://dx.doi.org/10.1093/mnras/stab2951.

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ABSTRACT The last phase of the formation of rocky planets is dominated by collisions among Moon- to Mars-sized planetary embryos. Simulations of this phase need to handle the difficulty of including the post-impact material without saturating the numerical integrator. A common approach is to include the collision-generated material by clustering it into few bodies with the same mass and uniformly scattering them around the collision point. However, this approach oversimplifies the properties of the collision material by neglecting features that can play important roles in the final structure and composition of the system. In this study, we present a statistical analysis of the orbital architecture, mass, and size distributions of the material generated through embryo–embryo collisions and show how they can be used to develop a model that can be directly incorporated into the numerical integrations. For instance, results of our analysis indicate that the masses of the fragments follow an exponential distribution with an exponent of −2.21 ± 0.17 over the range of 10−7 to 2 × 10−2 Earth-masses. The distribution of the post-impact velocities show that a large number of fragments are scattered towards the central star. The latter is a new finding that may be quite relevant to the delivery of material from the outer regions of the asteroid belt to the accretion zones of terrestrial planets. Finally, we present an analytical model for the 2D distribution of fragments that can be directly incorporated into numerical integrations.
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Dougherty, Ralph C. "Molecular orbital treatment of gas-phase ion molecule collision rates: Reactive and nonreactive collisions." Mass Spectrometry Reviews 20, no. 3 (2001): 142–52. http://dx.doi.org/10.1002/mas.10002.

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Choksi, Nick, Eugene Chiang, Harold C. Connolly, Zack Gainsforth, and Andrew J. Westphal. "Chondrules from high-velocity collisions: thermal histories and the agglomeration problem." Monthly Notices of the Royal Astronomical Society 503, no. 3 (February 22, 2021): 3297–308. http://dx.doi.org/10.1093/mnras/stab503.

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ABSTRACT We assess whether chondrules, once-molten mm-sized spheres filling the oldest meteorites, could have formed from super-km s−1 collisions between planetesimals in the solar nebula. High-velocity collisions release hot and dense clouds of silicate vapour which entrain and heat chondrule precursors. Thermal histories of CB chondrules are reproduced for colliding bodies ∼10–100 km in radius. The slower cooling rates of non-CB, porphyritic chondrules point to colliders with radii ≳ 500 km. How chondrules, collisionally dispersed into the nebula, agglomerated into meteorite parent bodies remains a mystery. The same orbital eccentricities and inclinations that enable energetic collisions prevent planetesimals from re-accreting chondrules efficiently and without damage; thus the sedimentary laminations of the CB/CH chondrite Isheyevo are hard to explain by direct fallback of collisional ejecta. At the same time, planetesimal surfaces may be littered with the shattered remains of chondrules. The micron-sized igneous particles recovered from comet 81P/Wild-2 may have originated from in-situ collisions and subsequent accretion in the proto-Kuiper belt, obviating the need to transport igneous solids across the nebula. Asteroid sample returns from Hayabusa2 and OSIRIS-REx may similarly contain chondrule fragments.
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Dissertations / Theses on the topic "Orbital Collisions"

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Diaz, Christina R. "A STUDY OF THE COLLISIONAL EVOLUTION OF ORBITAL DEBRIS IN GEOPOTENTIAL WELLS AND GEO DISPOSAL ORBITS." DigitalCommons@CalPoly, 2013. https://digitalcommons.calpoly.edu/theses/1063.

