DOCSLIB.ORG

Orbit Transfer Optimization of Spacecraft with Impulsive Thrusts Using Genetic Algorithm

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Orbit Transfer Optimization of Spacecraft with Impulsive Thrusts Using Genetic Algorithm ORBIT TRANSFER OPTIMIZATION OF SPACECRAFT WITH IMPULSIVE THRUSTS USING GENETIC ALGORITHM A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY AHMET YILMAZ IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN MECHANICAL ENGINEERING SEPTEMBER 2012 Approval of the thesis: ORBIT TRANSFER OPTIMIZATION OF A SPACECRAFT WITH IMPULSIVE THRUST USING GENETIC ALGORITHM Submitted by AHMET YILMAZ in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department, Middle East Technical University by, Prof. Dr. Canan Özgen Dean, Graduate School of Natural and Applied Sciences Prof. Dr. Süha Oral Head of Department, Mechanical Engineering Prof. Dr. M. Kemal Özgören Supervisor, Mechanical Engineering Dept., METU Examining Committee Members Prof. Dr. S. Kemal İder Mechanical Engineering Dept., METU Prof. Dr.M. Kemal Özgören Mechanical Engineering Dept., METU Prof. Dr. Ozan Tekinalp Aerospace Engineering Dept., METU Asst. Prof. Dr. Yiğit Yazıcıoğlu Mechanical Engineering Dept., METU Başar SEÇKİN, M.Sc. Roketsan Missile Industries Inc. Date: I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work. Name, Last name: Ahmet Yılmaz Signature : iii ABSTRACT ORBIT TRANSFER OPTIMIZATION OF A SPACECRAFT WITH IMPULSIVE THRUST USING GENETIC ALGORITHM Yılmaz, Ahmet M.S., Department of Mechanical Engineering Supervisor: Prof. Dr. M.Kemal Özgören September 2012, 127 pages This thesis addresses the orbit transfer optimization problem of a spacecraft. The optimal orbit transfer is the process of altering the orbit of a spacecraft with minimum propellant consumption. The spacecrafts are needed to realize orbit transfer to reach, change or keep its orbit. The spacecraft may be a satellite or the last stage of a launch vehicle that is operated at the exo-atmospheric region. In this study, a genetic algorithm based orbit transfer method has been developed. The applicability of genetic algorithm based orbit transfer method has been verified using orbit transfers which are optimal at specific cases. The solution to orbit transfer problem is also searched using steepest descent algorithm. While genetic algorithm can reach the optimal solution, steepest descent algorithm can reach optimal solution when a good initial prediction is provided. The effects of the initial orbital values on the orbit transfer solutions are also studied. Keywords: Orbit transfer, optimal orbit transfer, minimum propellant consumption, impulsive maneuvers, genetic algorithms. iv ÖZ GENETİK ALOGRİTMA KULLANILARAK BİR UZAY ARACININ DARBESEL İTKİYLE YÖRÜNGE TRANSFER OPTİMİZASYONU Yılmaz, Ahmet Yüksek Lisans, Makina Mühendisliği Bölümü Tez Yöneticisi: Prof. Dr. M.Kemal Özgören Eylül 2012, 127 sayfa Bu tez çalışması bir uzay aracının yörünge transfer eniyileme problemini içermektedir. Eniyilenmiş yörünge transferi asgari yakıt tüketimi ile uzay aracının yörüngesinin değiştirilmesidir. Uzay araçları yörüngeye erişmek, değiştirmek ve korumak amaçlı yörünge transferi gerçekleştirirler. Uzay aracı uydu ya da atmosfer dışı bölgede kullanılan uydu fırlatma aracı son kademesidir. Bu çalışmada bir genetik algoritma tabanlı yörünge transfer metodu geliştirilmiştir. Genetik algoritma tabanlı yörünge transfer yönteminin uygulanabilirliğinin belirli koşullarda eniyilenmiş yörünge transferleri kullanılarak doğrulanmıştır. Yörünge transfer problemine çözüm ayrıca ‘steepest descent’ algoritması ile de aranmıştır. Genetik algoritma eniyilenmiş sonuca ulaşabilirken, ‘steepest descent’ algoritması yanlızca iyi bir ilk tahmin sağlandığında eniyilenmiş sonuca ulaşabilmektedir. İlk yörünge değerlerinin yörünge transfer problem çözümüne etkileri de bu çalışmada incelenmiştir. Anahtar Kelimeler: Yörünge transferi, eniyilenmiş yörünge transferi, asgari yakıt tüketimi, darbeli manevra, genetik algoritma. v ACKNOWLEDGMENTS I would like to express sincere gratitude and thanks to my thesis supervisor Prof. Dr. M. Kemal Özgören for his invaluable guidance and encouragement throughout this study. I would also like to express my sincere appreciation to my colleagues in ROKETSAN who contributed to this thesis with valuable suggestions and comments. I would like to especially thank to İlke Akbulut, Başar Seçkin, Osman Yücel and Ezgi Civek. I can never thank enough my love İlkay Keneş, who has supported me with such remarkable patience and sensitivity. Without her love and patience, I could not handle these difficult months with that much ease. Very special thanks go to my family who has always supported me throughout my life. Their endless love, support and sacrifices have enabled this study’s completion. The work presented in this thesis could not have been accomplished without the support from many individuals. Finally, my thanks go to all those who are not specifically mentioned here. Ankara, 5 August 2012 Ahmet Yılmaz vi TABLE OF CONTENTS ABSTRACT ...................................................................................................... iv ÖZ .................................................................................................................. v ACKNOWLEDGMENTS ...................................................................................... vi TABLE OF CONTENTS ......................................................................................vii LIST OF TABLES ............................................................................................. xi LIST OF FIGURES ........................................................................................... xv LIST OF SYMBOLS ......................................................................................... xvii LIST OF ABBREVIATIONS ............................................................................. xviii CHAPTERS ....................................................................................................... 