Orbital Mechanics by John E. Prussing

Orbital Mechanics

byJohn E. Prussing, Bruce A. Conway

Hardcover | December 26, 2012

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One of the major challenges of modern space mission design is the orbital mechanics - determining how to get a spacecraft to its destination using a limited amount of propellant. Recent missions such as Voyager and Galileo required gravity assist maneuvers at several planets to accomplishtheir objectives. Today's students of aerospace engineering face the challenge of calculating these types of complex spacecraft trajectories. This classroom-tested textbook takes its title from an elective course which has been taught to senior undergraduates and first-year graduate students for the past 22 years. The subject of orbital mechanics is developed starting from the first principles, using Newton's laws of motion and the law ofgravitation to prove Kepler's empirical laws of planetary motion. Unlike many texts the authors also use first principles to derive other important results including Kepler's equation, Lambert's time-of-flight equation, the rocket equation, the Hill-Clohessy-Wiltshire equations of relative motion,Gauss' equations for the variation of the elements, and the Gauss and Laplace methods of orbit determination. The subject of orbit transfer receives special attention. Optimal orbit transfers such as the Hohmann transfer, minimum-fuel transfers using more than two impulses, and non-coplanar orbitaltransfer are discussed. Patched-conic interplanetary trajectories including gravity-assist maneuvers are the subject of an entire chapter and are particularly relevant to modern space missions.

About The Author

John E. Prussing is Professor Emeritus of Aerospace Engineering at the University of Illinois at Urbana-Champaign (UIUC), 2007present. Bruce A. Conway is Professor at the University of Illinois Urbana-Champaign.
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Details & Specs

Title:Orbital MechanicsFormat:HardcoverDimensions:304 pages, 9.25 × 6.12 × 0.98 inPublished:December 26, 2012Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199837708

ISBN - 13:9780199837700

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Table of Contents

1. The n-body ProblemIntroductionEquations of Motion for the n-Body ProblemJustification of the Two-body ModelThe Two-Body ProblemThe Elliptic OrbitParabolic, Hyperbolic, and Rectilinear OrbitsEnergy of the Orbit2. Position in Orbit as a Function of TimeIntroductionPosition and Tme in an Elliptic OrbitSolution for the Eccentric AnomalyThe f and g Functions and SeriesPosition versus Time in Hyperbolic and Parabolic Orbits: Universal Variables3. The Orbit in SpaceIntroductionThe Orbital ElementsDetermining the Orbital Elements from r and vVelocity Hodographs4. The Three-Body ProblemIntroductionStationary Solutions of the Three-Body ProblemThe Circular Restricted ProblemSurfaces of Zero VelocityStability of the Equilibrium PointsPeriodic Orbits in the Restricted CaseInvariant ManifoldsSpecial Solutions5. Lambert's ProblemIntroductionTransfer Orbits Between Specified PointsLambert's TheoremProperties of the Solutions to Lambert's EquationThe Terminal Velocity VectorsApplications of Lambert's EquationMultiple-Revolution Lambert Solutions6. Rocket DynamicsIntroductionThe Rocket EquationSolution of the Rocket Equation in Field-Free SpaceSolution of the Rocket Equation with External ForcesRocket Payloads and StagingOptimal Staging7. Impulsive Orbit TransferIntroductionThe Impulsive Thrust ApproximationTwo-Impulse Transfer Reaction between Circular OrbitsThe Hohmann TransferCoplanar Extensions of the Hohmann TransferNoncoplanar Extensions of the Hohmann TransferConditions for Intercept and Rendezvous8. Continuous-Thrust TransferIntroductionEquation of MotionPropellant ConsumptionQuasi-Circular Orbit TransferThe Effects of Non-Constant MassOptimal Quasi-Circular Orbit TransferConstant Radial Thrust AccelerationShifted Circular Orbits9. Interplanetary Mission AnalysisIntroductionSphere of InfluencePatched Conic MethodVelocity Change from Circular to Hyperbolic OrbitPlanetary Flyby (Gravity-Assist) TrajectoriesGravity-Assist Applications10. Linear Orbit TheoryIntroductionLinearizationLinearization of the Equations of MotionThe Hill-Clohessy-Wiltshire (CW) EquationsThe Solution of the CW EquationsLinear Impulsive RendezvousState Transition Matrix for a General Conic Orbit11. PerturbationIntroductionThe Perturbation EquationsEffect of Atmospheric DragEffect of Earth OblatenessEffects of Solar-Lunar Attraction12. Canonical Systems and the Lagrange EquationsIntroductionHamilton's EquationCanonical TransformationsNecessary and Sufficient Conditions for a Canonical TransformationGenerating FunctionsJacobi's TheoremCanonical Equations for a Two-Body ProblemThe Delaunay VariablesAverage Effects of Earth Oblateness Using Delaunay VariablesLagrange Equations13. Perturbations Due to Nonspherical Terms in the Earth's PotentialIntroductionEffects of the Zonal Harmonic TermsShort-Period VariationsLong-Period VariationsVariations at O(J22)The Potential in Terms of Conventional ElementsVariation Due to the Tesseral HarmonicsResonance of a Near Geostationary Orbit14. Orbit DeterminationIntroductionAngles-Only Orbit DeterminationLaplacian Initial Orbit DeterminationGaussian Initial Orbit DeterminationOrbit Determination from Two Position VectorsDifferential CorrectionAppendix 1: Astronomical ConstantsAppendix 2: Physical Characteristics of the PlanetsAppendix 3: Elements of the Planetary Orbits