Orbital Motion in Strongly Perturbed Environments

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1 Springer Praxis Books Orbital Motion in Strongly Perturbed Environments Applications to Asteroid, Comet and Planetary Satellite Orbiters Bearbeitet von Daniel J Scheeres 1. Auflage Buch. xviii, 390 S. Hardcover ISBN Format (B x L): 16,8 x 24 cm Gewicht: 854 g Weitere Fachgebiete > Physik, Astronomie > Astronomie: Allgemeines > Astronomische Beobachtung: Observatorien, Instrumente, Methoden schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, ebooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte.

2 Preface... XV I. Modeling 1. Introduction and Background Background ABriefHistoryofAsteroidExploration OpticalObservations RadarObservations Distant Flybys Rendezvous FutureMissions ABriefHistoryofCometExploration Ground-BasedObservations Spacecraft Observations A Brief History of Planetary Satellite Exploration EarlyGround-BasedObservations Flyby Spacecraft Observations Spacecraft Rendezvous Observations ModernGround-BasedObservations Future Spacecraft Missions NotationandDefinitions Vectors,DyadicsandHigher-OrderTensors Functions DifferentialEquationsandSolutions Modeling Small Body Environments HeliocentricandPlanetocentricOrbits Asteroids Comets Planetary Satellites VII

3 VIII 2.2 MassandDensityofSmallBodies SpinStatesofSmallBodies UniformRotators ComplexRotators SynchronousRotators Size,ShapeandMorphology ShapeModelFormats ShapesBasedonHigh-ResolutionImagery ShapesBasedonRadarRange-DopplerImaging ShapesBasedonLightCurveAnalysis SurfaceCharacteristics MassDistributionMorphology GravitationalPotentials Spherical Harmonics Models Closed-FormGravitationalPotentials Other Gravity Field Representations OtherForcesandPerturbations Third-BodyGravitationalPerturbations SolarPhotonPerturbation Comet Outgassing Pressure Models II. Dynamics 3. Non-Perturbed Solutions TheTwo-BodyProblem TheTwo-BodyProblemStatement ClassicalIntegralsofMotion AdditionalIntegralsandtheOrbitTrajectory MotioninTime RotationalDynamicsofSmallBodies TheInertiaDyadic OrientationoftheRigidBody Euler sequations ConservedQuantities ProblemStatementandParameterDefinitions Angular Velocity in the Body-Fixed Frame AnalyticSolutionforType-IIEulerAngles SpecificationoftheRotationalDynamics Equations of Motion for a Small Body Orbiter NewtonianEquationsofMotion Lagrangian Form of the Equations Body-Fixed Frame Orbit-Fixed Frame HamiltonianFormoftheEquations... 93

4 IX 4.4 Lagrange Planetary and Gauss Equations Lagrange Planetary Equations GaussEquations Properties of Solution Reduction to Time Invariant Hamiltonian Dynamical Systems PropertiesofGeneralTrajectories InitialConditionsandHigher-OrderExpansions SolutionsAnalyticinaParameter EigenstructureoftheStateTransitionMatrix ConservationPrinciples NonlinearIntegrals InitialConditionsasLocalIntegralsofMotion LinearIntegrals Equilibrium Points and Stability FormoftheStateTransitionMatrix EigenstructureoftheStateTransitionMatrix General Motion in the Vicinity of an Equilibrium Point ConstraintsDuetoIntegrals Periodic Orbits and Stability DefinitionofaPeriodicOrbit FloquetTheory Stability of Periodic Orbits UnityEigenvaluesforTimeInvariantSystems Periodic Orbit Families General Trajectories and Stability Surfaces of Section and PoincaréMaps SurfaceofSectionMaps PoincaréMaps Linearized Poincaré Map Periodic Orbits and Stability Periodic Orbit Families Isolation of Periodic Orbits at Constant Jacobi Values Continuation of Periodic Orbits with Jacobi Energy Stability Transitions along a Periodic Orbit Family Solution and Characterization Methods NumericalIntegration Lagrangian, Hamiltonian and Orbit Element Computations StateTransitionMatrixComputations CommonIntegrators VerificationofaNumericalIntegrator sperformance Computation of Equilibrium Solutions GeneralAlgorithm ComplicationsfromAdditionalIntegrals Stability Computation