1 CHAPTER 1 INTRODUCTION ............................................................................................ 1 1.1 INTRODUCTION .............................................................................................1 1.2 MOTIVATION .................................................................................................4 1.3 LITERATURE SURVEY ......................................................................................6 1.4 SCOPE ......................................................................................................... 11 1.5 THESIS OUTLINE .......................................................................................... 12 CHAPTER 2 MATHEMATICAL MODEL .............................................................................. 13 2.1 ORBITAL ELEMENTS ..................................................................................... 13 2.2 ORBITAL MOTION ........................................................................................ 19 2.2.1 Kepler’s Laws ............................................................................................ 19 2.2.1.1 Kepler’s First Law ............................................................................... 19 2.2.1.2 Kepler’s Second Law .......................................................................... 20 2.2.1.3 Kepler’s Third Law ............................................................................. 22 2.2.2 Newton’s Law of Gravitational Attraction ..................................................... 23 vii 2.2.3 Two Body Problem .................................................................................... 24 2.2.4 Rocket Equation ........................................................................................ 26 2.2.5 Orbit Transfer Force Models ....................................................................... 29 2.2.5.1 Continuous Force Model ..................................................................... 29 2.2.5.2 Impulsive Force Model ........................................................................ 31 CHAPTER 3 ORBIT TRANSFER OPTIMIZATION PROBLEM ................................................ 37 3.1 OPTIMAL ORBIT TRANSFERS ......................................................................... 37 3.1.1 Hohmann Orbit Transfer (Coplanar Orbit Transfer) ....................................... 37 3.1.2 Only Inclination Change (OIC) Orbit Transfer .............................................. 41 3.2 ORBIT TRANSFER OPTIMIZATION PROBLEM .................................................. 44 3.3 OPTIMIZATION METHODS ............................................................................ 51 3.3.1 Genetic Algorithm ..................................................................................... 52 3.3.2 Steepest Descent Optimization Method ....................................................... 56 3.4 COMPARISON OF OPTIMIZATION METHODS FOR ORBIT TRANSFER OPTIMIZATION ....................................................................................................... 57 3.4.1 Problem-1 Coplanar Circular-Circular Orbit Transfer ..................................... 57 3.4.1.1 Application Of Genetic Algorithm Method To Problem-1 ......................... 59 3.4.1.2 Application Of Steepest Descent Algorithm To Problem-1 ...................... 60 3.4.2 Problem-2
Load more

Recommended publications
  • Astrodynamics
    Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities
    [Show full text]
  • Stability of the Moons Orbits in Solar System in the Restricted Three-Body
    Stability of the Moons orbits in Solar system in the restricted three-body problem Sergey V. Ershkov, Institute for Time Nature Explorations, M.V. Lomonosov's Moscow State University, Leninskie gory, 1-12, Moscow 119991, Russia e-mail: [email protected] Abstract: We consider the equations of motion of three-body problem in a Lagrange form (which means a consideration of relative motions of 3-bodies in regard to each other). Analyzing such a system of equations, we consider in details the case of moon‟s motion of negligible mass m₃ around the 2-nd of two giant-bodies m₁, m₂ (which are rotating around their common centre of masses on Kepler’s trajectories), the mass of which is assumed to be less than the mass of central body. Under assumptions of R3BP, we obtain the equations of motion which describe the relative mutual motion of the centre of mass of 2-nd giant-body m₂ (Planet) and the centre of mass of 3-rd body (Moon) with additional effective mass m₂ placed in that centre of mass (m₂ + m₃), where is the dimensionless dynamical parameter. They should be rotating around their common centre of masses on Kepler‟s elliptic orbits. For negligible effective mass (m₂ + m₃) it gives the equations of motion which should describe a quasi-elliptic orbit of 3-rd body (Moon) around the 2-nd body m₂ (Planet) for most of the moons of the Planets in Solar system. But the orbit of Earth‟s Moon should be considered as non-constant elliptic motion for the effective mass 0.0178m₂ placed in the centre of mass for the 3-rd body (Moon).
