DOCSLIB.ORG

Mae180a:Spacecraftguidancei

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Mae180a:Spacecraftguidancei MAE180A:SPACECRAFTGUIDANCEI Course Description: This is a course in Spacecraft Dynamics.The principles of Astrodynamics are studied,includingthetwobodyorbitalmotioninconicorbits,aswellasorbitdeterminationtechniques from radar observations. Basic spacecraft dynamics are addressed by studying orbital maneuvers, insertionintospecialspacecraftorbits,andinterplanetarymissionsintheSolarSystem. Prerequisite:Upperdivisionstandinginphysics,mathematics,orengineeringdepartment. Instructor:JavierUrzay, Email:[email protected] Office:564EBUII,Phone:8585346123. OfficeHours:Thursdays2:003:00PM,andMondays3:004:00PM,at564EBUII. Reader:WilliamHayes, Email:[email protected] Lectures:TuesdaysandThursdays,11:001:50PM,WLH2112.Totalnumberoflectures:10. Textbook(Required):“FundamentalsofAstrodynamics,”Bate,R.R.,Mueller,D.D.&White,J.E.;Dover Publications,1971.Supplementarymaterialwillbeprovidedinclass. Homeworks: There will be 4 homework assignments. Homework will be assigned each week and collected on Tuesdays on the 7th, 14th, 21st and 28th of July, at the beginning of the lecture. No late homeworkswillbeaccepted.Homeworksolutionsmustbeclean,clearandneatlywritten. Exams:MidtermExam:Thursday16th,11:0012:30PM,WLH2112. FinalExam:August1st,8:0011:00AM,locationTBA. Both exams will consist of two parts: i) Short Questions (closed books, closed notes, no calculator), and ii) Problems (open book and open notes, calculator required). No Blue Books required. GradingScheme:20%Homeworks+35%MidtermExam+45%FinalExam. AcademicIntegrity:UCSDPolicyonIntegrityofScholarshipwillbefollowed. Accomodations for students with disabilities: Requests for appropriate accommodations must be presentedtotheinstructor,andstudentsmustregisterwiththeOfficeforStudentswithDisabilitiesto verifytheireligibilityforappropriateaccommodations. TENTATIVEOUTLINE I.MECHANICSOFPARTICLEMOTION. 1.Newton’slaws: Newton’s laws of motion. Newton’s law of universal gravitation. Universal gravitational constant. Gravitationalacceleration.Standardgravitationalparameter.Weight. 2.Scalarandvectorquantities: Scalars.Vectors.Unitvector.Vectoraddition.Pseudovectors.Resolutionofavector.Scalarproduct.Cross product.Momentofavector.Timederivativeofavector. 3.Kinematics: Velocityandacceleration.Curvilinearplanarmotioninpolarcoordinates.Radialandangularcomponents. Tangentialandnormalcomponents.Intrinsiccoordinates.Generalcaseofspacekinematics:absoluteand relativemotion.MotionrelativetotherotatingEarth. 4.Examples. II.PLANETSANDSATELLITESORBITS. 1.TheNbodyproblem: Total gravitational force. General equation of motion. Earthsatelliteplanets system, Earthsatellite relativeaccelerationandperturbationeffectsfromplanets. 2.Thetwobodyproblem: The equation of relative motion. Constants of the motion: angular momentum, areolar velocity and mechanicalenergy.Trajectoryequation.Orbiteccentricity.Semilatusrectum.OrbitalHamiltonian.Orbit classification: elliptic, circular, parabolic and hyperbolic orbits. Orbital period. Circular speed. Escape speed.Hyperbolicexcessspeed.Turningangle.Canonicalunits.Referenceorbit. 3.Examples. III.ORBITDETERMINATIONFROMOBSERVATIONS. 1.Coordinatesystems: The heliocentricecliptic coordinate system. Ecliptic and equatorial planes. Vernal equinox direction. Precessionoftheequinoxes.Nutation.Thegeocentricequatorialcoordinatesystem.Therightascension declination system. Celestial sphere.The perifocal coordinate system. The topocentrichorizon coordinatesystem.Zenithandnadirdirections. 2.Classicalorbitalelements: Semimajoraxis.Eccentricity.Inclination.Longitudeoftheascendingnode.Argumentoftheperiapsis. Longitudeoftheperiapsis.Trueanomalyatepoch.Argumentoflatitudeatepoch.Truelongitudeat epoch.Eulerangles.Directandretrogradeorbitmotion. 3.Orbitdeterminationfromvelocityandpositionvectors: Fundamentalvectors:angularmomentumvector,nodevectorandeccentricityvector.Inverseproblem. 