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This thesis will present the effects of the orbital debris evolution in two key areas: the geosynchronous disposal orbit regime known as “graveyard” and the two geopotential wells found in 105◦ W and 75◦ E longitude bins. After developing a GEO specific orbit propagator for NASA Johnson Space Center’s Orbital Debris Of- fice, collisions were simulated throughout these regimes using a low velocity breakup model. This model considered the effects of perturbations particularly non-spherical Earth effects (specifically sectorial and zonal harmonics), lunar effects, third body effects and solar radiation pressure effects. The results show that CDPROP does well in simulating the presence of the Eastern and Western geopotential wells, as well as catching drifting GEO objects. It does not do as well in catching East-West trapped objects. Three collision test cases were then simulated in graveyard and the East and West geopotential wells.
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Opperman, Roedolph A. (Roedolph Adriaan). "Astronaut Extravehicular Activity : safety, injury & countermeasures; &, Orbital collisions & space debris : incidence, impact & international policy." Thesis, Massachusetts Institute of Technology, 2010. http://hdl.handle.net/1721.1/62498.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics; and, (S.M. in Technology and Policy)--Massachusetts Institute of Technology, Engineering Systems Division, Technology and Policy Program, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 155-161).
Extravehicular Activity (EVA) spacesuits are a key enabling technology which allow astronauts to survive and work in the harsh environment of space. Of the entire spacesuit, the gloves may perhaps be considered the most difficult engineering design issue. A significant number of astronauts sustain hand and shoulder injuries during extravehicular activity (EVA) training and operations. In extreme cases these injuries lead to fingernail delamination (onycholysis) or rotator cuff tears and require medical or surgical intervention. In an effort to better understand the causal mechanisms of injury, a study consisting of modeling, statistical and experimental analyses was performed in section I of this thesis. A cursory musculoskeletal modeling tool was developed for use in comparing various spacesuit hard upper torso designs. The modeling effort focuses on optimizing comfort and range of motion of the shoulder joint within the suit. The statistical analysis investigated correlations between the anthropometrics of the hand and susceptibility to injury. A database of 192 male crewmembers' injury records and anthropometrics was sourced from NASA's Johnson Space Center. Hand circumference and width of the metacarpophalangeal (MCP) joint were found to be significantly associated with injuries by the Kruskal-Wallis test. Experimental testing was conducted to characterize skin blood flow and contact pressure inside the glove. This was done as part of NASA's effort to evaluate a hypothesis that fingernail delamination is caused by decreasing blood flow in the finger tips due to compression of the skin inside the extravehicular mobility unit (EMU) glove. The initial investigation consisted of a series of skin blood flow and contact pressure tests of the bare finger, and showed that blood flow decreased to approximately 60% of baseline value with increasing force, however, this occurred more rapidly for finger pads (4N) than for finger tips (ION). A gripping test of a pressure bulb using the bare hand was also performed at a moderate pressure of 13.33kPa (100mmHg) and at a high pressure of 26.66kPa (200mmHg), and showed that blood flow decreased 50% and 45%, respectively. Excessive hyperperfusion was observed for all tests following contact force or pressure, which may also contribute to the onset of delamination. Preliminary data from gripping tests inside the EMU glove in a hypobaric chamber at NASA's Johnson Space Center show that skin blood flow decreased by 45% and 40% when gripping at 3 moderate and high pressures, respectively. These tests show that finger skin blood flow is significantly altered by contact force/pressure, and that occlusion is more sensitive when it is applied to the finger pad than the finger tip. Our results indicate that the pressure on the finger pads required to articulate stiff gloves is more likely to impact blood flow than the pressure on the fingertips associated with tight or ill-fitting gloves. Improving the flexibility of the gloves will therefore not only benefit operational performance, but may also be an effective approach in reducing the incidence of finger injury. Space Policy Abstract EVA injury is only one of many dangers astronauts face in the extreme environment of space. Orbital debris presents a significant threat to astronaut safety and is a growing cause of concern. Since the dawn of satellites in the early 1950's, space debris from intentionally exploded spacecraft, dead satellites, and on-orbit collisions has significantly increased and currently outnumbers operational space hardware. Adding to this phenomenon, the advent of commercial spaceflight and the recent space activities in China and India to establish themselves as spacefairing nations are bound to accelerate the rate of space debris accumulating in low Earth orbit, thus, exacerbating the problem. The policies regulating orbital debris were drafted in the 1960s and 1970s and fail to effectively address the dynamic nature of the debris problem. These policies are not legally enforced under international law and implementation is entirely voluntary. Space debris is a relevant issue in international space cooperation. Unless regulated, some projections indicate space debris will reach a point of critical density, after which the debris will grow exponentially, as more fragments are generated by collisions than are removed by atmospheric drag. Space debris proliferation negatively impacts human spaceflight safety, presents a hazard to orbiting space assets, and may lead to portions of near-Earth orbit becoming inaccessible, thus limiting mission operations. The aim of this research effort was to review current international space policy, legislation and mitigation strategies in light of two recent orbital collision episodes. The first is the February 2009 collision between a defunct Russian Cosmos spacecraft and a commercial Iridium satellite. The second is China's display of technological prowess during the January 2007 intentional demolition of its inactive Fengyun-IC weather satellite using a SC-19 antisatellite (ASAT) missile. In each case the stakeholders, politics, policies, and consequences of the collision are analyzed. The results of this analysis as well as recommendations for alternative mitigation and regulatory strategies are presented.
by Roedolph A. Opperman.
S.M.in Technology and Policy
S.M.
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Gao, Junwen. "Two-electron processes and correlation effects in ion-atom collisions : a close-coupling approach at intermediate energies." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS117.