    [Show full text]
  • Optimisation of Propellant Consumption for Power Limited Rockets
    Delft University of Technology Faculty Electrical Engineering, Mathematics and Computer Science Delft Institute of Applied Mathematics Optimisation of Propellant Consumption for Power Limited Rockets. What Role do Power Limited Rockets have in Future Spaceflight Missions? (Dutch title: Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten. De rol van deze raketten in toekomstige ruimtevlucht missies. ) A thesis submitted to the Delft Institute of Applied Mathematics as part to obtain the degree of BACHELOR OF SCIENCE in APPLIED MATHEMATICS by NATHALIE OUDHOF Delft, the Netherlands December 2017 Copyright c 2017 by Nathalie Oudhof. All rights reserved. BSc thesis APPLIED MATHEMATICS \ Optimisation of Propellant Consumption for Power Limited Rockets What Role do Power Limite Rockets have in Future Spaceflight Missions?" (Dutch title: \Optimaliseren van brandstofverbruik voor vermogen gelimiteerde raketten De rol van deze raketten in toekomstige ruimtevlucht missies.)" NATHALIE OUDHOF Delft University of Technology Supervisor Dr. P.M. Visser Other members of the committee Dr.ir. W.G.M. Groenevelt Drs. E.M. van Elderen 21 December, 2017 Delft Abstract In this thesis we look at the most cost-effective trajectory for power limited rockets, i.e. the trajectory which costs the least amount of propellant. First some background information as well as the differences between thrust limited and power limited rockets will be discussed. Then the optimal trajectory for thrust limited rockets, the Hohmann Transfer Orbit, will be explained. Using Optimal Control Theory, the optimal trajectory for power limited rockets can be found. Three trajectories will be discussed: Low Earth Orbit to Geostationary Earth Orbit, Earth to Mars and Earth to Saturn. After this we compare the propellant use of the thrust limited rockets for these trajectories with the power limited rockets.
    [Show full text]
  • Flight and Orbital Mechanics
    Flight and Orbital Mechanics Lecture slides Challenge the future 1 Flight and Orbital Mechanics AE2-104, lecture hours 21-24: Interplanetary flight Ron Noomen October 25, 2012 AE2104 Flight and Orbital Mechanics 1 | Example: Galileo VEEGA trajectory Questions: • what is the purpose of this mission? • what propulsion technique(s) are used? • why this Venus- Earth-Earth sequence? • …. [NASA, 2010] AE2104 Flight and Orbital Mechanics 2 | Overview • Solar System • Hohmann transfer orbits • Synodic period • Launch, arrival dates • Fast transfer orbits • Round trip travel times • Gravity Assists AE2104 Flight and Orbital Mechanics 3 | Learning goals The student should be able to: • describe and explain the concept of an interplanetary transfer, including that of patched conics; • compute the main parameters of a Hohmann transfer between arbitrary planets (including the required ΔV); • compute the main parameters of a fast transfer between arbitrary planets (including the required ΔV); • derive the equation for the synodic period of an arbitrary pair of planets, and compute its numerical value; • derive the equations for launch and arrival epochs, for a Hohmann transfer between arbitrary planets; • derive the equations for the length of the main mission phases of a round trip mission, using Hohmann transfers; and • describe the mechanics of a Gravity Assist, and compute the changes in velocity and energy. Lecture material: • these slides (incl. footnotes) AE2104 Flight and Orbital Mechanics 4 | Introduction The Solar System (not to scale): [Aerospace
    [Show full text]
  • Download Paper
    Ever Wonder What’s in Molniya? We Do. John T. McGraw J. T. McGraw and Associates, LLC and University of New Mexico Peter C. Zimmer J. T. McGraw and Associates, LLC Mark R. Ackermann J. T. McGraw and Associates, LLC ABSTRACT Molniya orbits are high inclination, high eccentricity orbits which provide the utility of long apogee dwell time over northern continents, with the additional benefit of obviating the largest orbital perturbation introduced by the Earth’s nonspherical (oblate) gravitational potential. We review the few earlier surveys of the Molniya domain and evaluate results from a new, large area unbiased survey of the northern Molniya domain. We detect 120 Molniya objects in a three hour survey of ~ 1300 square degrees of the sky to a limiting magnitude of about 16.5. Future Molniya surveys will discover a significant number of objects, including debris, and monitoring these objects might provide useful data with respect to orbital perturbations including solar radiation and Earth atmosphere drag effects. 