Mathematics in Space Debris Removal
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Low Thrust Manoeuvres to Perform Large Changes of RAAN Or Inclination in LEO
Facoltà di Ingegneria Corso di Laurea Magistrale in Ingegneria Aerospaziale Master Thesis Low Thrust Manoeuvres To Perform Large Changes of RAAN or Inclination in LEO Academic Tutor: Prof. Lorenzo CASALINO Candidate: Filippo GRISOT July 2018 “It is possible for ordinary people to choose to be extraordinary” E. Musk ii Filippo Grisot – Master Thesis iii Filippo Grisot – Master Thesis Acknowledgments I would like to address my sincere acknowledgments to my professor Lorenzo Casalino, for your huge help in these moths, for your willingness, for your professionalism and for your kindness. It was very stimulating, as well as fun, working with you. I would like to thank all my course-mates, for the time spent together inside and outside the “Poli”, for the help in passing the exams, for the fun and the desperation we shared throughout these years. I would like to especially express my gratitude to Emanuele, Gianluca, Giulia, Lorenzo and Fabio who, more than everyone, had to bear with me. I would like to also thank all my extra-Poli friends, especially Alberto, for your support and the long talks throughout these years, Zach, for being so close although the great distance between us, Bea’s family, for all the Sundays and summers spent together, and my soccer team Belfiga FC, for being the crazy lovable people you are. A huge acknowledgment needs to be address to my family: to my grandfather Luciano, for being a great friend; to my grandmother Bianca, for teaching me what “fighting” means; to my grandparents Beppe and Etta, for protecting me -
Arxiv:2011.13376V1 [Astro-Ph.EP] 26 Nov 2020 Welsh Et Al
On the estimation of circumbinary orbital properties Benjamin C. Bromley Department of Physics & Astronomy, University of Utah, 115 S 1400 E, Rm 201, Salt Lake City, UT 84112 [email protected] Scott J. Kenyon Smithsonian Astrophysical Observatory, 60 Garden St., Cambridge, MA 02138 [email protected] ABSTRACT We describe a fast, approximate method to characterize the orbits of satellites around a central binary in numerical simulations. A goal is to distinguish the free eccentricity | random motion of a satellite relative to a dynamically cool orbit | from oscillatory modes driven by the central binary's time-varying gravitational potential. We assess the performance of the method using the Kepler-16, Kepler-47, and Pluto-Charon systems. We then apply the method to a simulation of orbital damping in a circumbinary environment, resolving relative speeds between small bodies that are slow enough to promote mergers and growth. These results illustrate how dynamical cooling can set the stage for the formation of Tatooine-like planets around stellar binaries and the small moons around the Pluto-Charon binary planet. Subject headings: planets and satellites: formation { planets and satellites: individual: Pluto 1. Introduction Planet formation seems inevitable around nearly all stars. Even the rapidly changing gravitational field around a binary does not prevent planets from settling there (e.g., Armstrong et al. 2014). Recent observations have revealed stable planets around binaries involving main sequence stars (e.g., Kepler-16; Doyle et al. 2011), as well as evolved compact stars (the neutron star-white dwarf binary PSR B1620- 26; Sigurdsson et al. 2003). The Kepler mission (Borucki et al. -
Kessler Syndrome
Kessler Syndrome March 20, 2021 What is Kessler Syndrome? The Kessler syndrome, also called the Kessler effect, collisional cascading or ablation cascade, is a scenario in which the density of objects in Low Earth Orbit (LEO) is high enough that collisions between objects could cause a cascade where each collision generates space debris that increases the likelihood of further collisions. Who proposed it? It is a theory proposed by NASA scientist Donald J. Kessler in 1978, used to describe a self-sustaining cascading collision of space debris in LEO. In an article published on June 1, 1978 in the American Journal of Geophysical Research, the authors Donald J. Kessler and Burton G. Cour-Palais, two NASA experts, identified the risk of an exponential increase in the number of space debris or orbital debris under the effect of mutual collisions. The two authors believed that a belt formed by these objects or fragments of objects around the Earth would soon form. Eventually threatening space activities, this phenomenon will be popularized a few years later under the name of Kessler syndrome Implications One implication is that the distribution of debris in orbit could render space activities and the use of satellites in specific orbital ranges impractical for many generations. The Kessler syndrome is troublesome because of the domino effect and feedback runaway wherein impacts between objects of sizable mass spall off debris from the force of the collision Every satellite, space probe, and manned mission has the potential to produce space debris. A cascading Kessler syndrome becomes more likely as satellites in orbit increase in number. -
Solving the Space Debris Crisis Paul B
