Introductory orbit dynamics

Inhaltsverzeichnis1. The Simplified Two-Body Problem.1.1 Position, Velocity and Acceleration.1.2 The Attraction Force.1.3 Shape of Path.1.4 The Eccentricity Vector.Suggested Reading.Problems.2. Kepler Orbits.2.1 Angular Momentum.2.2 Period.2.3 Vis-Viva Integral.2.4 Velocities.2.5 Potential Energy.2.6 Total Energy.2.7 Kepler Laws.2.8 Time of Flight.2.9 The Anomalies.2.10 A Universal Variable.2.11 Kepler Equations.2.12 Lambert Equations.2.13 Orbital Elements.2.14 Tethered Satellites.3. Orbit Insertion.3.1 Insertion into Periapsis (or Apoapsis).3.2 Insertion into an Arbitrary Point of the Orbit.4. Transfer.4.1 Single Impulse.4.2 Coplanar Transfer.4.3 Change of Orbital Plane.4.4 Transfer to a Prescribed Target Orbit.4.5 Hohmann Transfer.4.6 Hohmann Transfer Onto Larger Circular Orbit.4.7 Energy Increase Due to Velocity Kick.4.8 Fuel Requirements.4.9 Energy Increase for Hohmann Transfer.4.10 Mass Losses Considered.4.11 Transfer Time for Hohmann Transfer.4.12 Several Impulses, Continuous Impulse.4.13 Launch Windows.5. The Gravitational Potential.5.1 Approximate Potential Surrounding a Body of Arbitrary Shape.5.2 Potential Surrounding a Body of Arbitrary Shape.5.3 Potential Surrounding a Body of Revolution.5.4 Perturbation Force in Gravitational Potential.5.5 Flattening.5.6 Inertia Moments.5.7 The Earth.6. Variation of Geometric Orbital Elements.6.1 Perturbation Force and Velocity Change.6.2 Rate of Change of Magnitude of Semi-Major Axis.6.3 Rate of Change of Eccentricity.6.4 Rate of Change of Right Ascension of Ascending Node.6.5 Rate of Change of Orientation of Line of Apsides.6.6 Rate of Change of Inclination.7. Secular Variations of the Orbital Elements.7.1 Precession of the Orbital Plane.7.2 Rotation of the Line of Apsides.7.3 Major Axis, Eccentricity, Inclination.8. Orbital Periods.8.1 Absolute Period.8.2 Nodal Period.8.3 Apsidal Period.Problems Ill.9. Other Perturbations.9.1 Air Resistance.9.2 Circular Orbit.9.3 Upper Limit of the Atmosphere.9.4 Elliptic Orbit.9.5 The Solar Wind.9.6 Satellite Temperature.10. Satellites from Infinity.10.1 Hyperbolic Orbits.10.2 The Collision Radius.10.3 Primary Master and Secondary Master.10.4 Energy Gain.10.5 Influence Sphere.10.6 The Spacecraft as Satellite of the Secondary Master.10.7 Perturbation Acceleration.10.8 The Spacecraft as a Satellite of the Primary Master.10.9 The Tisserand Equation.11. The General Two-Body Problem.11.1 Orbits.11.2 The Earth-Moon System.11.3 The Sun — (Earth + Moon) System.Problem.12. Satellites in the Earth-Moon System.12.1 The Moon.12.2 A Point Satellite in the Earth-Moon System.12.3 Satellites Within the Lunar Orbital Plane.12.4 An Energy Consideration.12.5 Hill’s Curves.12.6 Libration Points.13. Tidal Forces.Appendix A: Space Data.Appendix B: Engineering Data.Appendix C: Nomenclature.Appendix D: Answers to Selected Problems.Author Index.