4.Transformationofcoordinates: Rotational transformation matrix. Transformation from geocentricequatorial to topocentrichorizon coordinates.Transformationfromperifocaltogeocentricequatorialcoordinates. 5.Orbitdeterminationfromasingleradarobservation: Position and velocity relative to the radar site.Position and velocity from the geocentricequatorial coordinatesystem. 6.Orbitdeterminationfromthreepositionobservations: TheGibbsianmethod.Determinationofthesatellitevelocity. 7.InfluencesofEarth’soblateness: Thereferenceellipsoid.Equatorialandpolarradius.EccentricityoftheEarth.Astronomical,geodeticand geocentric latitudes. Station coordinates. Position of the Topocentrichorizon system on an ellipsoidal Earth. 8.Themeasurementoftime: Apparentsolartime.Meansolartime.Siderealtime.TimezonesandtheUniversaltime.TheGreenwich meridianlongitude. 9.Groundtrackofasatellite: Ground trace on a rotating and nonrotating Earth. Maximum latitude above equator. Spacecraft elevationangle.Spacecrafthorizon.Subsatellitepoint.Swathwidth.Launchazimuth.(Lecture5) 10.Examples. IV.ORBITALMANEUVERS. 1.Inplaneorbitmaneuvers: Orbitalvelocity.Simplecoplanarorbitchange.Generalcoplanarmaneuver.TheHohmanntransfer.Time ofFlight.Generalcoplanartransfer.Timeofflightasafunctionoftheeccentricanomaly.(Lecture6) 2.Outofplaneorbitmaneuvers: Simpleplanechanges. 3.Timeofflightasafunctionoftheeccentricanomaly: Timeofflightontheellipticalorbit.Kepler’sequation.Meanmotion.Meananomaly.Timeofflighton parabolicandhyperbolicorbits. 4.Propulsionformaneuvers: Thrust.Massofpropellant.Specificimpulse. 5.Examples. V.SPECIALORBITS. 1.LowaltitudeEarthorbits: LEOorbits.VanAllenbeltradiationanddrageffects.Regressionofthelineofnodes.Rotationoftheline ofapsides. 2.HighaltitudeEarthorbits: The Geosynchronous orbit (GEO). The Geosynchronous transfer orbit (GTO). The GEO mission. Supersynchronousorbits.TheGraveyardorbit.SunSynchronousorbits.TheMolniyaorbit. VI.INTERPLANETARYMISSIONS. 1.TheSolarsystem: GeometryoftheSolarsystem.Theeclipticplane.Theastronomicalunit.TheAstronomicalAlmanac. 2.Patchedconicapproximation: Sphere of influence. Heliocentric transfer orbits. Mission stages. Transfer stage. Orbital velocity at departure. Time of flight transfer. Departure stage. Phase angle at departure. Launch opportunity. Synodic period. Escape from the Earth’s sphere of influence. Hyperbolic excess velocity. Velocity and pointofinjection.Departurebodyofrevolution.Launchwindow.Arrivalatthetargetplanet.Offsetmiss distance.Effectivecollisionsection.Establishmentofplanetaryorbitatarrival. 3.Gravityassistedmaneuvers: Spacecraft velocity decrease and increase maneuvers. Maximum turning angle. Maximum spacecraft velocityincrease. 4.Examples. MAE180A:SPACECRAFTGUIDANCE SUMMERSESSIONI MECHANICALANDAEROSPACEENGINEERING UNIVERSITYOFCALIFORNIASANDIEGO SPECIALLECTURE ThursdayJuly30th,11:00AM12:00PM,479EBUII “MAKINGTHESPACESHUTTLEAFLYINGMACHINE”, BY Dr.LEER.SCHERER. Dr.SchererwasinvolvedintheSpaceProgramfromitsbeginningintheearly1960's.Heserveda total of 22 years in NASA. Assignments included Director of Unmanned Lunar Programs (NASA Headquarters),DirectoroftheApolloLunarExplorationOffice(NASAHeadquarters),CenterDirector of Dryden Flight Research Center, and Center Director of Kennedy Space Center. In industry he worked for General Dynamics as Marketing Director for Atlas Launch Services to satellite users. Since retirement he has acted as a consultant on Space matters to industry and to the federal government.Dr.SchererholdsaB.Sc.degree(MarineEngineering)fromtheU.S.NavalAcademy andaB.Sc.degree(AeronauticalEngineering)fromtheNavyPostGraduateSchool.Healsohasa ProfessionalDegree(AeronauticalEngineering)fromtheCaliforniaInstituteofTechnology(Caltech), andanHonoraryDoctorateinEngineeringfromtheUniversityofCentralFlorida. HislecturewillbrieflyreviewthehistoryofmannedspaceflightandfocusontheSpaceShuttle. TheMAEcommunityiscordiallyinvited. .