5 X 6.3 ComputationofPeriodicOrbits GeneralAlgorithm Reduction of the State Transition Matrix to a Linear PoincaréMap GeneralAlgorithmRevisited Stability Computation Families of Periodic Orbits Semi-Analytical Solutions: Higher-Order Solution Expansions AnalyticSolutions Moulton smethodofanalyticcontinuation GeneratingFunctionApproaches MeanMotionDerivations First-OrderSolutions Short-PeriodTerms MultipleAveragingTimeScales Averaging the Lagrange Planetary Equations DiscreteOrbitUpdates PhaseSpaceConstraints III. Applications to Asteroids, Comets and Planetary Satellites 7. Uniformly Rotating Bodies: Asteroid 433 Eros Modelof433Eros EquationsofMotion Lagrangian Dynamics Lagrange Planetary Equations AnalyticCharacterization PerturbationsfromAsteroidOblateness Analytical Stability Analysis of Polar Orbits EffectofTransientPerturbations PhaseSpaceCharacterization Stability against Impact Orbit Stability Characterizations Out-of-PlaneOrbits Complex Rotators: Asteroid 4179 Toutatis Model of 4179 Toutatis EquationsofMotion AnalyticalCharacterization C 20 Dynamics Doubly-AveragedSolutions PhaseSpaceCharacterization NumericalIntegrations PeriodicOrbits

6 XI 9. Binary Asteroids: 1999 KW Model of 1999 KW TheFullTwo-BodyProblem TheRestrictedFullThree-BodyProblem EquationsofMotionofaParticle Equilibrium Solutions Stability of the L 4,5 points PeriodicOrbitComputations The Surface Environment on Asteroids SurfaceSpecification SurfaceGeopotential SurfaceForcesandEnvironment StationaryandStableMotion RocheLobeandtheGuaranteedReturnSpeed SurfaceEscapeSpeeds Controlled Hovering Motion at an Asteroid Motivation Near-InertialHovering Body-fixedHovering Solar Radiation Pressure: Exact Analysis Models EquationsofMotion PointMasswithNoRotation PointMasswithRotation AnalysisoftheNo-RotationCase AnalysisoftheRotationCase Equilibrium Points of the System Spacecraft Capture Solar Radiation Pressure: Averaged Analysis SRPPerturbationFormulationandAveraging No-RotationSolution FrozenOrbits SpecialSolutions RotationSolution FrozenOrbits SpecialSolutions Characteristic Values of Λ Discussion

7 XII 14. Small Bodies: Asteroid Itokawa ModelofItokawa Maximum Orbital Stability Limits on Semi-Major Axis NominalStableOrbitDesign MassDistributionPerturbationandAveraging RobustnessoftheFrozenOrbitSolutions Stability of Relative Equilibria Stability of Ecliptic Solutions Stability of Terminator Solutions OblatenessPerturbations Perturbation from Ellipticity Comet Outgassing ContinuouslyOutgassingFields JetOutgassingFields Planetary Satellites: Exact Analysis ModelofEuropa EquationsofMotion NormalizedEquationsofMotion ClassicalAnalysisoftheProblem JacobiIntegralandZero-VelocityCurves Equilibrium Points Local Motion about Equilibria PeriodicOrbitsintheHillProblem AdvancedDynamicsintheHillThree-BodyProblem Transit,CaptureandEscape Higher-OrderExpansion Planetary Satellites: Averaged Analysis MotivationandModel Dynamics of Planetary Satellite Orbiters TidalPerturbationModel AveragingAssumptions The Secular Lagrange Equations AnalyticalIntegrationoftheEquations Stability and Time-to-Impact Extension to Other Planetary Satellite Orbiters Small Planetary Satellites: Deimos ModelofDeimos EquationsofMotion DynamicsaboutDeimos Zero-Velocity Curves and Equilibrium Points GeneralTrajectories PeriodicOrbits

8 XIII IV. Appendices A. Two-Body Orbit Relations B. Fourier Series Expansions of Radius Functions C. Averaging Results D. Canonical Transformations E. Legendre Polynomials and Associated Functions F. Elliptic Functions and Integrals References Index