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Cette thèse présente une théorie non perturbative pour décrire les processus multi-électroniques intervenant au cours des collisions ion-atome. Le traitement choisi est semiclassique en ce sens que le mouvement relatif cible-projectile est décrit par des trajectoires classiques (mouvement rectiligne uniforme), tandis que la dynamique électronique est traitée quantiquement, en résolvant de manière non perturbative l’équation de Schrödinger dépendante du temps. Cette approche théorique a été codée au cours de la thèse dans une nouvelle version du code informatique à deux électrons actifs et mise en œuvre à l'étude de plusieurs systèmes de collision. Outre le développement long et complexe et les tests du code, les trois dernières années ont été spécialement consacrées à la compréhension de la physique d'événements spécifiques de diffusion de particules lourdes. Nous avons entrepris l’étude de trois types de systèmes de collision : par ordre d’apparition dans cette thèse, (i) collisions ion-ion faiblement chargé avec une extrême importance de la corrélation électronique (H+ - H-), (ii) collisions entre projectiles multiplement chargés et atome (C4+ - He) et (iii) collisions He+ - He avec un traitement très original prenant en compte des trois électrons dans la dynamique. Le choix de ces systèmes était guidé sur des systèmes benchmark pour lesquels des résultats expérimentaux et théoriques étaient disponibles, et présentant des questions ouvertes, liées par exemple à de forts désaccords entre les données existantes.Systématiquement, nous avons essayé de produire des résultats avec une convergence contrôlée permettant des interprétations physiques originales
This thesis presents a non perturbative theory to describe multi-electronic processes occurring in the course of ion-atom collisions. The treatment is semiclassical in that the relative target-projectile motion is described by classical straight-line constant velocity trajectories, while the electronic dynamics is treated quantum mechanically, by solving non perturbatively the time-dependent Schödinger equation. The treatment has been implemented in a new version of two-active-electron computer code. Besides the long and complex development and tests of the code, the last three years have been especially devoted to understanding of the physics of specific heavy particle scattering events. We have undertaken the study of three collision systems with various features: (i) low charge ion-ion collisions with an extreme importance of electronic correlation (H+ + H− collisions), (ii) multiply charged projectile-atom collisions (C4+ + He) and (iii) He+ + He collisions with the dynamical treatment of the three electrons. Our guideline was always to target systems for which experimental and theoretical results were available (at least in some energy domain), with still open questions, related, for example, to strong disagreement between the various data. We have tried as much as our computing resources and allowed it to produce results with controlled convergence. These investigations were carried out in a very wide, up to three decades, energy domain with same collision description (i.e. same basis sets), which brought continuity and coherence on the predictions and the interpretations of the results and of the underlying mechanisms giving rise to the processes considered
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Polzine, Benjamin. "The Collisional Evolution of Orbital Debris in Geopotential Wells and Disposal Orbits." DigitalCommons@CalPoly, 2017. https://digitalcommons.calpoly.edu/theses/1703.

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This thesis investigates the orbital debris evolution in the geosynchronous disposal orbit regime and within geosynchronous orbits effected by the geopotential wells. A propagator is developed for the accurate simulation of GEO specific orbits and the required perturbations are determined and described. Collisions are then simulated in the selected regimes using a low velocity breakup model derived from the NASA EVOLVE breakup model. The simulations described in this thesis consider a set of perturbations including the geopotential, solar and lunar gravity, and solar radiation pressure forces. This thesis is based on a prior paper and additionally seeks to address an issue in simulating East-West trapped objects. The results show that this propagator successfully simulates the presence of all wells and the East-West entrapment, and the required perturbations are outlined. Five collision test cases were simulated, one for each type of entrapment and an additional for the disposal orbit.
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Rodríguez, del Río Óscar. "Ejection-collision orbits in the restricted three-body problem." Doctoral thesis, Universitat Politècnica de Catalunya, 2021. http://hdl.handle.net/10803/672338.