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]
  • Orbit Determination Methods and Techniques
    PROJECTE FINAL DE CARRERA (PFC) GEOSAR Mission: Orbit Determination Methods and Techniques Marc Fernàndez Uson PFC Advisor: Prof. Antoni Broquetas Ibars May 2016 PROJECTE FINAL DE CARRERA (PFC) GEOSAR Mission: Orbit Determination Methods and Techniques Marc Fernàndez Uson ABSTRACT ABSTRACT Multiple applications such as land stability control, natural risks prevention or accurate numerical weather prediction models from water vapour atmospheric mapping would substantially benefit from permanent radar monitoring given their fast evolution is not observable with present Low Earth Orbit based systems. In order to overcome this drawback, GEOstationary Synthetic Aperture Radar missions (GEOSAR) are presently being studied. GEOSAR missions are based on operating a radar payload hosted by a communication satellite in a geostationary orbit. Due to orbital perturbations, the satellite does not follow a perfectly circular orbit, but has a slight eccentricity and inclination that can be used to form the synthetic aperture required to obtain images. Several sources affect the along-track phase history in GEOSAR missions causing unwanted fluctuations which may result in image defocusing. The main expected contributors to azimuth phase noise are orbit determination errors, radar carrier frequency drifts, the Atmospheric Phase Screen (APS), and satellite attitude instabilities and structural vibration. In order to obtain an accurate image of the scene after SAR processing, the range history of every point of the scene must be known. This fact requires a high precision orbit modeling and the use of suitable techniques for atmospheric phase screen compensation, which are well beyond the usual orbit determination requirement of satellites in GEO orbits. The other influencing factors like oscillator drift and attitude instability, vibration, etc., must be controlled or compensated.
    [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]
  • Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling
    Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling by Zachary James Folcik B.S. Computer Science Michigan Technological University, 2000 SUBMITTED TO THE DEPARTMENT OF AERONAUTICS AND ASTRONAUTICS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN AERONAUTICS AND ASTRONAUTICS AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 2008 © 2008 Massachusetts Institute of Technology. All rights reserved. Signature of Author:_______________________________________________________ Department of Aeronautics and Astronautics May 23, 2008 Certified by:_____________________________________________________________ Dr. Paul J. Cefola Lecturer, Department of Aeronautics and Astronautics Thesis Supervisor Certified by:_____________________________________________________________ Professor Jonathan P. How Professor, Department of Aeronautics and Astronautics Thesis Advisor Accepted by:_____________________________________________________________ Professor David L. Darmofal Associate Department Head Chair, Committee on Graduate Students 1 [This page intentionally left blank.] 2 Orbit Determination Using Modern Filters/Smoothers and Continuous Thrust Modeling by Zachary James Folcik Submitted to the Department of Aeronautics and Astronautics on May 23, 2008 in Partial Fulfillment of the Requirements for the Degree of Master of Science in Aeronautics and Astronautics ABSTRACT The development of electric propulsion technology for spacecraft has led to reduced costs and longer lifespans for certain
    [Show full text]
  • Statistical Orbit Determination
    Preface The modem field of orbit determination (OD) originated with Kepler's inter­ pretations of the observations made by Tycho Brahe of the planetary motions. Based on the work of Kepler, Newton was able to establish the mathematical foundation of celestial mechanics. During the ensuing centuries, the efforts to im­ prove the understanding of the motion of celestial bodies and artificial satellites in the modem era have been a major stimulus in areas of mathematics, astronomy, computational methodology and physics. Based on Newton's foundations, early efforts to determine the orbit were focused on a deterministic approach in which a few observations, distributed across the sky during a single arc, were used to find the position and velocity vector of a celestial body at some epoch. This uniquely categorized the orbit. Such problems are deterministic in the sense that they use the same number of independent observations as there are unknowns. With the advent of daily observing programs and the realization that the or­ bits evolve continuously, the foundation of modem precision orbit determination evolved from the attempts to use a large number of observations to determine the orbit. Such problems are over-determined in that they utilize far more observa­ tions than the number required by the deterministic approach. The development of the digital computer in the decade of the 1960s allowed numerical approaches to supplement the essentially analytical basis for describing the satellite motion and allowed a far more rigorous representation of the force models that affect the motion. This book is based on four decades of classroom instmction and graduate- level research.