Journal of Air Law and Commerce Volume 83 | Issue 3 Article 2 2018 Solving the Space Debris Crisis Paul B. Larsen Georgetown University Law Center, [email protected] Follow this and additional works at: https://scholar.smu.edu/jalc Part of the Air and Space Law Commons Recommended Citation Paul B. Larsen, Solving the Space Debris Crisis, 83 J. Air L. & Com. 475 (2018) https://scholar.smu.edu/jalc/vol83/iss3/2 This Article is brought to you for free and open access by the Law Journals at SMU Scholar. It has been accepted for inclusion in Journal of Air Law and Commerce by an authorized administrator of SMU Scholar. For more information, please visit http://digitalrepository.smu.edu. SOLVING THE SPACE DEBRIS CRISIS PAUL B. LARSEN* ABSTRACT Space debris is a growing public safety problem. As described by the Kessler Syndrome,1 the increasing accumulation of debris will soon hinder and eventually preclude access to outer space unless the trend is swiftly reversed. The Inter-Agency Space Deb- ris Coordination Committee’s (IADC) Space Debris Mitigation Guidelines, as adopted by the United Nations (UN) Committee for the Peaceful Uses of Outer Space (COPUOS), are voluntary but are enforced as mandatory regulations by major space pow- ers; however, the guidelines only apply to new debris. The Euro- pean Space Agency’s (ESA) 2017 Space Debris Conference concluded that existing space debris guidelines are inadequate and must be further strengthened in order to successfully con- trol space debris.2 * The author taught air and space law for more than forty years respectively at Southern Methodist University and at Georgetown University. -
Gravity Recovery by Kinematic State Vector Perturbation from Satellite-To-Satellite Tracking for GRACE-Like Orbits Over Long Arcs
Gravity Recovery by Kinematic State Vector Perturbation from Satellite-to-Satellite Tracking for GRACE-like Orbits over Long Arcs by Nlingilili Habana Report No. 514 Geodetic Science The Ohio State University Columbus, Ohio 43210 January 2020 Gravity Recovery by Kinematic State Vector Perturbation from Satellite-to-Satellite Tracking for GRACE-like Orbits over Long Arcs By Nlingilili Habana Report No. 514 Geodetic Science The Ohio State University Columbus, Ohio 43210 January 2020 Copyright by Nlingilili Habana 2020 Preface This report was prepared for and submitted to the Graduate School of The Ohio State University as a dissertation in partial fulfillment of the requirements for the Degree of Doctor of Philosophy ii Abstract To improve on the understanding of Earth dynamics, a perturbation theory aimed at geopotential recovery, based on purely kinematic state vectors, is implemented. The method was originally proposed in the study by Xu (2008). It is a perturbation method based on Cartesian coordinates that is not subject to singularities that burden most conventional methods of gravity recovery from satellite-to-satellite tracking. The principal focus of the theory is to make the gravity recovery process more efficient, for example, by reducing the number of nuisance parameters associated with arc endpoint conditions in the estimation process. The theory aims to do this by maximizing the benefits of pure kinematic tracking by GNSS over long arcs. However, the practical feasibility of this theory has never been tested numerically. In this study, the formulation of the perturbation theory is first modified to make it numerically practicable. It is then shown, with realistic simulations, that Xu’s original goal of an iterative solution is not achievable under the constraints imposed by numerical integration error. -
Patched Conic Approximation), Ballistic Capture Method [16]
U.P.B. Sci. Bull., Series D, Vol. 81 Iss.1, 2019 ISSN 1454-2358 AUTOMATIC CONTROL OF A SPACECRAFT TRANSFER TRAJECTORY FROM AN EARTH ORBIT TO A MOON ORBIT Florentin-Alin BUŢU1, Romulus LUNGU2 The paper addresses a Spacecraft transfer from an elliptical orbit around the Earth to a circular orbit around the Moon. The geometric parameters of the transfer trajectory are computed, consisting of two orbital arcs, one elliptical and one hyperbolic. Then the state equations are set, describing the dynamics of the three bodies (Spacecraft, Earth and Moon) relative to the Sun. A nonlinear control law (orbit controller) is designed and the parameters of the reference orbit are computed (for each orbital arc);The MATLAB/Simulink model of the automatic control system is designed and with this, by numerical simulation, the transfer path (composed of the two orbit arcs) of the Spacecraft is plotted relative to the Earth and relative to the Moon, the evolution of the Keplerian parameters, the components of the position and velocity vector errors relative to the reference trajectory, as well as the components of the command vector. Keywords: elliptical orbit, nonlinear control, reference orbit. 1. Introduction Considering that the Spacecraft (S) runs an elliptical orbit, with Earth (P) located in one of the ellipse foci, the S transfer over a circular orbit around the Moon (L) is done by traversing a trajectory composed of two orbital arcs, one elliptical and one hyperbolic. From the multitude of papers studied on this topic in order to elaborate the present paper, we mention mainly the following [1] - [15]. -
Spacecraft Conjunction Assessment and Collision Avoidance Best Practices Handbook