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The main objective of this dissertation is the study of the ejection-collision (EC) orbits in the circular and planar Restricted Three Body Problem (RTBP from now on). In particular, we will focus on the analytical and numerical study of a very specific type of EC orbits, that we denote as n-EC orbits. An n-EC orbit is an orbit such that the particle ejects from one primary and reaches n times a relative maximum in the distance with respect to the primary from which it ejected before colliding with it. In this way, we will study numerically in depth this kind of orbits and we will show analytically that for a sufficiently large value of the Jacobi constant (for which we will give an expression in terms of the mass parameter and the value of n) there exist exactly four n-EC orbits with well-defined characteristics. These results generalize and improve the previous results for the particular case of n=1, and we will see that they can be easily extrapolated to the Hill problem. Besides, we will observe numerically that the evolution of these four original families of n-EC orbits present a very rich dynamics.It is well-known that the system that defines the motion of the particle is not well defined at the points where the primaries are located. For this reason, we have used two different techniques to regularize the collision, the McGehee regularization and the Levi-Civita regularization. Thus, in this dissertation we have analyzed the advantages and disadvantages of each regularization and the different methods that can be used to detect collisions. Since this dissertation will be mainly focused on values of the Jacobi constant greater than those associated to the equilibrium point L1, these two local regularizations will be enough. For less restrictive values of the Jacobi constant we will see that there exist other global regularizations or alternatively, we can simply work with local regularizations in a neighbourhood of each primary.On the other hand, from the numerical point of view we have analyzed the global behaviour of the ejection orbits in the RTBP. We have studied the relation between the family of Lyapunov periodic orbits around the equilibrium point L1 and the ejection orbits for values of the Jacobi constant such that the associated Hill regions only allow a bounded motion for these orbits. In particular, we have seen that a chaotic infinity of heteroclinic connections between one primary and the Lyapunov periodic orbits around the equilibrium point L1 are obtained. As a consequence a chaotic infinity of ejection-collision orbits is also derived. Besides, we will see that we can construct colour diagrams that allow to describe the global dynamics of the ejection orbits given a range of time. These colour diagrams provide a very precise understanding of the dynamics of these orbits.Finally, we have made a first exploration of the spatial case of the circular restricted three body problem (RTBP 3D). In this first approach we have not used the classical Kustaanheimo–Stiefel regularization, instead we have decided to use a 3D version of the McGehee regularization. This presents some problems that we have analyzed and addressed,
L'objectiu principal d'aquesta dissertació és l'estudi de les òrbites d'ejecció-col·lisió (EC) al problema restringit de tres cossos circular i pla (RTBP a partir d'ara). En particular, ens centrarem en l'estudi analític i numèric d'unes òrbites d'EC molt particulars, a les quals hem anomenat òrbites de n-EC. Aquestes òrbites de n-EC, són òrbites tal que la partícula ejecta d'un primari, assoleix n màxims en la distància respecte al primari del qual han ejectat per a continuació tornar a col·lisionar amb ell. D'aquesta forma numèricament estudiarem en profunditat aquest tipus d'òrbites i analíticament demostrarem que per un valor prou gran de la constant de Jacobi (per la qual donarem una expressió en termes del paràmetre de masses i el valor de n) existeixen exactament quatre òrbites de n-EC amb unes característiques ben determinades. Aquests resultats generalitzen i milloren els resultats previs pel cas particular de n=1, i veurem que es poden extrapolar fàcilment al problema de Hill. A més, numèricament veurem que l'evolució d'aquestes quatre famílies d'òrbites de n-EC originals presenta una dinàmica molt rica.És ben sabut, que el sistema que defineix el moviment de la partícula no està ben definit als punts on es troben situats els primaris. Per aquest motiu hem utilitzat dues tècniques de regularització de la col·lisió, la regularització de McGehee i la regularització de Levi-Civita. D'aquesta forma, en aquesta memòria hem analitzat els avantatges i els inconvenients de cada regularització, i els diferents mètodes que es poden utilitzar per detectar col·lisions. Com que gran part d'aquesta memòria es focalitzarà en valors de la constant de Jacobi més grans que l'associat al punt d'equilibri L1 aquestes dues regularitzacions de caràcter local seran suficients. Per valors menys restrictius de la constant de Jacobi veurem que existeixen altres regularitzacions de caràcter global o que simplement podem treballar amb regularitzacions locals a l'entorn de cada primari.Per altra banda, numèricament hem analitzat el comportament global de les òrbites d'ejecció al RTBP. Hem estudiat la relació entre la família de les òrbites periòdiques de Lyapunov al voltant del punt d'equilibri lineal L1 i les òrbites d'ejecció que es duu a terme al rang de valors de la constant de Jacobi tals que les regions de Hill associades només permeten un moviment fitat per a aquestes òrbites. En particular, hem vist que s'obté una infinitat caòtica de connexions heteroclíniques entre un primari i l'òrbita periòdica de Lyapunov al voltant del punt d'equilibri lineal L1. Com a conseqüència, també es deriva una infinitat caòtica d'òrbites d'ejecció-col·lisió. A més, veurem que podem construir uns diagrames de color que ens permeten descriure la dinàmica global de les òrbites d'ejecció donat un interval de temps. Aquests diagrames proporcionen una comprensió molt precisa de la dinàmica d'aquestes òrbites.Finalment, hem fet una primera exploració del cas espacial del problema restringit de tres cossos circular (RTBP 3D). En aquesta primera aproximació no hem utilitzat la clàssica regularització de Kustaanheimo-Stiefel i hem decidit utilitzar una versió 3D de la regularització de McGehee. Això presenta alguns problemes, que hem analitzat i abordat, però aquesta aproximació és suficient per obtenir un primer resultat numèric sobre òrbites de 1-EC i per il·lustrar la complexitat del cas 3D.
Matemàtica aplicada
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Labbe, Clément. "Autonomous Orbit Control with on-board collision risk management." Thesis, KTH, Rymdteknik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-299367.

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Many satellites have an orbit of reference defined according to their mission. The satellites need therefore to navigate as close as possible to their reference orbit. However, due to external forces, the trajectory of a satellite is disturbed and actions need to be taken. For now, the trajectories of the satellites are monitored by the operations of satellites department which gives appropriate instructions of navigation to the satellites. These steps require a certain amount of time and involvement which could be used for other purposes. A solution could be to make the satellites autonomous. The satellites would take their own decisions depending on their trajectory. The navigation control would be therefore much more efficient, precise and quicker. Besides, the autonomous orbit control could be coupled with an avoidance collision risk management. The satellites would decide themselves if an avoidance maneuver needs to be considered. The alerts of collisions would be given by the ground segment. In order to advance in this progress, this internship enables to analyse the feasibility of the implementation of the two concepts by testing them on an experiments satellite. To do so, tests plans were defined, tests procedures were executed and post-treatment tools were developed for analysing the results of the tests. Critical computational cases were considered as well. The tests were executed in real operations conditions.
Många satelliter har en referensbana definierad enligt deras uppdrag. Satelliterna behöver därför navigera så nära deras referensbana som möjligt. På grund av externa krafter störs dock satellitbanan och åtgärder måste vidtas. För närvarande övervakas satellitbanorna av satellitavdelningar på marken vilka ger lämpliga instruktioner för navigering till satelliterna. Dessa steg kräver en tid och engagemang som skulle kunna användas för andra ändamål. En lösning är att göra satelliterna autonoma. Satelliterna skulle då kunna ta sina egna beslut beroende på deras bana. Navigeringskontrollen skulle därför vara mycket mer effektiv, exakt och snabbare. Dessutom kan den autonoma banregleringen kopplas till riskhantering för undvikande av kollision med rymdskrot och andra satelliter. Satelliterna skulle själva avgöra om en undvikande manöver måste övervägas. Varningar om kollisioner skulle ges av marksegmentet. För att gå vidare i denna utveckling analyserar detta arbete genomförbarheten av implementeringen av olika koncept för undanmanövrar genom att testa dem på en experimentsatellit. För att göra detta definierades testplaner, testprocedurer utfördes och efterbehandlingsverktyg utvecklades för analys av testresultaten. Kritiska beräkningsfall togs fram. Testerna utfördes under verkliga driftsförhållanden.
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Anilkumar, A. K. "NEW PERSPECTIVES FOR ANALYZING THE BREAKUP, ENVIRONMENT, EVOLUTION, COLLISION RISK AND REENTRY OF SPACE DEBRIS OBJECTS." Thesis, Indian Institute of Science, 2004. http://hdl.handle.net/2005/80.