    [Show full text]
  • New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion
    New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion Michelle Chernick∗ and Simone D'Amicoy Aeronautics and Astronautics, Stanford University, Stanford, California, 94305, USA This paper addresses the fuel-optimal guidance and control of the relative motion for formation-flying and rendezvous using impulsive maneuvers. To meet the requirements of future multi-satellite missions, closed-form solutions of the inverse relative dynamics are sought in arbitrary orbits. Time constraints dictated by mission operations and relevant perturbations acting on the formation are taken into account by splitting the optimal recon- figuration in a guidance (long-term) and control (short-term) layer. Both problems are cast in relative orbit element space which allows the simple inclusion of secular and long-periodic perturbations through a state transition matrix and the translation of the fuel-optimal optimization into a minimum-length path-planning problem. Due to the proper choice of state variables, both guidance and control problems can be solved (semi-)analytically leading to optimal, predictable maneuvering schemes for simple on-board implementation. Besides generalizing previous work, this paper finds four new in-plane and out-of-plane (semi-)analytical solutions to the optimal control problem in the cases of unperturbed ec- centric and perturbed near-circular orbits. A general delta-v lower bound is formulated which provides insight into the optimality of the control solutions, and a strong analogy between elliptic Hohmann transfers and formation-flying control is established. Finally, the functionality, performance, and benefits of the new impulsive maneuvering schemes are rigorously assessed through numerical integration of the equations of motion and a systematic comparison with primer vector optimal control.
    [Show full text]
  • Multiple Solutions for Asteroid Orbits: Computational Procedure and Applications
    A&A 431, 729–746 (2005) Astronomy DOI: 10.1051/0004-6361:20041737 & c ESO 2005 Astrophysics Multiple solutions for asteroid orbits: Computational procedure and applications A. Milani1,M.E.Sansaturio2,G.Tommei1, O. Arratia2, and S. R. Chesley3 1 Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy e-mail: [milani;tommei]@mail.dm.unipi.it 2 E.T.S. de Ingenieros Industriales, University of Valladolid Paseo del Cauce 47011 Valladolid, Spain e-mail: [meusan;oscarr]@eis.uva.es 3 Jet Propulsion Laboratory, 4800 Oak Grove Drive, CA-91109 Pasadena, USA e-mail: [email protected] Received 27 July 2004 / Accepted 20 October 2004 Abstract. We describe the Multiple Solutions Method, a one-dimensional sampling of the six-dimensional orbital confidence region that is widely applicable in the field of asteroid orbit determination. In many situations there is one predominant direction of uncertainty in an orbit determination or orbital prediction, i.e., a “weak” direction. The idea is to record Multiple Solutions by following this, typically curved, weak direction, or Line Of Variations (LOV). In this paper we describe the method and give new insights into the mathematics behind this tool. We pay particular attention to the problem of how to ensure that the coordinate systems are properly scaled so that the weak direction really reflects the intrinsic direction of greatest uncertainty. We also describe how the multiple solutions can be used even in the absence of a nominal orbit solution, which substantially broadens the realm of applications. There are numerous applications for multiple solutions; we discuss a few problems in asteroid orbit determination and prediction where we have had good success with the method.