National Aeronautics and Space Administration National Aeronautics and Space Administration NASA Spacecraft Conjunction Assessment and Collision Avoidance Best Practices Handbook December 2020 NASA/SP-20205011318 The cover photo is an image from the Hubble Space Telescope showing galaxies NGC 4038 and NGC 4039, also known as the Antennae Galaxies, locked in a deadly embrace. Once normal spiral galaxies, the pair have spent the past few hundred million years sparring with one another. Image can be found at: https://images.nasa.gov/details-GSFC_20171208_Archive_e001327 ii NASA Spacecraft Conjunction Assessment and Collision Avoidance Best Practices Handbook DOCUMENT HISTORY LOG Status Document Effective Description (Baseline/Revision/ Version Date Canceled) Baseline V0 iii NASA Spacecraft Conjunction Assessment and Collision Avoidance Best Practices Handbook THIS PAGE INTENTIONALLY LEFT BLANK iv NASA Spacecraft Conjunction Assessment and Collision Avoidance Best Practices Handbook Table of Contents Preface ................................................................................................................ 1 1. Introduction ................................................................................................... 3 2. Roles and Responsibilities ............................................................................ 5 3. History ........................................................................................................... 7 USSPACECOM CA Process ............................................................. -
Small Satellites and Space Debris Mitigation
chapter 11 Small Satellites and Space Debris Mitigation Cordula Steinkogler* i Introduction Almost six decades of spaceflight have left a large quantity of debris in outer space. Due to the continuous increase in space activities, the amount of space debris is constantly growing. While in 2005 the total mass of catalogued objects in Earth orbit was an estimated 5,000 tons, this number had risen to approxi- mately 6,000 tons by 2010 and amounts to over 6,600 tons today.1 At present, approximately 17,000 space objects with sizes ranging from a few centimetres to several meters are officially catalogued.2 Of these, however, only approximately * The author would like to thank Prof Otto Koudelka (Graz University of Technology), Dr Manuel Metz (German Aerospace Center), Attila Matas (ITU) and Vladimir Agapov (Russian Academy of Sciences) for the valuable advice and useful material they provided on technical matters. 1 National Aeronautics and Space Administration, ‘Monthly Effective Mass of Objects in Earth Orbit by Region’ (Orbital Debris Quarterly News, January 2015) <http://orbitaldebris.jsc.nasa .gov/newsletter/newsletter.html>. 2 National Aeronautics and Space Administration, ‘Satellite Box Score’ (Orbital Debris Quarterly News, January 2015) <http://orbitaldebris.jsc.nasa.gov/newsletter/newsletter.html>. See also United States Strategic Command, ‘Satellite Situation Report’ <https://www.space-track.org> (as of 6 June 2015). Note that according to the esa space debris risk assessment model esa MASTER 2009 the current number of space objects larger than 10 cm is approximately 29,000. See Institute of Aerospace Systems – Technische Universität Braunschweig, Maintenance of the esa MASTER Model – Final Report (European Space Agency 2011) 336. -
AAS Paper Kessler Syndromefinalfinal
(Preprint) AAS 10-016 THE KESSLER SYNDROME: IMPLICATIONS TO FUTURE SPACE OPERATIONS Donald J. Kessler,* Nicholas L. Johnson,† and J.-C. Liou,‡ and Mark Matney ☺ The term “Kessler Syndrome” is an orbital debris term that has become popular outside the professional orbital debris community without ever having a strict definition. The intended definition grew out of a 1978 JGR paper predicting that fragments from random collisions between catalogued objects in low Earth orbit would become an important source of small debris beginning in about the year 2000, and that afterwards, “…the debris flux will increase exponentially with time, even though a zero net input may be maintained”. The purpose of this pa- per is to clarify the intended definition of the term, to put the implications into perspective after 30 years of research by the international scientific community, and to discuss what this research may mean to future space operations. The conclusion is reached that while popular use of the term may have exaggerated and distorted the conclusions of the 1978 paper, the result of all research to date confirms that we are now entering a time when the orbital debris environment will increasingly be controlled by random collisions. Without adequate collision avoidance capabilities, control of the future environment requires that we fully implement current mitigation guidelines by not leaving future payloads and rocket bodies in orbit after their useful life. In addition, we will likely be re- quired to return some objects already in orbit. INTRODUCTION Since the beginning of the space program through the 1970’s, it was generally believed that NORAD was tracking all man-made objects in Earth orbit and that the catalogued objects repre- sented the major collision threat to other operational spacecraft. -
The Existence and Dangers of the Accumulation of Space Debris in Low Earth Orbit and How Analogies Can Be Used to Better Explain Complexities in New Technologies