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Vikram Sarabhai Space Centre,Trivandrum
In the space surrounding the earth there are two major regions where orbital debris causes concern. They are the Low Earth Orbits (LEO) up to about 2000 km, and Geosynchronous Orbits (GEO) at an altitude of around 36000 km. The impact of the debris accumulations are in principle the same in the two regions; nevertheless they require different approaches and solutions, due to the fact that the perturbations in the orbital decay due to atmospheric drag effects predominates in LEO, gravitational forces including earth’s oblateness and luni solar effects dominating in GEO are different in these two regions. In LEO it is generally known that the debris population dominates even the natural meteoroid population for object sizes 1 mm and larger. This thesis focuses the study mainly in the LEO region. Since the first satellite breakup in 1961 up to 01 January 2003 more than 180 spacecraft and rocket bodies have been known to fragment in orbit. The resulting debris fragments constitute nearly 40% of the 9000 or more of the presently tracked and catalogued objects by USSPACECOM. The catalogued fragment count does not include the much more numerous fragments, which are too small to be detected from ground. Hence in order to describe the trackable orbital debris environment, it is important to develop mathematical models to simulate the trackable fragments and later expand it to untrackable objects. Apart from the need to better characterize the orbital debris environment down to sub millimeter particles, there is also a pressing necessity of simulation tools able to model in a realistic way the long term evolution of space debris, to highlight areas, which require further investigations, and to study the actual mitigation effects of space policy measures. The present thesis has provided newer perspectives for five major issues in space debris modeling studies. The issues are (i) breakup modeling, (ii) environment modeling, (iii) evolution of the debris environment, (iv) collision probability analysis and (v) reentry prediction. The Chapter 1 briefly describes an overview of space debris environment and the issues associated with the growing space debris populations. A literature survey of important earlier work carried out regarding the above mentioned five issues are provided in the Chapter 2. The new contributions of the thesis commence from Chapter 3. The Chapter 3 proposes a new breakup model to simulate the creation of debris objects by explosion in LEO named “A Semi Stochastic Environment Modeling for Breakup in LEO” (ASSEMBLE). This model is based on a study of the characteristics of the fragments from on orbit breakups as provided in the TLE sets for the INDIAN PSLV-TES mission spent upper stage breakup. It turned out that based on the physical mechanisms in the breakup process the apogee, perigee heights (limited by the breakup altitude) closely fit suitable Laplace distributions and the eccentricity follows a lognormal distribution. The location parameters of these depend on the orbit of the parent body at the time of breakup and their scale parameters on the intensity of explosion. The distribution of the ballistic coefficient in the catalogue was also found to follow a lognormal distribution. These observations were used to arrive at the proper physical, aerodynamic, and orbital characteristics of the fragments. Subsequently it has been applied as an inverse problem to simulate and further validate it based on some more typical well known historical on orbit fragmentation events. All the simulated results compare quite well with the observations both at the time of breakup and at a later epoch. This model is called semi stochastic in nature since the size and mass characteristics have to be obtained from empirical relations and is capable of simulating the complete scenario of the breakup. A new stochastic environment model of the debris scenario in LEO that is simple and impressionistic in nature named SIMPLE is proposed in Chapter 4. Firstly among the orbital debris, the distribution of the orbital elements namely altitude, perigee height, eccentricity and the ballistic coefficient values for TLE sets of data in each of the years were analyzed to arrive at their characteristic probability distributions. It is observed that the altitude distribution for the number of fragments exhibits peaks and it turned out that such a feature can be best modeled with a tertiary mixture of Laplace distributions with eight parameters. It was noticed that no statistically significant variations could be observed for the parameters across the years. Hence it is concluded that the probability density function of the altitude distribution of the debris objects has some kind of equilibrium and it follows a three component mixture of Laplace distributions. For the eccentricity ‘e’ and the ballistic parameter ‘B’ values the present analysis showed that they could be acceptably quite well fitted by Lognormal distributions with two parameters. In the case of eccentricity also the describing parameter values do not vary much across the years. But for the parameters of the B distribution there is some trend across the years which perhaps may be attributed to causes such as decay effect, miniaturization of space systems and even the uncertainty in the measurement data of B. However in the absence of definitive cause that can be attributed for the variation across the years, it turns out to be best to have the most recent value as the model value. Lastly the same kind of analysis has also been carried out with respect to the various inclination bands. Here the orbital parameters are analyzed with respect to the inclination bands as is done in ORDEM (Kessler et al 1997, Liou et al 2001) for near circular orbits in LEO. The five inclination bands considered here are 0-36 deg (in ORDEM they consider 19-36 deg, and did not consider 0-19 deg), 36-61 deg, 61-73 deg, 73-91 deg and 91- 180 deg, and corresponding to each band, the altitude, eccentricity and B values were modeled. It is found that the third band shows the models with single Laplace distribution for altitude and Lognormal for eccentricity and B fit quite well. The altitude of other bands is modeled using tertiary mixture of Laplace distributions, with the ‘e’ and ‘B’ following once again a Lognormal distribution. The number of parameter values in SIMPLE is, in general, just 8 for each description of altitude or perigee distributions whereas in ORDEM96 it is more. The present SIMPLE model captures closely all the peak densities without losing the accuracy at other altitudes. The Chapter 5 treats the evolution of the debris objects generated by on orbit breakup. A novel innovative approach based on the propagation of an equivalent fragment in a three dimensional bin of semi major axis, eccentricity, and the ballistic coefficient (a, e, B) together with a constant gain Kalman filter technique is described in this chapter. This new approach propagates the number density in a bin of ‘a’ and ‘e’ rapidly and accurately without propagating each and every of the space debris objects in the above bin. It is able to assimilate the information from other breakups as well with the passage of time. Further this approach expands the scenario to provide suitable equivalent ballistic coefficient values for the conglomeration of the fragments in the various bins. The heart of the technique is to use a constant Kalman gain filter, which is optimal to track the dynamically evolving fragment scenario and further expand the scenario to provide time varying equivalent ballistic coefficients for the various bins. In the next chapter 6 a new approach for the collision probability assessment utilizing the closed form solution of Wiesel (1989) by the way of a three dimensional look up table, which takes only air drag effect and an exponential model of the atmosphere, is presented. This approach can serve as a reference collision probability assessment tool for LEO debris cloud environment. This approach takes into account the dynamical behavior of the debris objects propagation and the model utilizes a simple propagation for quick assessment of collision probability. This chapter also brings out a comparison of presently available collision probability assessment algorithms based on their complexities, application areas and sample space on which they operate. Further the quantitative assessment of the collision probability estimates between different presently available methods is carried out and the obtained collision probabilities are match qualitatively. The Chapter 7 utilizes once again the efficient and robust constant Kalman gain filter approach that is able to handle the many uncertain, variable, and complex features existing in the scenario to predict the reentry time of the risk objects. The constant gain obtained by using only a simple orbit propagator by considering drag alone is capable of handling the other modeling errors in a real life situation. A detailed validation of the approach was carried out based on a few recently reentered objects and comparison of the results with the predictions of other agencies during IADC reentry campaigns are also presented. The final Chapter 8 provides the conclusions based on the present work carried together with suggestions for future efforts needed in the study of space debris. Also the application of the techniques evolved in the present work to other areas such as atmospheric data assimilation and forecasting have also been suggested.
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8

