Analytic methods of orbit prediction and control : low-thrust and impulsive propulsion applications

In this book, analytic methods of orbit prediction and control are investigated for important low-thrust and impulsive orbit change and station-keeping applications, and the results compared with actual exact numerically-integrated counterparts to evaluate their accuracy and applicability. With one eye on future autonomous on-orbit navigation applications both in near-circular and general elliptic orbit, with minimal computational effort and high accuracy, the orbit prediction and control segments of such autonomous navigation systems are explored by also taking into account the shadowing effect where no thrust is allowed, such as for electric propulsion applications. This book shows that many of these orbit prediction and station-keeping problems can be solved entirely in analytic form with very high accuracy, and allow the practitioners to solve similar problems by tailoring them to their own applications, and to better understand and evaluate the pertinent variables and parameters that drive and influence the resulting description and evolution of the orbits. Cover Title Page Copyright Page Table of Contents Preface Chapter 1: Orbit Raising with Low-Thrust Tangential Acceleration in the Presence of Earth Shadow NOMENCLATURE 1.1 INTRODUCTION 1.2 GENERAL ANALYSIS 1.3 ANALYTIC INTEGRATION WITH INTERMITTENT THRUSTING 1.4 ANALYTIC INTEGRATION FOR NEAR-CIRCULAR ORBITS WITH CONTINUOUS THRUST 1.5 COMPARISON WITH A NUMERICALLY INTEGRATED EXACT NONSINGULAR SET FOR CONTINUOUS THRUST 1.6 ANALYTIC INTEGRATION FOR NEAR-CIRCULAR ORBITS WITH RESPECT TO THE MEAN MOTION: A SERIES SOLUTION 1.7 CONCLUSION REFERENCES Chapter 2: Low-Thrust Eccentricity-Constrained Orbit Raising NOMENCLATURE 2.1 INTRODUCTION 2.2 ANALYSIS 2.3 MODIFIED STRATEGY FOR ECCENTRICITY CONTROL 2.4 CONCLUSION REFERENCES Chapter 3: Low-Thrust Inclination Control in the Presence of Earth Shadow NOMENCLATURE 3.1 INTRODUCTION 3.2 ANALYSIS 3.3 ALGORITHMS OF THE TWO-SWITCH TRANSFER 3.4 CONCLUSION REFERENCES Chapter 4: Orbit Plane Control Strategies for Inclined Geosynchronous Satellite Constellations NOMENCLATURE 4.1 INTRODUCTION 4.2 GENERAL DISCUSSION 4.3 INCLINATION CONTROL STRATEGY WITH ANALYTIC ORBIT PREDICTION 4.4 INCLINATION CONTROL AND NODE ADJUST MANEUVER STRATEGY WITH ANALYTIC ORBIT PREDICTION 4.5 INCLINATION CONTROL STRATEGY WITH NUMERICAL ORBIT PROPAGATION 4.6 CONCLUSION REFERENCES Chapter 5: Optimal Steering for North–South Stationkeeping of Geostationary Spacecraft NOMENCLATURE 5.1 INTRODUCTION 5.2 GENERAL ANALYSIS OF NORTH–SOUTH DRIFT: IMPULSIVE MANEUVERING 5.3 MECHANICS OF LOW-THRUST MANEUVERING 5.4 SUBOPTIMAL STRATEGY 5.5 OPTIMAL (i, V) STEERING 5.6 RESULTS 5.7 CONCLUSION REFERENCES Chapter 6: Optimal Thrust Pitch Profiles for Constrained Orbit Control in Near-Circular and Elliptical Orbits NOMENCLATURE 6.1 