    [Show full text]
  • Mercury's Resonant Rotation from Secular Orbital Elements
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institute of Transport Research:Publications Mercury’s resonant rotation from secular orbital elements Alexander Stark a, Jürgen Oberst a,b, Hauke Hussmann a a German Aerospace Center, Institute of Planetary Research, D-12489 Berlin, Germany b Moscow State University for Geodesy and Cartography, RU-105064 Moscow, Russia The final publication is available at Springer via http://dx.doi.org/10.1007/s10569-015-9633-4. Abstract We used recently produced Solar System ephemerides, which incorpo- rate two years of ranging observations to the MESSENGER spacecraft, to extract the secular orbital elements for Mercury and associated uncer- tainties. As Mercury is in a stable 3:2 spin-orbit resonance these values constitute an important reference for the planet’s measured rotational pa- rameters, which in turn strongly bear on physical interpretation of Mer- cury’s interior structure. In particular, we derive a mean orbital period of (87.96934962 ± 0.00000037) days and (assuming a perfect resonance) a spin rate of (6.138506839 ± 0.000000028) ◦/day. The difference between this ro- tation rate and the currently adopted rotation rate (Archinal et al., 2011) corresponds to a longitudinal displacement of approx. 67 m per year at the equator. Moreover, we present a basic approach for the calculation of the orientation of the instantaneous Laplace and Cassini planes of Mercury. The analysis allows us to assess the uncertainties in physical parameters of the planet, when derived from observations of Mercury’s rotation. 1 1 Introduction Mercury’s orbit is not inertially stable but exposed to various perturbations which over long time scales lead to a chaotic motion (Laskar, 1989).
    [Show full text]
  • SATELLITES ORBIT ELEMENTS : EPHEMERIS, Keplerian ELEMENTS, STATE VECTORS
    www.myreaders.info www.myreaders.info Return to Website SATELLITES ORBIT ELEMENTS : EPHEMERIS, Keplerian ELEMENTS, STATE VECTORS RC Chakraborty (Retd), Former Director, DRDO, Delhi & Visiting Professor, JUET, Guna, www.myreaders.info, [email protected], www.myreaders.info/html/orbital_mechanics.html, Revised Dec. 16, 2015 (This is Sec. 5, pp 164 - 192, of Orbital Mechanics - Model & Simulation Software (OM-MSS), Sec 1 to 10, pp 1 - 402.) OM-MSS Page 164 OM-MSS Section - 5 -------------------------------------------------------------------------------------------------------43 www.myreaders.info SATELLITES ORBIT ELEMENTS : EPHEMERIS, Keplerian ELEMENTS, STATE VECTORS Satellite Ephemeris is Expressed either by 'Keplerian elements' or by 'State Vectors', that uniquely identify a specific orbit. A satellite is an object that moves around a larger object. Thousands of Satellites launched into orbit around Earth. First, look into the Preliminaries about 'Satellite Orbit', before moving to Satellite Ephemeris data and conversion utilities of the OM-MSS software. (a) Satellite : An artificial object, intentionally placed into orbit. Thousands of Satellites have been launched into orbit around Earth. A few Satellites called Space Probes have been placed into orbit around Moon, Mercury, Venus, Mars, Jupiter, Saturn, etc. The Motion of a Satellite is a direct consequence of the Gravity of a body (earth), around which the satellite travels without any propulsion. The Moon is the Earth's only natural Satellite, moves around Earth in the same kind of orbit. (b) Earth Gravity and Satellite Motion : As satellite move around Earth, it is pulled in by the gravitational force (centripetal) of the Earth. Contrary to this pull, the rotating motion of satellite around Earth has an associated force (centrifugal) which pushes it away from the Earth.