1. SPECIALIZED ORBITS Earth Orbital Space (EOS) supports many versions of specialized satellite orbits defined by a combination of satellite mission and orbital dynamics. Surely the most well-known family of specialized orbits is the geostationary orbits proposed by science fiction author Arthur C. Clarke in 1945 [1] that lie sensibly in the plane of Earth’s equator, with orbital period that matches the Earth’s rotation period. Satellites in these orbits, and the closely related geosynchronous orbits, appear from Earth to remain constantly overhead, allowing continuous communication with the majority of the hemisphere below. Constellations of three geostationary satellites equally spaced in orbit (~ 120° separation) can maintain near-global communication and terrestrial surveillance.
    [Show full text]
  • Stellar Dynamics and Stellar Phenomena Near a Massive Black Hole
    Stellar Dynamics and Stellar Phenomena Near A Massive Black Hole Tal Alexander Department of Particle Physics and Astrophysics, Weizmann Institute of Science, 234 Herzl St, Rehovot, Israel 76100; email: [email protected] | Author's original version. To appear in Annual Review of Astronomy and Astrophysics. See final published version in ARA&A website: www.annualreviews.org/doi/10.1146/annurev-astro-091916-055306 Annu. Rev. Astron. Astrophys. 2017. Keywords 55:1{41 massive black holes, stellar kinematics, stellar dynamics, Galactic This article's doi: Center 10.1146/((please add article doi)) Copyright c 2017 by Annual Reviews. Abstract All rights reserved Most galactic nuclei harbor a massive black hole (MBH), whose birth and evolution are closely linked to those of its host galaxy. The unique conditions near the MBH: high velocity and density in the steep po- tential of a massive singular relativistic object, lead to unusual modes of stellar birth, evolution, dynamics and death. A complex network of dynamical mechanisms, operating on multiple timescales, deflect stars arXiv:1701.04762v1 [astro-ph.GA] 17 Jan 2017 to orbits that intercept the MBH. Such close encounters lead to ener- getic interactions with observable signatures and consequences for the evolution of the MBH and its stellar environment. Galactic nuclei are astrophysical laboratories that test and challenge our understanding of MBH formation, strong gravity, stellar dynamics, and stellar physics. I review from a theoretical perspective the wide range of stellar phe- nomena that occur near MBHs, focusing on the role of stellar dynamics near an isolated MBH in a relaxed stellar cusp.
    [Show full text]
  • Up, Up, and Away by James J
    www.astrosociety.org/uitc No. 34 - Spring 1996 © 1996, Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, CA 94112. Up, Up, and Away by James J. Secosky, Bloomfield Central School and George Musser, Astronomical Society of the Pacific Want to take a tour of space? Then just flip around the channels on cable TV. Weather Channel forecasts, CNN newscasts, ESPN sportscasts: They all depend on satellites in Earth orbit. Or call your friends on Mauritius, Madagascar, or Maui: A satellite will relay your voice. Worried about the ozone hole over Antarctica or mass graves in Bosnia? Orbital outposts are keeping watch. The challenge these days is finding something that doesn't involve satellites in one way or other. And satellites are just one perk of the Space Age. Farther afield, robotic space probes have examined all the planets except Pluto, leading to a revolution in the Earth sciences -- from studies of plate tectonics to models of global warming -- now that scientists can compare our world to its planetary siblings. Over 300 people from 26 countries have gone into space, including the 24 astronauts who went on or near the Moon. Who knows how many will go in the next hundred years? In short, space travel has become a part of our lives. But what goes on behind the scenes? It turns out that satellites and spaceships depend on some of the most basic concepts of physics. So space travel isn't just fun to think about; it is a firm grounding in many of the principles that govern our world and our universe.