INTRODUCTION 6.2 MAXIMIZATION OF THE CHANGES IN SEMIMAJOR AXIS AND ECCENTRICITY IN NEAR-CIRCULAR ORBIT IN THE PRESENCE OF A SHADOW ARC 6.3 SPITZER STRATEGY 6.4 CONTINUOUS-THRUST ELLIPTICAL CASE 6.5 SIMULTANEOUS CIRCULARIZATION AND ORBIT ROTATION IN THE NEAR-CIRCULAR CASE 6.6 CONCLUSION REFERENCES Chapter 7: Constrained Circularization in Elliptical Orbit Using Low Thrust with the Effect of Shadowing NOMENCLATURE 7.1 INTRODUCTION 7.2 MAXIMIZATION OF THE CHANGE IN ECCENTRICITY SUBJECT TO ZERO CHANGE IN THE SEMIMAJOR AXIS FOR DISCONTINUOUS THRUSTING IN AN ELLIPTICAL ORBIT 7.3 MAXIMIZATION OF THE CHANGE IN SEMIMAJOR AXIS SUBJECT TO ZERO CHANGE IN THE ECCENTRICITY FOR DISCONTINUOUS THRUSTING IN AN ELLIPTICAL ORBIT 7.4 FURTHER NUMERICAL COMPARISONS 7.5 ANALYTIC INTEGRATIONS FOR THE SPITZER SCHEME 7.6 CONCLUSION REFERENCES Chapter 8: Efficient Analytic Computation of Fractional Reentering Debris from an Idealized Isotropic Explosion in a General Elliptical Orbit NOMENCLATURE 8.1 INTRODUCTION 8.2 GENERAL ANALYSIS 8.3 ANALYTIC INVERSE SOLUTION 8.4 CONCLUSION REFERENCES Chapter 9: Optimal Low-Thrust Transfer in a General Circular Orbit Using Analytic Averaging of the System Dynamics NOMENCLATURE 9.1 INTRODUCTION 9.2 ANALYTIC AVERAGING OF THE THREE-STATE DYNAMICS FOR THE THRUST-ONLY CASE (i THEORY) 9.3 PRECISION INTEGRATION OPTIMIZATION USING THE FOUR-STATE SYSTEM 9.4 PRECISION INTEGRATION OPTIMIZATION USING THE FOUR-STATE SYSTEM UNDER THE INFLUENCE OF J2 9.5 THREE-STATE AVERAGED SYSTEM WITH J2 9.6 AVERAGING OF THE J2-PERTURBED FOUR-STATE DYNAMICS USING NUMERICAL QUADRATURE 9.7 CONCLUSION REFERENCES Chapter 10: Derivation of the Equations for the Variation of the Orbital Elements in Polar Coordinates for Elliptical and Hyperbolic Trajectories NOMENCLATURE 10.1 INTRODUCTION 10.2 GENERAL ANALYSIS 10.3 CONCLUSION REFERENCES Chapter 11: Analysis of the Effects of Drag and Zonal Harmonics on a Near-Circular Orbit NOMENCLATURE 11.1 INTRODUCTION 11.2 ANALYSIS 11.3 BREAKWELL’S ANALYSIS OF THE J2 PERTURBATION REFERENCES Chapter 12: Analysis of the Effects of the Solar Gravity Perturbation on a Spacecraft in Near-Circular Orbit about a Planet: Application to the VOIR Venus Orbiter Mission NOMENCLATURE 12.1 INTRODUCTION 12.2 ANALYSIS 12.3 VARIATION OF THE INCLINATION DUE TO SOLAR GRAVITATIONAL PERTURBATIONS 12.4 VARIATION OF THE RIGHT ASCENSION OF THE NODE 12.5 IN-PLANE EFFECTS DUE TO SOLAR GRAVITATIONAL PERTURBATIONS 12.6 VARIATION OF THE ECCENTRICITY DUE TO SOLAR GRAVITATIONAL PERTURBATIONS 12.7 CONCLUSION REFERENCES Chapter 13: Theory of the Displacement of the Vacant Focus Due to a Small Impulse and Relative Motion in Near-Circular Orbit NOMENCLATURE 13.1 INTRODUCTION 13.2 DISPLACEMENT OF VACANT FOCUS DUE TO A SMALL IMPULSE 13.3 RELATIVE MOTION OF TWO CLOSE SATELLITES IN NEAR-CIRCULAR ORBITS 13.4 SENSITIVITY ANALYSIS OF HOHMANN TRANSFER VELOCITY CHANGES REFERENCES Index Supporting Materials