Simmons, Skyler C. "Analysis of Multiple Collision-Based Periodic Orbits in Dimension Higher than One." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5584.

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We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many of these orbits feature regularizable collisions between the masses. We demonstrate existence of the periodic orbits after performing the appropriate regularization. Stability, including linear stability, for the orbits is then computed using a technique due to Roberts. We point out other interesting features of the orbits as appropriate. When applicable, the results are extended to a broader family of orbits with similar behavior.
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Yan, Duokui. "Four-body Problem with Collision Singularity." Diss., CLICK HERE for online access, 2009. http://contentdm.lib.byu.edu/ETD/image/etd3111.pdf.

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Fleischer, Stefan [Verfasser], and Andreas [Gutachter] Knauf. "Improbability Results on Collision and Non-Collision Orbits in Multibody Systems via the Poincaré Surface Method / Stefan Fleischer ; Gutachter: Andreas Knauf." Erlangen : Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), 2018. http://d-nb.info/1154308715/34.

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Books on the topic "Orbital Collisions"

1

Uchida, Masaki. Spectroscopic Study on Charge-Spin-Orbital Coupled Phenomena in Mott-Transition Oxides. Tokyo: Springer Japan, 2013.

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Target earth!: Asteroid collisions past and future. Blue Ridge Summit, PA: Tab Books, 1991.

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Babadzhanov, P. B. Meteornye potoki asteroidov, peresekai︠u︡shchikh orbitu Zemli: Meteor showers of the Earth-crossing asteroids = Selʹkhoi meteorii asteroidoi madori zaminro burranda. Dushanbe: "Donish", 2009.

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The Velikovsky heresies: Worlds in collision and ancient catastrophes revisited. Rochester, Vt: Bear & Company, 2012.

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A methodology for selective removal of orbital debris. [Washington, DC: National Aeronautics and Space Administration, 1992.

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Feng, Eric Quinn. A time-dependent molecular orbital approach to ion-solid surface collisions. 1991.

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Uchida, Masaki. Spectroscopic Study on Charge-Spin-Orbital Coupled Phenomena in Mott-Transition Oxides. Springer, 2016.

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United States. National Aeronautics and Space Administration., ed. Oblique hypervelocity impact simulation for multi-layer orbital debris shielding (NAG 9-744): Final report. [Washington, DC: National Aeronautics and Space Administration, 1996.

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United States. National Aeronautics and Space Administration., ed. Oblique hypervelocity impact simulation for multi-layer orbital debris shielding (NAG 9-744): Final report. [Washington, DC: National Aeronautics and Space Administration, 1996.