    [Show full text]
  • Positioning: Drift Orbit and Station Acquisition
    Orbits Supplement GEOSTATIONARY ORBIT PERTURBATIONS INFLUENCE OF ASPHERICITY OF THE EARTH: The gravitational potential of the Earth is no longer µ/r, but varies with longitude. A tangential acceleration is created, depending on the longitudinal location of the satellite, with four points of stable equilibrium: two stable equilibrium points (L 75° E, 105° W) two unstable equilibrium points ( 15° W, 162° E) This tangential acceleration causes a drift of the satellite longitude. Longitudinal drift d'/dt in terms of the longitude about a point of stable equilibrium expresses as: (d/dt)2 - k cos 2 = constant Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF EARTH ASPHERICITY VARIATION IN THE LONGITUDINAL ACCELERATION OF A GEOSTATIONARY SATELLITE: Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN & MOON ATTRACTION Gravitational attraction by the sun and moon causes the satellite orbital inclination to change with time. The evolution of the inclination vector is mainly a combination of variations: period 13.66 days with 0.0035° amplitude period 182.65 days with 0.023° amplitude long term drift The long term drift is given by: -4 dix/dt = H = (-3.6 sin M) 10 ° /day -4 diy/dt = K = (23.4 +.2.7 cos M) 10 °/day where M is the moon ascending node longitude: M = 12.111 -0.052954 T (T: days from 1/1/1950) 2 2 2 2 cos d = H / (H + K ); i/t = (H + K ) Depending on time within the 18 year period of M d varies from 81.1° to 98.9° i/t varies from 0.75°/year to 0.95°/year Orbits Supplement GEO PERTURBATIONS (CONT'D) INFLUENCE OF SUN RADIATION PRESSURE Due to sun radiation pressure, eccentricity arises: EFFECT OF NON-ZERO ECCENTRICITY L = difference between longitude of geostationary satellite and geosynchronous satellite (24 hour period orbit with e0) With non-zero eccentricity the satellite track undergoes a periodic motion about the subsatellite point at perigee.
    [Show full text]
  • Molniya" Type Orbits
    EXAMINATION OF THE LIFETIME, EVOLUTION AND RE-ENTRY FEATURES FOR THE "MOLNIYA" TYPE ORBITS Yu.F. Kolyuka, N.M. Ivanov, T.I. Afanasieva, T.A. Gridchina Mission Control Center, 4, Pionerskaya str., Korolev, Moscow Region, 141070, Russia, [email protected] ABSTRACT Space vehicles of the "Molniya" series, launched into the special highly elliptical orbits with a period of ~ 12 hours, are intended for solution of telecommunication problems in stretched territories of the former USSR and nowadays − Russia, and also for providing the connectivity between Russia and other countries. The inclination of standard orbits of such a kind of satellites is near to the critical value i ≈ 63.4 deg and their initial minimal altitude normally has a value Hmin ~ 500 km. As a rule, the “Molniya" satellites of a concrete series form the groups with determined disposition of orbital planes on an ascending node longitude that allows to ensure requirements of the continuous link between any points in northern hemisphere. The first satellite of the "Molniya" series has been inserted into designed orbit in 1964. Up to now it is launched over 160 space vehicles of such a kind. As well as all artificial satellites, space vehicles "Molniya" undergo the action of various perturbing forces influencing a change of their orbital parameters. However in case of space vehicles "Molniya" these changes of parameters have a specific character and in many things they differ from the perturbations which are taking place for the majority of standard orbits of the artificial satellites with rather small eccentricity. In particular, to strong enough variations (first of all, at the expense of the luni-solar attraction) it is subjected the orbit perigee distance rπ that can lead to such reduction Hmin when further flight of the satellite on its orbit becomes impossible, it re-entries and falls to the Earth.