    [Show full text]
  • Astrodynamic Fundamentals for Deflecting Hazardous Near-Earth Objects
    IAC-09-C1.3.1 Astrodynamic Fundamentals for Deflecting Hazardous Near-Earth Objects∗ Bong Wie† Asteroid Deflection Research Center Iowa State University, Ames, IA 50011, United States [email protected] Abstract mate change caused by this asteroid impact may have caused the dinosaur extinction. On June 30, 1908, an The John V. Breakwell Memorial Lecture for the As- asteroid or comet estimated at 30 to 50 m in diameter trodynamics Symposium of the 60th International As- exploded in the skies above Tunguska, Siberia. Known tronautical Congress (IAC) presents a tutorial overview as the Tunguska Event, the explosion flattened trees and of the astrodynamical problem of deflecting a near-Earth killed other vegetation over a 500,000-acre area with an object (NEO) that is on a collision course toward Earth. energy level equivalent to about 500 Hiroshima nuclear This lecture focuses on the astrodynamic fundamentals bombs. of such a technically challenging, complex engineering In the early 1990s, scientists around the world initi- problem. Although various deflection technologies have ated studies to prevent NEOs from striking Earth [1]. been proposed during the past two decades, there is no However, it is now 2009, and there is no consensus on consensus on how to reliably deflect them in a timely how to reliably deflect them in a timely manner even manner. Consequently, now is the time to develop prac- though various mitigation approaches have been inves- tically viable technologies that can be used to mitigate tigated during the past two decades [1-8]. Consequently, threats from NEOs while also advancing space explo- now is the time for initiating a concerted R&D effort for ration.
    [Show full text]
  • 2. Orbital Mechanics MAE 342 2016
    2/12/20 Orbital Mechanics Space System Design, MAE 342, Princeton University Robert Stengel Conic section orbits Equations of motion Momentum and energy Kepler’s Equation Position and velocity in orbit Copyright 2016 by Robert Stengel. All rights reserved. For educational use only. http://www.princeton.edu/~stengel/MAE342.html 1 1 Orbits 101 Satellites Escape and Capture (Comets, Meteorites) 2 2 1 2/12/20 Two-Body Orbits are Conic Sections 3 3 Classical Orbital Elements Dimension and Time a : Semi-major axis e : Eccentricity t p : Time of perigee passage Orientation Ω :Longitude of the Ascending/Descending Node i : Inclination of the Orbital Plane ω: Argument of Perigee 4 4 2 2/12/20 Orientation of an Elliptical Orbit First Point of Aries 5 5 Orbits 102 (2-Body Problem) • e.g., – Sun and Earth or – Earth and Moon or – Earth and Satellite • Circular orbit: radius and velocity are constant • Low Earth orbit: 17,000 mph = 24,000 ft/s = 7.3 km/s • Super-circular velocities – Earth to Moon: 24,550 mph = 36,000 ft/s = 11.1 km/s – Escape: 25,000 mph = 36,600 ft/s = 11.3 km/s • Near escape velocity, small changes have huge influence on apogee 6 6 3 2/12/20 Newton’s 2nd Law § Particle of fixed mass (also called a point mass) acted upon by a force changes velocity with § acceleration proportional to and in direction of force § Inertial reference frame § Ratio of force to acceleration is the mass of the particle: F = m a d dv(t) ⎣⎡mv(t)⎦⎤ = m = ma(t) = F ⎡ ⎤ dt dt vx (t) ⎡ f ⎤ ⎢ ⎥ x ⎡ ⎤ d ⎢ ⎥ fx f ⎢ ⎥ m ⎢ vy (t) ⎥ = ⎢ y ⎥ F = fy = force vector dt
    [Show full text]
  • Space Object Self-Tracker On-Board Orbit Determination Analysis Stacie M
    Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-24-2016 Space Object Self-Tracker On-Board Orbit Determination Analysis Stacie M. Flamos Follow this and additional works at: https://scholar.afit.edu/etd Part of the Space Vehicles Commons Recommended Citation Flamos, Stacie M., "Space Object Self-Tracker On-Board Orbit Determination Analysis" (2016). Theses and Dissertations. 430. https://scholar.afit.edu/etd/430 This Thesis is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. SPACE OBJECT SELF-TRACKER ON-BOARD ORBIT DETERMINATION ANALYSIS THESIS Stacie M. Flamos, Civilian, USAF AFIT-ENY-MS-16-M-209 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED The views expressed in this document are those of the author and do not reflect the official policy or position of the United States Air Force, the United States Department of Defense or the United States Government. This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENY-MS-16-M-209 SPACE OBJECT SELF-TRACKER ON-BOARD ORBIT DETERMINATION ANALYSIS THESIS Presented to the Faculty Department of Aeronatics and Astronautics Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command in Partial Fulfillment of the Requirements for the Degree of Master of Science Stacie M.
    [Show full text]