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Tessendorf, Waylon. Orbital Maneuver Handbook: Orbital Maneuvers, Space Rendezvous, and Collision Avoidance. Lulu Press, Inc., 2015.

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Book chapters on the topic "Orbital Collisions"

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Pelton, Joseph N. "Tracking of Orbital Debris and Avoidance of Satellite Collisions." In Handbook of Satellite Applications, 1275–87. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-23386-4_106.

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Pelton, Joseph N. "Tracking of Orbital Debris and Avoidance of Satellite Collisions." In Handbook of Satellite Applications, 1–13. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4614-6423-5_106-2.

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Micha, David A., and Keith Runge. "Electronic Energy and Charge Transfer in Slow Atomic Collisions: A Time-Dependent Molecular Orbital Approach." In Nato ASI Series, 247–65. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4899-2326-4_19.

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Chen, Lei, Xian-Zong Bai, Yan-Gang Liang, and Ke-Bo Li. "Calculation of Collision Probability." In Orbital Data Applications for Space Objects, 135–83. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2963-9_5.

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Chen, Lei, Xian-Zong Bai, Yan-Gang Liang, and Ke-Bo Li. "Application of Collision Probability." In Orbital Data Applications for Space Objects, 185–246. Singapore: Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2963-9_6.

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Yoshinaga, Keiko, Eiichiro Kokubo, and Junichiro Makino. "Long-Term Orbital Evolution of Protoplanets." In Collisional Processes in the Solar System, 173–80. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0712-2_11.

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van der Burgt, P. J. M., J. van Eck, and H. G. M. Heideman. "Orbital Angular Momentum Exchange in Post-Collision Interaction." In Fundamental Processes in Atomic Collision Physics, 619–25. Boston, MA: Springer US, 1985. http://dx.doi.org/10.1007/978-1-4613-2125-5_28.

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Walker, R., R. Crowther, J. Wilkinson, P. H. Stokes, and G. G. Swinerd. "Orbital Debris Collision Risks to Satellite Constellations." In Mission Design & Implementation of Satellite Constellations, 317–26. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5088-0_28.

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Muinonen, Karri, Jenni Virtanen, and Edward Bowell. "Collision Probability for Earth-Crossing Asteroids Using Orbital Ranging." In Dynamics of Natural and Artificial Celestial Bodies, 93–101. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-017-1327-6_11.

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Faber, N. T. "Collisional N-body simulations and time-dependent orbital complexity." In Chaos in Astronomy, 183–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75826-6_17.

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Conference papers on the topic "Orbital Collisions"

1

Spain, Eileen M., Chris J. Smith, Mark J. Dalberth, and Stephen R. Leone. "Orbital alignment and vector correlations in inelastic atomic collisions." In The eighteenth international conference on the physics of electronic and atomic collisions. AIP, 1993. http://dx.doi.org/10.1063/1.45280.

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Cowardin, Heather, Phillip Anz-Meador, James Murray, J. C. Liou, Eric Christiansen, Marlon Sorge, Norman Fitz-Coy, and Tom Huynh. "Updates to the DebriSat Project in Support of Improving Breakup Models and Orbital Debris Risk Assessments." In 2019 15th Hypervelocity Impact Symposium. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/hvis2019-066.

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Abstract Existing DOD and NASA satellite breakup models are based on a key laboratory test, the 1992 Satellite Orbital debris Characterization Impact Test (SOCIT), which has supported many applications and matched on-orbit events involving older satellite designs reasonably well over the years. To update and improve these models, the NASA Orbital Debris Program Office, in collaboration with the Air Force Space and Missile Systems Center, The Aerospace Corporation, and the University of Florida, conducted a hypervelocity impact test using a high-fidelity mock-up satellite, DebriSat, in controlled and instrumented laboratory conditions. DebriSat is representative of present-day LEO satellites, having been constructed with modern spacecraft materials and techniques. The DebriSat fragment ensemble provided a variety of shapes, bulk densities, and dimensions. Fragments down to 2 mm in size are being characterized by their physical and derived properties. A subset of fragments will be analyzed further in laboratory radar and optical facilities to update the existing radar-based NASA Size Estimation Model (SEM) and develop a comparable optical-based SEM. Thoroughly understanding size estimates from ground-based optical and radar sensors is one of the key parameters used in assessing the environment and the risks that debris present to operational spacecraft. The data will inform updates to the current NASA Standard Satellite Breakup Model (SSBM);, which was formulated using laboratory and ground-based measurements of on-orbit fragmentation events to describe an average breakup for spacecraft and upper stage collisions and explosions. DebriSat will extend the laboratory data ensemble. The DebriSat shape and density categories provide a baseline for non-spherical projectile hypervelocity impact testing for damage assessment. The data from these tests, simulations, and analyses will be used to update the NASA Orbital Debris Engineering Model (ORDEM) with more realistic simulations of catastrophic fragmentation events for modern satellites and to assess the risk posed by the orbital debris environment. This paper provides an overview of the project, updates on the characterization process, and the NASA analysis status.
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Lapierre, L., P. Y. Cheng, Shan S. Ju, Y. M. Hahn, and Hai-Lung Dai. "Orientation and molecular orbital dependences in electronic relaxation collisions studied through van der Waals complexes." In OE/LASE '92, edited by Cheuk-Yiu Ng. SPIE, 1992. http://dx.doi.org/10.1117/12.58146.

