Spacecraft Navigation and Guidance

1. Orbital Mechanics.- 1.1 Introduction.- 1.2 The Two-Body Problem.- 1.3 Orbital Elements and Reference Axes.- 1.3.1 Position and Velocity from the Orbital Elements.- 1.3.2 Orbital Elements from the Position and Velocity.- 1.3.3 Numerical Examples.- 1.4 Time in Orbit.- 1.4.1 Solution for Ellipse.- 1.4.2 Solution for Hyperbola.- 1.4.3 Computations starting from Time in Orbit.- 1.5 Lambert’s Time of Flight Theorem.- 1.6 Orbital Manoeuvres.- 1.6.1 Coplanar Transfer Manoeuvres.- 1.6.2 Injection into an Interplanetary Orbit.- 1.6.3 Plane Change to inject into a Geostationary Orbit.- 1.7 Patched Conies.- 1.7.1 Spheres of Influence.- 1.7.2 Time in Julian Days.- 1.7.3 A Solar Polar Mission.- 1.8 Numerical Integration of Orbits.- 1.8.1 Cowell’s Method.- 1.8.2 Encke’s Method.- 1.9 Software.- 2. The Launch Phase.- 2.1 Introduction.- 2.2 Propulsion.- 2.2.1 Basics.- 2.2.2 Staging.- 2.3 Launch Systems.- 2.4 Trajectory Dynamics.- 2.4.1 Equations of Motion.- 2.4.2 Gravitational Forces.- 2.4.3 Rocket Thrust.- 2.4.4 Aerodynamic Forces.- 2.4.5 Final Orbital Elements.- 2.5 Computation of the Nominal Ascent Trajectory.- 2.6 A Computed Example: Ariane 4.- 2.7 Optimization of the Ascent.- 2.7.1 Solution for the Flat Earth.- 2.7.2 Improvement of the Nominal Trajectory.- 2.8 In-flight Guidance.- 2.9 The Guidance and Navigation System.- 2.10 Software.- 3. Earth Satellites: Perturbations and Manoeuvres.- 3.1 Introduction.- 3.2 Variation of the Orbital Elements.- 3.2.1 Rates of Change of the Elements.- 3.2.2 Use of Radial and Transverse Components.- 3.2.3 Use of Tangential and Normal Components.- 3.2.4 Summary of Equations in Radial-Transverse Axes.- 3.2.5 Summary of Equations in Tangential-Normal Axes.- 3.2.6 Equations Applicable at Zero Eccentricity.- 3.2.7 The Singularity at Zero Inclination.- 3.3 Gravitational Field of the Earth.- 3.3.1 Expansion of Spherical Harmonics.- 3.3.2 Evaluation for an Oblate Earth.- 3.3.3 Analytical Results for an Oblate Earth.- 3.4 Perturbations from the Sun and the Moon.- 3.5 Effect of Atmospheric Drag.- 3.6 Illustrative Computations of Perturbations.- 3.7 Correcting Low Earth Orbits.- 3.8 Geostationary Orbits.- 3.8.1 Introduction.- 3.8.2 North-South Perturbations due to the Moon and Sun.- 3.8.3 East-West Perturbations due to Triaxial Effects.- 3.8.4 East-West Perturbations due to Solar Pressure.- 3.9 Rendezvous Guidance.- 3.9.1 Introduction.- 3.9.2 Guidance Strategy.- 3.9.3 Examples by Simulation.- 3.9.4 Other references to Rendezvous and Docking.- 3.10 Software.- 4. Orbit Determination.- 4.1 Introduction.- 4.2 First Estimates of Orbits.- 4.2.1 Transformation to Observables.- 4.2.2 Planetary Orbits.- 4.2.3 Computer Examples of Planetary Orbits.- 4.2.4 Spacecraft Orbits.- 4.2.5 Computer Example of Earth Satellite.- 4.3 Refinement of Orbits.- 4.3.1 Batch Least-Squares Fitting.- 4.3.2 Generation of Partial Derivatives.- 4.3.3 The Square Root Information Filter.- 4.3.4 Bias Terms and the Consider Matrix.- 4.4 Sequential Estimation.- 4.4.1 Non-constant Parameters.- 4.4.2 Time Update with Sequential SRIF.- 4.4.3 Measurement Update with sequential SRIF.- 4.4.4 Sequential Estimation with Covariance Filters.- 4.4.5 SRIF Example with an Earth Satellite Orbit.- 4.4.6 SRIF Example for a Spacecraft Approaching a Comet.- 4.5 Software.- 5. Midcourse and Gravity Assist Manoeuvres.- 5.1 Introduction.- 5.2 Midcourse Manoeuvres.- 5.2.1 Nominal Trajectory to Jupiter.- 5.2.2 Errors at Heliocentric Injection Ill.- 5.2.3 Fixed Time Guidance.- 5.2.4 Variable Time Guidance.- 5.2.5 Parametric Results.- 5.3 Gravity Assist Manoeuvres.- 5.3.1 Introduction.- 5.3.2 Gravity Assist in Two Dimensions.- 5.3.3 Gravity Assist in Three Dimensions.- 5.3.4 An Example: Comet Nucleus Sample Return.- 5.4 Software.- 6. Low Thrust Missions.- 6.1 Introduction.- 6.2 Electric Propulsion.- 6.3 Optimization of Low Thrust Trajectories.- 6.3.1 Optimization in Two Dimensions.- 6.3.2 Parameterized Optimization in Three Dimensions.- 6.3.3 Numerical Example.- 6.3.4 Controllability.- 6.4 Guidance on Low Thrust Trajectories.- 6.4.1 Introduction.- 6.4.2 Analysis.- 6.4.3 The Linear Quadratic Control Problem.- 6.4.4 Numerical Example of Feedback Guidance.- 6.5 Software.- 7. Atmospheric Entry.- 7.1 Introduction.- 7.2 Flight Equations.- 7.2.1 Equations of Motion.- 7.2.2 Aerodynamic Lift and Drag.- 7.2.3 Heating.- 7.3 Entry Corridors.- 7.3.1 Parameters.- 7.3.2 Condition for Level Flight.- 7.3.3 The Limit of Total Acceleration.- 7.3.4 The Limit of Rate of Heating.- 7.4 Ballistic Entry with No Lift.- 7.5 Guided Entry using Lift.- 7.5.1 Lift and the Guidance System.- 7.5.2 The Nominal Trajectory.- 7.5.3 Feedback Guidance in the Upper Atmosphere.- 7.5.4 Feedback Guidance in the Lower Atmosphere.- 7.6 Software.- A. Appendices.- A.1 Perturbations from the Sun and Moon in Geostationary Orbit.- A.2 Perturbations due to Solar Pressure in Geostationary Orbit.- A.3 Angular Information from Doppler Tracking.- A.4 Ephemeris of the Sun.- A.5 Sequential UD Covariance Filter.- A.6 Global Positioning System.