Introductory Orbit Dynamics

ISBN-13: 9783322903396 / Niemiecki / Miękka / 2012 / 193 str.

Fred P. Rimrott; Fred P. Rimrott

Opis

The study of the dynamics of satellites has a unique fascination for student and lecturer alike. It is not only a logical subject explainable by the few basic principles of mechanics, but has contributed so extensibly to the formulation of mechanics in the first place, and is still continuing to do so. With the launching of Sputnik I on October 4, 1957, engineers have entered the field for good, and the study of the dynamics of spacecraft is taking its rightful place as a subject within engineering mechanics. The primary purpose of the present text is to acquaint engineering students with the fundamentals of spacecraft orbit dynamics. The text is intended for senior undergraduate or for graduate students, as well as for engineers in the various branches of the aerospace industry. Students using the text are expected to know the rudiments of astronomy and to have an adequate com mand of elementary dynamics, of differential and integral calculus, and of vector and matrix algebra. Vec tors and tensors appear in matrix form, since the matrix formulation is not only well suited for computer programming, but also because it affords a quick and intelligible assessment of the problem situation, so essential for engineering practice.

Spis treści

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 Rate of 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.