The Existence and Dangers of the Accumulation of Space Debris in Low Earth Orbit and How Analogies Can Be Used to Better Explain Complexities in New Technologies A Research Paper submitted to the Department of Engineering and Society Presented to the Faculty of the School of Engineering and Applied Science University of Virginia • Charlottesville, Virginia In Partial Fulfillment of the Requirements for the Degree Bachelor of Science, School of Engineering Colin Purcell Spring 2021 On my honor as a University Student, I have neither given nor received unauthorized aid on this assignment as defined by the Honor Guidelines for Thesis-Related Assignments Advisor Kathryn A. Neeley, Associate Professor of STS, Department of Engineering and Society Overcrowding of Low Earth Orbit Governments, civilians and especially private companies are launching rockets and satellites at unprecedented rates (Stephen Clark, 2021, n.p). This rise is shown in Figure 1 and is predominantly caused by the increase in spacecraft launched by private companies. These satellites serve many purposes such as communication, imagery and even global wifi in the near future. While these spacecraft provide many benefits, some trouble will arise in the future if more attention is not paid to the potential for overcrowding space. Of the 2,666 satellites in orbit around the Earth, 1,918 or 72% are in Low Earth Orbit (LEO) (Datta, 2020). This congestion has the potential to lead to collisions between spacecraft causing damage and even destroying operational satellites. Figure 1: Number of spacecraft launched per year by different groups (Lafleur, 2017) This image shows the progression of how many spacecraft were launched each year from the beginning of space exploration to 2017. -
Outer Space: How Shall the World's Governments Establish Order Among Competing Interests?
Washington International Law Journal Volume 29 Number 1 12-23-2019 Outer Space: How Shall the World's Governments Establish Order Among Competing Interests? Paul B. Larsen Follow this and additional works at: https://digitalcommons.law.uw.edu/wilj Part of the Air and Space Law Commons Recommended Citation Paul B. Larsen, Outer Space: How Shall the World's Governments Establish Order Among Competing Interests?, 29 Wash. L. Rev. 1 (2019). Available at: https://digitalcommons.law.uw.edu/wilj/vol29/iss1/3 This Article is brought to you for free and open access by the Law Reviews and Journals at UW Law Digital Commons. It has been accepted for inclusion in Washington International Law Journal by an authorized editor of UW Law Digital Commons. For more information, please contact [email protected]. Copyright © 2019 Washington International Law Journal Association OUTER SPACE: HOW SHALL THE WORLD’S GOVERNMENTS ESTABLISH ORDER AMONG COMPETING INTERESTS? Paul B. Larsen† Abstract: We are in a period of transition in outer space; it is becoming increasingly congested. As one example, small satellites are beginning to interfere with astronomical observations. The objective of this article is to examine and evaluate how the various outer space interests interact, coordinate or conflict with each other. This article examines legal order options and the consequences of choosing among those options. Cite as: Paul B. Larsen, Outer Space: How Shall the World’s Governments Establish Order Among Competing Interests?, 29 WASH. INT’L L.J. 1 (2019). I. INTRODUCTION: WHY ORDER IN OUTER SPACE? Outer space seems unlimited; at least it so appeared in 1957 when Sputnik was launched. -
Space Junk: K-12 Educator's Guide
K-12 Educator’s Guide K-12 Educator’s Guide Table of Contents: Satellite History..................... 4 Try This: Astrolabe................. .13 Careers in Science................ 7 Puzzle: Crossword...................14 Try This: Clean-Up................ 10 Puzzle: Word Search...............15 Try This: Orbital Fun............. 11 Resources for Teachers..........16 Try This: Satellite Tracking.......12 Science Standards..................18 This K-12 Educator’s Guide includes supplemental information and activities to help extend the learning experience associated with watching Space Junk. The film tells the story of a growing ring of orbiting debris located 22,000 miles above Earth—a troubling legacy of 50 years of launching our dreams into space. That debris field casts a shadow over the future of space exploration. This Educator’s Guide presents a historical timeline of satellite launches and the background science to help learners understand the physics of space junk. Space Junk also challenges students to imagine solutions to the problems we now face in space. While the film’s message is a cautionary tale, it also seeks to inspire a new age of innovation. Today’s K-12 students are tomorrow’s scientists and engineers who will forge the future of space exploration and discovery. This Guide also includes hands-on activities and a complete presentation of how the film can be used to support classroom learning in context with the National Science Education Standards. Learning Goals for K-12 Students: • The basic physical principles of orbital mechanics have enabled a half-century of rapid innovation in satellite technology, impacting our daily lives. • Actions have consequences. The benefits of satellite technology have been great, but the orbital debris field has grown to become a new and pressing challenge.