Introductory Orbit Dynamics

1. 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.- Suggested Reading.- Problems.- 3. Orbit Insertion.- 3.1 Insertion into Periapsis (or Apoapsis).- 3.2 Insertion into an Arbitrary Point of the Orbit.- Problems.- 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.- Suggested Reading.- Problems.- 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.- Suggested Reading.- Problems.- 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 Rateof Change of Inclination.- Problems.- 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.- Problems.- 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.- Suggested Reading.- Problems.- 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.- Suggested Reading.- Problems.- 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.- Suggested Reading.- Problems.- 13. Tidal Forces.- Suggested Reading.- Problems.- Appendix A: Space Data.- Appendix B: Engineering Data.- Appendix C: Nomenclature.- Appendix D: Answers to Selected Problems.- Author Index.