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Igenbergs, Katharina, Markus Wallerberger, Josef Schweinzer, and Friedrich Aumayr. "Atomic-orbital close-coupling calculations for collisions involving fusion relevant highly charged impurity ions using very large basis sets." In THE 17TH INTERNATIONAL CONFERENCE ON ATOMIC PROCESSES IN PLASMAS (ICAPIP). AIP, 2012. http://dx.doi.org/10.1063/1.4707883.

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BENDISCH, J., and D. REX. "Collision avoidance analysis." In Orbital Debris Conference: Technical Issues andFuture Directions. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-1338.

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VILAS, FAITH, MICHAEL COLLINS, PAUL KRAMER, G. ARNDT, and JERRY SUDDATH. "Collision warning and avoidance considerations for the Space Shuttleand Space Station Freedom." In Orbital Debris Conference: Technical Issues andFuture Directions. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1990. http://dx.doi.org/10.2514/6.1990-1337.

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Bermejo Ballesteros, Juan, José María Vergara Pérez, Alejandro Fernández Soler, and Javier Cubas Cano. "Mubody, an astrodynamics open-source Python library focused on libration points." In Symposium on Space Educational Activities (SSAE). Universitat Politècnica de Catalunya, 2022. http://dx.doi.org/10.5821/conference-9788419184405.040.

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Mubody is an astrodynamics open-source Python library focused on the libration points. Such points result from the equilibrium of the gravitational forces between two massive bodies as the Sun and Earth, for example. The library is mainly intended for the generation of orbits in these regions, which is not a straightforward process, specially if perturbations are considered. Currently, the library allows to generate Lissajous orbits in the second Lagrange point of the Sun-Earth system under the influence of perturbations such as the Earth orbit eccentricity. The next milestone, as a result of a master student work, is the incorporation of Halo orbits and the expansion to all three collinear libration points from any two massive bodies of the Solar System. This tool has been developed as part of a PhD, motivated by the need of performing mission analysis in libration point regions. Nevertheless, since its creation it has also proven to be an excellent academic tool for both enhancing the library itself and using its results for further studies (collision risk, thermal analysis, formation flight control, etc). As a result, the tool has rapidly evolved, building onto the knowledge and experience that the students gather while working on their academic projects (bachelor’s degree dissertations, master theses, subjects, internships). The participation on the library development provides students with experience in orbital mechanics, software design, version control and it compels them to ensure that their work can be readily used by others as it is properly documented. The project is hosted in GitLab under a MIT licence
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González Peréz, Luis Miguel, Johan Wideberg, and Borja GONZALEZ PEREZ-SOMARRIBA. "Bicycling-related accidents and factors contributing to injury." In CIT2016. Congreso de Ingeniería del Transporte. Valencia: Universitat Politècnica València, 2016. http://dx.doi.org/10.4995/cit2016.2016.3718.

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Objective: This study was conducted to find the epidemiological characteristics of bicycling-related maxillofacial fractures in a defined population, and identify factors contributing to injury. Methodology: A prospective study was carried out involving patients presenting with maxillofacial fractures sustained in bicycling-related accidents. Results: Between 908 of all cycling accidents attending for medical treatment, 122 patients (13% of all cycling accidents) were admitted with facial fractures between 2007 and 2014. Male and female ratio was 2.6:1, and the mean age was 29.4 years (standard deviation: 12.8, range: 12-79 years). Causes of injury included collisions (63%) and accidental falls (37%). The fracture patterns seen were mandibular (49%), zygomatic (32%), orbital (13%), nasal (7%), maxillary (2%), and frontal (2%). Condylar fractures were the most common of the mandibular fractures (63%). The most frequently observed concomitant lesions were orthopedic injuries. Conclusions: Bicycling-related maxillofacial injuries are common and therefore important to identify in order to design a sustainable transport system and for units that provide assistance to traffic accident victims. Missed diagnosis or delayed treatment can lead to facial deformities and functional problems. Wearing protective helmets and the improvement of the helmets design is one aspect that would be of interest for the prevention of injuries. Keywords: Cycling; bicycle-related trauma; maxillofacial fractures; risk factors; helmets.DOI: http://dx.doi.org/10.4995/CIT2016.2016.3718
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Hamed, Ahmed Refaat, Ahmed Badawy, Adel A. Omer, Mahmoud Ashry, and Wessam M. Hussein. "Multiple Debris Orbital Collision Avoidance." In 2019 IEEE Aerospace Conference. IEEE, 2019. http://dx.doi.org/10.1109/aero.2019.8742114.

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"Dynamic Orbital Debris Collision Risk Mitigation." In 55th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.iac-04-iaa.5.12.5.11.

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Reports on the topic "Orbital Collisions"

1

Godinez Vazquez, Humberto C. IMPACT Project Integrated Modeling of Perturbations in Atmospheres for Conjunction Tracking A New Orbital Prediction Model to Avoid Collisions in Space. Office of Scientific and Technical Information (OSTI), May 2014. http://dx.doi.org/10.2172/1131013.

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