    [Show full text]
  • Open Rosen Thesis.Pdf
    THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF AEROSPACE ENGINEERING END OF LIFE DISPOSAL OF SATELLITES IN HIGHLY ELLIPTICAL ORBITS MITCHELL ROSEN SPRING 2019 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Aerospace Engineering with honors in Aerospace Engineering Reviewed and approved* by the following: Dr. David Spencer Professor of Aerospace Engineering Thesis Supervisor Dr. Mark Maughmer Professor of Aerospace Engineering Honors Adviser * Signatures are on file in the Schreyer Honors College. i ABSTRACT Highly elliptical orbits allow for coverage of large parts of the Earth through a single satellite, simplifying communications in the globe’s northern reaches. These orbits are able to avoid drastic changes to the argument of periapse by using a critical inclination (63.4°) that cancels out the first level of the geopotential forces. However, this allows the next level of geopotential forces to take over, quickly de-orbiting satellites. Thus, a balance between the rate of change of the argument of periapse and the lifetime of the orbit is necessitated. This thesis sets out to find that balance. It is determined that an orbit with an inclination of 62.5° strikes that balance best. While this orbit is optimal off of the critical inclination, it is still near enough that to allow for potential use of inclination changes as a deorbiting method. Satellites are deorbited when the propellant remaining is enough to perform such a maneuver, and nothing more; therefore, the less change in velocity necessary for to deorbit, the better. Following the determination of an ideal highly elliptical orbit, the different methods of inclination change is tested against the usual method for deorbiting a satellite, an apoapse burn to lower the periapse, to find the most propellant- efficient method.
    [Show full text]
  • Spacex Rocket Data Satisfies Elementary Hohmann Transfer Formula E-Mail: [email protected] and [email protected]
    IOP Physics Education Phys. Educ. 55 P A P ER Phys. Educ. 55 (2020) 025011 (9pp) iopscience.org/ped 2020 SpaceX rocket data satisfies © 2020 IOP Publishing Ltd elementary Hohmann transfer PHEDA7 formula 025011 Michael J Ruiz and James Perkins M J Ruiz and J Perkins Department of Physics and Astronomy, University of North Carolina at Asheville, Asheville, NC 28804, United States of America SpaceX rocket data satisfies elementary Hohmann transfer formula E-mail: [email protected] and [email protected] Printed in the UK Abstract The private company SpaceX regularly launches satellites into geostationary PED orbits. SpaceX posts videos of these flights with telemetry data displaying the time from launch, altitude, and rocket speed in real time. In this paper 10.1088/1361-6552/ab5f4c this telemetry information is used to determine the velocity boost of the rocket as it leaves its circular parking orbit around the Earth to enter a Hohmann transfer orbit, an elliptical orbit on which the spacecraft reaches 1361-6552 a high altitude. A simple derivation is given for the Hohmann transfer velocity boost that introductory students can derive on their own with a little teacher guidance. They can then use the SpaceX telemetry data to verify the Published theoretical results, finding the discrepancy between observation and theory to be 3% or less. The students will love the rocket videos as the launches and 3 transfer burns are very exciting to watch. 2 Introduction Complex 39A at the NASA Kennedy Space Center in Cape Canaveral, Florida. This launch SpaceX is a company that ‘designs, manufactures and launches advanced rockets and spacecraft.
    [Show full text]
  • The Pennsylvania State University Schreyer Honors College
    THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE DEPARTMENT OF AEROSPACE ENGINEERING LONG TERM ORBITAL MODELING FOR OBJECTS IN GEOSTATIONARY EARTH ORBIT PHILIP CHOW SPRING 2015 A thesis submitted in partial fulfillment of the requirements for a baccalaureate degree in Aerospace Engineering with honors in Aerospace Engineering Reviewed and approved* by the following: David B. Spencer Professor of Aerospace Engineering Thesis Supervisor Robert G. Melton Professor of Aerospace Engineering Honors Adviser George A. Lesieutre Professor of Aerospace Engineering Head of Aerospace Engineering * Signatures are on file in the Schreyer Honors College. i ABSTRACT The suitability of different numerical integrators for the long term orbital modeling of a satellite in geostationary Earth orbit is examined. The integrators used are the ODE45 Runge- Kutta Method from MATLAB and the symplectic Euler method, assuming only spherical harmonics of the Earth and n-body perturbations from the Sun, Moon, and other planets. Results show that the energy drift associated with both integrators makes them unsuitable for long term modeling, and that the symplectic Euler method does not actually maintain constant energy. A possible factor in the energy drift of both integrators includes the model used for n-body perturbations; future work should focus on determining the extent that this affected the results and the steps necessary to correct the errors. ii TABLE OF CONTENTS LIST OF FIGURES ....................................................................................................
    [Show full text]